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History dependence and the formation of social preferences: an experimental study.



I. INTRODUCTION

Over the past three decades experimental economics has identified a number of settings where players in noncooperative games make choices that are inconsistent with maximizing their own monetary payoffs but allow them to help or harm others. For example, responders in ultimatum ultimatum (ŭl'tĭmā`təm), in international law, final, definitive terms submitted by one disputant nation to the other for immediate acceptance or rejection.  games consistently reject positive offers (Gtith, Schmittberger, and Schwartz Schwartz is a Canadian spices brand. It is also a common surname and may refer to:
  • Abe Schwartz (1881-1963), musician
  • Alan Schwartz (fl. late 20th century), businessperson
  • Allyson Schwartz (born 1948)
  • Alvin Schwartz (born 1916), Canadian writer
 1982; Roth 1995). Participants in VCM VCM Vinyl Chloride Monomer
VCM Variable Cylinder Management (Honda)
VCM Virtual Channel Memory
VCM Value Chain Management
VCM Voice-Coil Motor
VCM Vehicle Control Module
VCM Vignette Content Management
 public goods games consistently contribute positive amounts to the public good (Ledyard Ledyard (lĕd`yərd), town (1990 pop. 14,913), New London co., SE Conn., on the Thames River; settled c.1653, inc. 1836. It is a farm center. The site of Fort Decatur is marked there.  1995). To explain this "other-regarding" behavior, various theories of "social" preferences have been advanced. (1) In the most popular models, Fehr and Schmidt (1999) and Bolton Bolton or Bolton-le-Moors (bōl`tən-lə-mrz), city (1991 pop. 143,960) and metropolitan district, NW England, located in the Manchester metropolitan area.  and Ockenfels (2000), individuals care about not only their own outcomes but also the outcomes of others. By expanding the domain of preferences, such models provide a unified explanation within the framework of classical microeconomics microeconomics

Study of the economic behaviour of individual consumers, firms, and industries and the distribution of total production and income among them. It considers individuals both as suppliers of land, labour, and capital and as the ultimate consumers of the final
 for behavior in many experiments.

Reflecting their roots in classical microeconomics, a common feature of these distributional models of social preferences is an implicit assumption that preferences are complete and stable. It follows that these models are inherently static, rendering them unable to address how social preferences are formed when individuals are faced with a novel situation. This question is pertinent PERTINENT, evidence. Those facts which tend to prove the allegations of the party offering them, are called pertinent; those which have no such tendency are called impertinent, 8 Toull. n. 22. By pertinent is also meant that which belongs. Willes, 319.  since other-regarding behavior has been shown to change with experience in a number of experiments (e.g., Andreoni 1988; Armantier 2006; Cooper and Dutcher 2009; Cooper et al. 2003; List and Cherry 2000; Roth et al. 1991; Slonim Slonim (Belarusian: Сло́нім) is a city in Belarus in the Hrodna voblast and Slonim rayon, located at the junction of the Shchara and Isa rivers, 143 km southeast of Hrodna. The population in 1995 wss 53,100.  and Roth 1998). Such changes occur even if strategic uncertainty, payoff uncertainty, reduced error rates with experience, and repeated game effects are ruled out as possible explanations (Cooper and Stockman 2002a). (2) By process of elimination The process of elimination is a basic logical tool to solve real world problems. By subsequently removing options that may be deemed impossible, illogical, or can be easily ruled out due to some sort of explicit understanding relative to the entire set of options, the pool of , something related to subjects' social preferences must be responsible for their changing behavior.

Cooper and Stockman (2002a) is arguably ar·gu·a·ble  
adj.
1. Open to argument: an arguable question, still unresolved.

2. That can be argued plausibly; defensible in argument: three arguable points of law.
 the clearest illustration of the preceding points. We studied the minimal contributing set (MCS (1) See Microsoft Cluster Server.

(2) (Microsoft Consulting Services) The consulting arm of Microsoft which offers support for installation and maintenance of Microsoft applications and operating systems.
) game, a sequential step-level public goods game The Public goods game is a standard of experimental economics; in the basic game subjects secretly choose how many of their private tokens to put into the public pot. Each subject keeps the tokens they do not contribute plus an even split of the tokens in the pot (researchers  with three players. Each player faces a binary Meaning two. The principle behind digital computers. All input to the computer is converted into binary numbers made up of the two digits 0 and 1 (bits). For example, when you press the "A" key on your keyboard, the keyboard circuit generates and transfers the number 01000001 to the  decision: whether or not to contribute to a public good. If a player decides to contribute, a player-specific cost of contribution is deducted de·duct  
v. de·duct·ed, de·duct·ing, de·ducts

v.tr.
1. To take away (a quantity) from another; subtract.

2. To derive by deduction; deduce.

v.intr.
 from their initial endowment A transfer, generally as a gift, of money or property to an institution for a particular purpose. The bestowal of money as a permanent fund, the income of which is to be used for the benefit of a charity, college, or other institution. . The public good is provided if at least two players choose to contribute. For each player, the value of the public good is greater than their cost of contribution. It follows that in the unique subgame perfect equilibrium In game theory, a subgame perfect equilibrium is a refinement of a Nash equilibrium used in dynamic games. A strategy profile is a subgame perfect equilibrium if it represents a Nash equilibrium of every subgame of the original game.  the final two players choose to contribute and the public good is provided. The catch is that the cost of contribution is sharply rising through the order of play. A critical third player, defined as a third player who knows that exactly one of the two preceding players has contributed, therefore faces a dilemma. If this player contributes they gain the benefits of the public good, but those benefits will also be enjoyed by an individual with far lower costs of contribution who has chosen not to contribute.

As reported in Cooper and Stockman (2002a), the MCS game yields substantial levels of other-regarding behavior, specifically negative reciprocity reciprocity

In international trade, the granting of mutual concessions on tariffs, quotas, or other commercial restrictions. Reciprocity implies that these concessions are neither intended nor expected to be generalized to other countries with which the contracting parties
; depending on the treatment, up to 50% of critical third players do not contribute. More to the point, the behavior of critical third players in the MCS game changes with experience. In the most interesting case, the contribution rate by critical third players falls sharply with experience, dropping from an initial contribution rate of 80% to a low point of 50%. By extension, the average monetary payoff of critical third players declines with experience. Subjects are randomly rematched in each round, so repeated game effects cannot be responsible for this decline and the magnitude of the change is hard to square with subject errors in what is, after all, a straightforward binary choice. (3) Because this is a sequential game In game theory, a sequential game is a game where one player chooses his action before the others choose theirs. Importantly, the later players must have some information of the first's choice, otherwise the difference in time would have no strategic effect.  with perfect information, we can eliminate obvious causes for changes in the behavior of third players such as the resolution of strategic and/or payoff uncertainty. With the other leading candidates ruled out, something related to subjects' preferences is the likely cause of this dramatic change in critical third players' choices. This paper, along with the related works cited above, leaves us with a pressing question: why does subjects' behavior change Behavior change refers to any transformation or modification of human behavior. Such changes can occur intentionally, through behavior modification, without intention, or change rapidly in situations of mental illness.  with experience and what does this tell us about the formation of social preferences?

To address this, our current experimental design features two treatments that manipulate manipulate

To cause a security to sell at an artificial price. Although investment bankers are permitted to manipulate temporarily the stock they underwrite, most other forms of manipulation are illegal.
 the experience subjects receive in the first half of the experiment. One treatment emphasizes the monetary rewards of contributing when critical, pushing play toward the subgame perfect equilibrium. The second plays up fairness concerns, pushing subjects toward a Nash equilibrium Noun 1. Nash equilibrium - (game theory) a stable state of a system that involves several interacting participants in which no participant can gain by a change of strategy as long as all the other participants remain unchanged  in which the first two players contribute. In the second half of each experimental session, all subjects play the MCS game as described above. As a point of comparison, we use the data from Cooper and Stockman (2002a) as control sessions in which subjects play the MCS game for the entire session. Our analysis focuses on how subjects' differing experiences in the first half of the experiment affect their behavior as critical third players in the second half of the experiment.

We identify three main features in the experimental data. (1) Experience with either treatment makes subjects appear more like experienced subjects in control sessions than naive naive - Untutored in the perversities of some particular program or system; one who still tries to do things in an intuitive way, rather than the right way (in really good designs these coincide, but most designs aren't "really good" in the appropriate sense).  subjects. In other words Adv. 1. in other words - otherwise stated; "in other words, we are broke"
put differently
, experienced subjects in the treatment sessions behave differently than inexperienced in·ex·pe·ri·ence  
n.
1. Lack of experience.

2. Lack of the knowledge gained from experience.



in
 subjects in the control sessions. (2) Even though subjects have very different experiences in the first half of the experiment, subjects' behavior in the second half differs little across the two treatments. (3) The effects of previous experience are transient. By the final few periods of the experiment, behavior looks indistinguishable regardless of subjects' experiences in the first half of the experiment. The treatments also have no long-run impact on the likelihood the public good is provided. Together, these results indicate that while the amount of negative reciprocity changes with experience, there is little evidence of persistent history dependence.

To interpret this finding, we introduce three hypotheses about the formation of subjects' preferences. (The lack of strategic or payoff uncertainty largely eliminates explanations for the changes in critical third players' behavior that do not involve preference formation.) The hypothesis most consistent with the experimental data is the discovered preferences hypothesis suggested by Plott (1996). This hypothesis proposes that subjects confronted with a new situation have complete and stable preferences but do not necessarily know them. Instead, subjects learn their preferences with experience. Because subjects must learn their preferences, it is possible for behavior to change over time and even for variation in subjects' experiences to have a transient affect on their choices. However, since the underlying preferences are complete and stable, behavior should always converge con·verge  
v. con·verged, con·verg·ing, con·verg·es

v.intr.
1.
a. To tend toward or approach an intersecting point: lines that converge.

b.
 to the same outcome regardless of subjects' previous history. In other words, persistent history dependence should not be observed. Two other possibilities we explore are a constructed preferences hypothesis and a reference-point hypothesis. The former, drawn from psychology, holds that subjects have no meaningful preferences when faced with a novel setting and instead construct preferences on the spot. This hypothesis implies changing behavior as well as the possibility of persistent history dependence. The reference-point hypothesis predicts that subjects' choices depend on their beliefs about the distribution of choices by others. Models of social preferences that draw on psychological game theory (Geanakoplos, Pearce Pearce may refer to:

In places:
  • Pearce, Australian Capital Territory
People with the surname Pearce:
  • Pearce (surname)
See also
  • The Division of Pearce, an Australian Electoral Division in Western Australia
, and Stacchetti 1989), such as Rabin Ra·bin   , Yitzhak or Itzhak 1922-1995.

Israeli military and political leader who commanded Israeli forces in the Six-Day War (1967) and served as prime minister (1974-1977 and 1992-1995). He shared the 1994 Nobel Peace Prize.
 (1993), Dufwenberg and Kirchsteiger (2004), Falk n. 1. (Zool.) The razorbill.  and Fischbacher (2006), and Charness and Rabin (2003), are implicitly dynamic. Intuitively, a natural way to define an action as "kind" or "unkind" is to compare it with the typical choice of a population. As subjects' beliefs evolve about typical choices of others, changing behavior is predicted along with the possibility of persistent history dependence. Primarily due to the lack of persistent history dependence, but also because of their inability to predict a number of secondary features in the data, both of these hypotheses perform poorly relative to the discovered preference hypothesis in explaining our experimental results.

The strong performance of the discovered preferences hypothesis in our data is consistent with social preferences being complete and stable, subject to individuals having sufficient experience to learn their preferences, in line with the assumptions of classical microeconomics. As such, our results can be viewed as a complement to papers such as Andreoni and Miller (2002) which make a case that social preferences can be fit within the standard framework of microeconomics. Of course, we should not push this too far. While we view our result as an important piece of evidence, it isn't the last word on the matter. Our results make it clear that learning about preferences is an important element of the dynamics observed in other-regarding behavior. It does not necessarily follow that the constructed preference and reference hypotheses never explain changes in other-regarding behavior. For example, evidence from studies on children (e.g., Harbaugh, Krause, and Liday 2003) suggests that social preferences change permanently in response to individuals' experiences over extended periods of time consistent with the constructed preferences hypothesis. Likewise, the changes in the behavior of conditional cooperators in public goods games (Keser and van Winden Winden may refer to the following places:
  • in Germany:
  • Winden im Elztal, in the district of Emmendingen, Baden-Württemberg
 2000) and responders in ultimatum games (Bohnet and Zeckhauser 2004; Cooper and Dutcher 2009) are both consistent with the reference-point hypothesis. These two examples differ from the MCS game along an important dimension. In the MCS game it is obvious when a behavior is kind or not, but subjects can learn how unusual the kind or unkind actions are by observing how frequently they are used. In both VCM and ultimatum games there is more to learn, as it is unclear initially whether a specific contribution or offer should be considered kind or not. Thus, differing environments may change the stress on various channels through which other-regarding behavior changes. Further work is needed to determine the relationship between the type of game being played and what factors drive changes in other-regarding behavior.

On a related point, an interesting question is why we find evidence for discovered preferences but many laboratory studies, with even short time spans than our experiment, support the constructed preferences hypothesis. Many such examples exist in psychology and Bohnet and Huck huck  
n.
Huckaback.

Noun 1. huck - toweling consisting of coarse absorbent cotton or linen fabric
huckaback

toweling, towelling - any of various fabrics (linen or cotton) used to make towels
 (2004) and Stahl Stahl is a surname, and may refer to:
  • Agustín Stahl Puerto Rican physician, ethnologist, and botanist
  • Armin Mueller-Stahl
  • Ben Stahl (metal head)
  • Ben Stahl
  • Ben Stahl (artist)
  • Chick Stahl
  • Daniel Stahl
  • Floyd Stahl
  • Franklin Stahl
 and Haruvy (2008) provide examples from the literature on other-regarding behavior. In the conclusion we discuss why we find evidence for discovered rather than constructed preferences. The most likely reason is methodological--our design contains an unusually large number of repetitions, a critical feature since behavior takes some time to settle down. We would have reached far different conclusions if our analysis only concentrated on the first few periods of the second half of the experiment. This illustrates a general problem in the literature on other-regarding behavior where many papers rely on data from one-shot games or repeated games without feedback to estimate parameters for various models or to classify clas·si·fy  
tr.v. clas·si·fied, clas·si·fy·ing, clas·si·fies
1. To arrange or organize according to class or category.

2. To designate (a document, for example) as confidential, secret, or top secret.
 subjects into types (e.g., Andreoni and Miller 2002; Engelmann Engelmann may refer to:
  • Engelmann Oak, also called Pasadena Oak
  • Engelmann Spruce, a medium-sized evergreen tree
  • Engelmann syndrome, a rare autosomal dominant genetic disorder
Engelmann is the surname of:
  • Eduard Engelmann Jr.
 and Strobel Strobel is the surname of:
  • Aron Strobel
  • Eric Strobel
  • Greg Strobel
  • Heidi Strobel
  • Käte Strobel, German politician
  • Lee Strobel, American author
  • Pater Gabriel Strobl, entomologist
  • Zauner and Strobel, see Deuces Wild (band)
 2004). There are obvious advantages to this approach, as repeated game effects are eliminated and clean within subject comparisons are possible. However, in environments where behavior is shifting, such estimation estimation

In mathematics, use of a function or formula to derive a solution or make a prediction. Unlike approximation, it has precise connotations. In statistics, for example, it connotes the careful selection and testing of a function called an estimator.
 exercises must be treated with caution.

The organization of this paper is as follows. Section II lays out the MCS game. Section III describes our three primary hypotheses in detail. Section IV presents the experimental design and outlines our initial conjectures This is an incomplete list of mathematical conjectures. They are divided into four sections, according to their status in 2007.

See also:
  • Erdős conjecture, which lists conjectures of Paul Erdős and his collaborators
  • Unsolved problems in mathematics
 about the results. Section V summarizes the experimental procedures. Section VI presents the results and Section VII summarizes the paper and discusses the implications of the results.

II. THE MINIMAL CONTRIBUTING SET GAME

The MCS game is a three-person, step-level public goods game. (4) Payoffs are denominated in tokens. Each player is given an identical endowment of 12 tokens and then asked to decide whether to contribute a fixed portion of this endowment, referred to as their "cost of contribution," for the provision of a public good. The public good is provided if at least two of the three players choose to contribute. If the public good is provided all three players benefit, and each receives an additional 18 tokens. Contributions are not refunded in the event that the public good is not provided. The cost of contribution varies across players and across treatments, but in all cases is less than 18. It follows that all players are better off (monetarily) contributing to the public good if their decision determines whether or not the public good will be provided.

We study both sequential and simultaneous versions of the MCS game. In the simultaneous MCS game all players choose whether or not to contribute simultaneously, not knowing the decisions of others. The simultaneous MCS game has four pure strategy Nash equilibria (assuming that monetary payoffs and utility are equivalent). None of the players contributing to the public good is an equilibrium equilibrium, state of balance. When a body or a system is in equilibrium, there is no net tendency to change. In mechanics, equilibrium has to do with the forces acting on a body.  and is the only one in which the good is not provided. In the remaining three equilibria, the good is provided efficiently with exactly two of the three players contributing. In the sequential MCS game players make their decisions knowing both their position in the order of the play and the decisions made by the players who precede them. Players move in the order of their player numbers--Player 1 moves first, followed by Players 2 and 3. The sequential MCS game has a unique subgame perfect equilibrium in which the second and third players contribute and the first player does not.

The experimental design uses three cost structures where the three players have different costs of contribution as well as one cost structure in which all players have the same cost of contribution. Table 1 summarizes these four cost structures. Note that costs of contribution are always (weakly) increasing in player's position. Only one cost structure is used at any given point in time, and subjects never face any uncertainty about the cost structure. The equilibrium predictions, as described above, are identical for all of the games in our experiments.

The structure of the sequential MCS game suggests ex ante that concerns about fairness and reciprocity will push play away from the subgame perfect equilibrium. Consider the position of a "critical" third player, a third player who knows that one of the preceding players has contributed while the other has not. A critical third player faces no strategic uncertainty, and therefore knows that the public good will be provided if and only if he contributes. If this player cares solely about his monetary payoffs, he should always contribute. However, this player also knows that a preceding player has not contributed and will free-ride on provision of the public good. For sequential MCS games with differing costs of contribution, the critical third player faces substantially higher costs of contribution than this preceding player. We can easily imagine that a critical third player who cared about relative payoffs might resent re·sent  
tr.v. re·sent·ed, re·sent·ing, re·sents
To feel indignantly aggrieved at.



[French ressentir, to be angry, from Old French resentir,
 this, and therefore not contribute to punish pun·ish  
v. pun·ished, pun·ish·ing, pun·ish·es

v.tr.
1. To subject to a penalty for an offense, sin, or fault.

2. To inflict a penalty for (an offense).

3.
 the earlier player who did not contribute. Such actions destabilize de·sta·bi·lize  
tr.v. de·sta·bi·lized, de·sta·bi·liz·ing, de·sta·bi·liz·es
1. To upset the stability or smooth functioning of:
 the subgame
For subgame as a short video game contained in another, see minigame.


In game theory, a subgame is any part (a subset) of a game that meets the following criteria (the following terms allude to a game described in extensive form):
 perfect outcome. (5)

III. THREE HYPOTHESES REDUX Refers to being brought back, revived or restored. From the Latin "reducere."  

In the introduction, we briefly introduced three hypotheses regarding the formation of social preferences that potentially explain why the contribution rates by critical third players in the sequential MCS game change over time. In this section, we develop these hypotheses in more detail along with their implications for the persistence (1) In a CRT, the time a phosphor dot remains illuminated after being energized. Long-persistence phosphors reduce flicker, but generate ghost-like images that linger on screen for a fraction of a second.  of history dependence in critical third players' behavior in the sequential MCS game.

A. Constructed Preferences Hypothesis

Economists generally assume individuals have complete preferences--given two options, individuals are able to state which option they prefer (allowing for indifference Indifference
Antoinette, Marie

(1755–1793) queen of France to whom is attributed this statement on the solution to bread famine: “Let them eat cake.” [Fr. Hist.
). It is also typically assumed that preferences are stable (i.e., not changing over time). However, a broad array of psychological studies suggests that individuals are not endowed en·dow  
tr.v. en·dowed, en·dow·ing, en·dows
1. To provide with property, income, or a source of income.

2.
a.
 with complete and stable preferences (Bettman, Luce Luce   , Clare Boothe 1902-1987.

American writer and public official. She wrote several plays, including The Women (1936), and served as ambassador to Italy (1953-1956).

Noun 1.
, and Payne
:The name may also be spelt Paine.


The surname Payne stems from paganus, see pagan. People
  • King Payne, a Seminole chief
  • A.R.
 1998; Payne, Bettman, and Johnson 1992; Slovic 1995). Instead, when faced with a novel situation subjects are forced to construct their preferences on the spot. Given that their preferences are a work in progress, subjects' choices can often be quite sensitive to the details of how the problem is presented (Slovic 1995; Hoeffler and Ariely 1999).

Evidence in favor of upon the side of; favorable to; for the advantage of.

See also: favor
 constructed preferences often relies on framing and/or priming effects. Both types of effect give us insight into how constructed preferences could generate history dependence in the MCS game. Framing effects refer to changes in subjects' revealed preferences which are due solely to how a problem is presented. Consider preference reversals in experiments on choice under uncertainty, a canonical example of using framing effects to generate evidence in favor of constructed preferences (Slovic, Griffen Griffen can mean any of the following:
  • Griffin (surname)
  • Griffen, Austria, a town in the district of Völkermarkt in Carinthia
  • Griffen Island, West Virginia
, and Tversky 1990). Typically, gambles studied in preference reversal experiments have two important aspects, a probability of winning and a prize if the gambler wins. Virtually all individuals would agree on a ranking within these dimensions--ceteris paribus, a higher probability of winning is better, as is a larger prize. The problems occur when subjects must trade off higher probabilities of winning versus lower payoffs from winning (or vice versa VICE VERSA. On the contrary; on opposite sides. ). To simplify this problem, subjects may focus primarily on one of these aspects and then fine-tune their evaluation of a gamble to reflect the other aspect. This process is referred to as "anchoring and adjusting" (Slovic and Lichtenstein 1983). To the extent that the framing of the gamble affects which dimension is chosen as the anchor, subjects' preferences and their resulting choices can be reversed.

Our treatments do not draw on pure framing effects, since the game itself is changing rather than its presentation, but the process of anchoring and adjustment that underlies framing effects is directly applicable to our experiments. The problem facing critical third players in the sequential MCS game has two aspects--monetary payoffs and negative reciprocity. A subject in this position must decide whether it is more important to make as much money as possible or to punish earlier players who are attempting to free-fide on their contributions. Our treatments are designed to focus subjects' initial attention on different aspects of the problem. To the extent that this succeeds, the preferences constructed by subjects should differ across treatments leading to persistent history dependence.

Priming effects also directly relate to the content of our treatments. The term "priming effect" refers to cases where details of a subject's previous experience which are no longer payoff relevant establish a precedent for how current decisions should be made (e.g., Ariely, Loewenstein, and Prelec 2003; Tversky and Kahneman 1974). Our experiments with the MCS game expose subjects to very different experiences in the first half of the experiment, both in terms of what choices they make and what choices they observe by other players, priming them to make persistently different decisions in the second half of the experiment.

The constructed preferences hypothesis implies that subjects' choices will change over time as their preferences are constructed and, if different preferences are induced induced /in·duced/ (in-dldbomacst´)
1. produced artificially.

2. produced by induction.

induced,
adj artificially caused to occur.


induced

induction.
 by the treatments, persistently different behavior across treatments can emerge.

B. Discovered Preferences Hypothesis

The discovered preferences hypothesis is subtly different from the constructed preferences hypothesis. Under the constructed preferences hypothesis, individuals do not form preferences until they encounter a situation. Preferences are inherently mutable, altered even through seemingly seem·ing  
adj.
Apparent; ostensible.

n.
Outward appearance; semblance.



seeming·ly adv.
 irrelevant details such as how the options are presented. In contrast, the discovered preferences hypothesis suggested by Plott (1996) posits individuals who have complete and stable preferences, but do not know their preferences for a novel problem. With experience, individuals are able to learn their preferences and hence change their behavior to accord with their "discovered" preferences. The learning model of Cooper and Stockman (2002a) can be interpreted as a formalization for·mal·ize  
tr.v. for·mal·ized, for·mal·iz·ing, for·mal·iz·es
1. To give a definite form or shape to.

2.
a. To make formal.

b.
 of the discovered preferences hypothesis.

For our experiments, the main implication of the discovered preferences hypothesis is that history dependence will not be persistent. Regardless of what experiences subjects have early in the experiment, behavior should eventually converge to the same outcome. This does not mean that subjects' behavior cannot be temporarily affected by treatments like those studied here, but such effects will not be permanent.

C. Reference-Point Hypothesis

In models of social preferences that draw on psychological game theory (Geanakoplos, Pearce, and Stacchetti 1989), such as Rabin (1993), Dufwenberg and Kirchsteiger (2004), Falk and Fischbacher (2006), and Charness and Rabin (2003), subjects' preferences (and hence behavior) depend on their beliefs about the behavior of others. To the extent that beliefs change with experience, other-regarding behavior should change as well. There exists a growing body of experimental literature consistent with this idea. For example, Bohnet and Zeckhauser (2004) report ultimatum game The ultimatum game is an experimental economics game in which two parties interact anonymously and only once, so reciprocation is not an issue. The first player proposes how to divide a sum of money with the second party.  experiments in which responders are given information about the average offer made by the experimental population. They find that rejection rates are sensitive to this information. Presumably pre·sum·a·ble  
adj.
That can be presumed or taken for granted; reasonable as a supposition: presumable causes of the disaster.
 subjects tend to view a particular offer as more (less) fair if they know that offers in general have tended to be lower (higher). Closer to our MCS game experiments, Cooper and Dutcher (2009) report that rejection rates in ultimatum game experiments using either stranger or absolute stranger matching change with experience. Specifically, receiving a higher (lower) offer makes a responder more likely, ceteris paribus Ceteris Paribus

Latin phrase that translates approximately to "holding other things constant" and is usually rendered in English as "all other things being equal". In economics and finance, the term is used as a shorthand for indicating the effect of one economic variable on
, to reject (accept) the next offer he receives. This is consistent with the idea that behavior changes as responders gain information about what offers are fair. (6)

Similar arguments apply in the MCS game. A critical third player knows that one of the preceding players has been kind by contributing to the public good while the other has been unkind, but may have difficulty analyzing how kind/unkind this behavior is. A natural point of comparison is the behavior of the experimental population as a whole. For example, if most first and second players contribute to the public good, it may seem particularly unkind when either a first or second player does not contribute. This in turn may make critical third players more likely to reciprocate re·cip·ro·cate  
v. re·cip·ro·cat·ed, re·cip·ro·cat·ing, re·cip·ro·cates

v.tr.
1. To give or take mutually; interchange.

2. To show, feel, or give in response or return.

v.
 by not contributing. If an individual's perceptions of normal behavior depend on his beliefs about the behavior of others, the choices of critical third players may change over time as they become better informed about the distribution of choices by first and second players. Thus, learning about a reference-point against which to judge others' behavior may explain the changing behavior of critical third players in the MCS game. (7)

Unlike the constructed preferences hypothesis, the reference-point hypothesis does not imply that preferences are incomplete or unstable unstable,
adj 1. not firm or fixed in one place; likely to move.
2. capable of undergoing spontaneous change. A nuclide in an unstable state is called
radioactive. An atom in an unstable state is called
excited.
.

Under the reference-point hypothesis subjects kilow all along that they dislike behavior which is unusually unkind, but only with experience can they learn what behavior is unusual. The difference between the reference-point hypothesis and the discovered preferences hypothesis is subtler. The discovered preference hypothesis requires subjects to learn their unknown preferences which are exogenous Exogenous

Describes facts outside the control of the firm. Converse of endogenous.
 to the experiment. The reference-point hypothesis requires subjects to learn an input to their preferences, the typical behavior of players in the other roles, which is endogenous endogenous /en·dog·e·nous/ (en-doj´e-nus) produced within or caused by factors within the organism.

en·dog·e·nous
adj.
1. Originating or produced within an organism, tissue, or cell.
 to the experiment.

The reference-point hypothesis, like the constructive preferences hypothesis, implies that persistent history dependence can occur. This is due to the co-evolution of players' beliefs and actions. For example, suppose that subjects playing as third players in a session experience unusually high levels of contribution by Player is and 2s. These subjects should come to view a failure to contribute by the first two players as being unusual and therefore relatively unkind. If the reference-point hypothesis is correct, our fictitious Based upon a fabrication or pretense.

A fictitious name is an assumed name that differs from an individual's actual name. A fictitious action is a lawsuit brought not for the adjudication of an actual controversy between the parties but merely for the purpose of
 subjects should then be more inclined to not contribute when critical than would otherwise be the case. Given the payoff structure of the MCS game, this creates strong incentives for Player 1s and 2s to contribute even more. This in turn makes Player 3s perceive failures to contribute in an increasingly harsh light. Play is pushed to an equilibrium in which only the first two players contribute. If the history of play changes, then the beliefs which form also change and a different equilibrium emerges.

IV. EXPERIMENTAL DESIGN AND INITIAL HYPOTHESES

Each experimental session lasts for 40 periods. Subjects keep the same role (Player 1, Player 2, or Player 3) for all 40 periods and are randomly and anonymously matched in each period with two subjects in the other roles. Treatments vary by what version of the MCS game is played for the first 20 periods--the sequential MCS game with different contribution costs across players, the sequential MCS game with the same contribution costs for all players, or the simultaneous MCS game with different contribution costs across players-and what cost structure is used in the last 20 periods--3/6/9, 1/3/9, or 1/3/16 as they are labeled in Table 1. For all treatments, the sequential MCS game with different contribution costs across players is played in periods 21-40. For sessions where subjects play an MCS game (sequential or simultaneous) with different contribution costs across players in the first 20 periods, the same cost structure is used for all 40 periods. The resulting 3 x 3 design is summarized in Table 2. This table includes the number of sessions and the number of subjects used for each treatment. One third of the subjects in each treatment were third players, the role of greatest interest. (8)

For brevity Brevity
Adonis’ garden

of short life. [Br. Lit.: I Henry IV]

bubbles

symbolic of transitoriness of life. [Art: Hall, 54]

cherry fair

cherry orchards where fruit was briefly sold; symbolic of transience.
, we refer to the treatments by the version of the MCS game played in the first 20 periods (shortened to sequential/different, sequential/same, and simultaneous/different) and the cost structure used in the final 20 periods (3/6/9, 1/3/9, or 1/3/16). As an example, consider the 1/3/9 sequential/same treatment. In the first 20 periods subjects play the sequential MCS game with all players having a cost of contribution equal to six tokens. In the final 20 periods subjects switch to the sequential MCS game with costs of contribution of 1 token for Player 1, 3 tokens for Player 2, and 9 tokens for Player 3.

Cooper and Stockman (2002a) show that the behavior of critical third players in the sequential/different treatment changes with experience for all three cost structures. In the 1/3/9 and 3/6/9 sequential/different treatments, the contribution rate for critical third players rises over time. This increase is more rapid for the 3/6/9 treatment. For the 1/3/16 sequential/different treatment, the contribution rate for critical third players falls sharply with experience. The treatments in our experimental design are intended to give third players differing experiences, allowing us to observe whether these dynamics are subject to history dependence, persistent or otherwise.

Regardless of the cost structure used, critical third players face very different pressures in the first 20 periods depending on which version of the game they are playing. Consider the coordination problem faced by subjects--all players benefit if the public good is provided, but only two players need to contribute to generate this benefit. The sequential/different treatment offers two conflicting cues as to how this problem ought to be resolved, either via differences in costs or via order of play. The former cue cue,
n a stimulus that determines or may prompt the nature of a person's response.

cue Psychology Any sensory stimulus that evokes a learned patterned response. See Conditioning.
 stresses fairness while the latter puts more stress on the monetary advantages of contribution.

The other two treatments lessen less·en  
v. less·ened, less·en·ing, less·ens

v.tr.
1. To make less; reduce.

2. Archaic To make little of; belittle.

v.intr.
To become less; decrease.
 this tension in one direction or the other. In the simultaneous/different treatment only the first cue, differences in costs, is present. It seems natural for Player 3 to expect that the players with lower costs ought to provide the public good. We therefore expect lower contribution rates by critical third players for periods 1-20 in the simultaneous/different treatment than in the sequential/different treatment. (9) In the sequential/same treatment, only the second cue, order of play, is present. Unlike the simultaneous/same treatment, a critical third player knows he must contribute for the public good to be provided. Thus we expect higher contribution rates by critical third players in periods 1-20 of the sequential/same treatment than in the sequential/different treatment.

What impact do we predict differing experiences across treatments will have on play in periods 21-40? All three hypotheses described in the previous section are consistent with a prediction that the sequential/same treatment will initially bias contribution rates by critical third players upwards while the simultaneous/different treatment biases them down. However, the three hypotheses have differing implications for the persistence of these effects and for the specific pattern of responses to past history.

Consider the constructed preferences hypothesis. Critical third players in the sequential MCS game must decide how much weight to put on the two aspects of their decision problem, monetary payoffs and other-regarding concerns. Suppose subjects form preferences via a process of anchoring and adjustment. The sequential/same treatment stresses the monetary advantages of contribution. We therefore predict that, when compared to the control, the monetary aspects of the problem will be more likely to serve as the anchor in this treatment with secondary adjustments for concerns about fairness and reciprocity. On the other hand, the simultaneous/different treatment accentuates concerns about fairness and reciprocity and therefore can be expected to have the opposite effect as compared to the controls--concerns about fairness and reciprocity are more likely to serve as the anchor with secondary adjustments for monetary concerns. Because the treatments can permanently alter subjects' preferences, the constructed preferences hypothesis implies persistent history dependence. (10)

The story is largely the same for the discovered preferences hypothesis with an important caveat. Under the discovered preferences hypothesis, subjects have complete preferences which they learn with experience. The path by which they learn their preferences may be affected by the framing and priming effects that play a central role in the constructed preferences hypothesis, but these effects will be transitory.

In the long-run subjects' behavior as critical third players, holding the cost structure fixed, should not depend on what experience they received in periods 1-20.

The reference-point hypothesis makes similar predictions to the constructed preferences hypothesis, but through a different mechanism. Just as the sequential/same treatment pushes critical third players to contribute more frequently, this treatment also makes it more likely that third players will observe one of the preceding players not contributing. As such, it should seem less unkind for one of the first two players to not contribute. This in turn should make punishment less attractive, making it more likely critical third players will contribute in the sequential/same treatment than in the sequential/different treatment. Likewise, the simultaneous/different treatment makes it more likely that both Players 1 and 2 will contribute to the public good leading to lower contribution rates by critical third players.

As with the constructed preferences hypothesis, under the reference-point hypothesis the treatment effects can be persistent. This is not because subjects' preferences have permanently changed in any meaningful fashion, but rather because the norms learned are self-enforcing self-en·forc·ing
adj.
Holding within itself the means or a guarantee of its enforcement: a self-enforcing peace settlement. 
. If Player 3s come to believe one of the first two players not contribute is normal and hence not perceive this action as especially unkind, they are (under the reference-point hypothesis) more likely to contribute when critical. This increases incentives for one of the first two players to not contribute, which in turn reinforces the reference point of low contributions by Players 1 and 2. Similar logic applies in the case where Player 3s come to expect that Players 1 and 2 will contribute to the public good.

Beyond its broad predictions about the persistence of treatment effects, the reference-point hypothesis makes predictions about how the contribution rate for critical third players in the sequential MCS game will respond to their observed history of contributions by Players 1 and 2. These predictions allow us to distinguish between the reference point and constructed preference hypotheses even if the effect of differing experience in periods 1-20 on beliefs in periods 21-40 is insufficiently strong to yield different equilibria. In particular, the contribution rate in the current period for a critical third player is predicted to be negatively correlated cor·re·late  
v. cor·re·lat·ed, cor·re·lat·ing, cor·re·lates

v.tr.
1. To put or bring into causal, complementary, parallel, or reciprocal relation.

2.
 with the contribution rates this individual has observed in previous periods by Player 1s and by Player 2s.

Our ex ante expectations about the data are summarized by the following conjectures.

Conjecture CONJECTURE. Conjectures are ideas or notions founded on probabilities without any demonstration of their truth. Mascardus has defined conjecture: "rationable vestigium latentis veritatis, unde nascitur opinio sapientis;" or a slight degree of credence arising from evidence too weak or too  1: Holding the cost structure fixed, contribution rates by critical third players in periods 1-20 will be highest in the sequential/same treatment, second highest in the sequential/different treatment, and lowest in the simultaneous/different treatment. Additionally, the behavior of Player 1s and 2s will differ significantly across these three treatments in periods 1-20, giving Player 3s differing experiences with the behavior of others.

Conjecture 1 can be regarded as a necessary condition for getting useful results out of the experimental results--if we get no meaningful variation across treatments in periods 1-20, there is little reason to expect the treatments to have much impact on behavior in periods 21-40.

Conjecture 2: Holding the cost structure fixed, behavior by critical third players in periods 21-30 of the sequential/same and simultaneous/different treatments will differ from behavior in periods 1-10 of the sequential/different treatment.

Conjecture 2 is also critical for drawing interesting conclusions from the data. If Conjecture 2 is false, then we can conclude little other than critical third players in the treatments failed to see a relationship between their experiences in periods 1-20 and the problem facing them in periods 21-40. If Conjecture 2 is true, subjects in the sequential/same and simultaneous/different treatment gain something from their experiences in periods 1-20 of the treatments that they apply to play of the sequential MCS game with different contribution costs across players, distinguishing them from naive subjects in the control treatments. This allows us to study the nature and persistence of history dependence.

Conjecture 3: Holding the cost structure fixed, contribution rates by critical third players in periods 21-30 will be highest in the sequential/same treatment, second highest in the control (sequential/different) treatment, and lowest in the simultaneous/different treatment.

In other words, the treatments will have an initial effect on the contribution rates. Experience in the treatments will cause critical third players to be more likely to contribute after the crossover Crossover

The point on a stock chart when a security and an indicator intersect. Crossovers are used by technical analysts to aid in forecasting the future movements in the price of a stock. In most technical analysis models, a crossover is a signal to either buy or sell.
 to the sequential MCS game with different contribution costs across players if they were more likely to contribute in periods 1-20.

Conjecture 4: Holding the cost structure fixed, we expect contribution rates by critical third players in periods 31-40 to be highest in the sequential/same treatment, second highest in the sequential/different treatment, and lowest in the simultaneous/different treatment. As compared to Conjecture 3, Conjecture 4 holds that any history dependence will be persistent.

V. EXPERIMENTAL PROCEDURES

Subjects were recruited from among students at the University of Pittsburgh Pittsburgh (pĭts`bərg), city (1990 pop. 369,879), seat of Allegheny co., SW Pa., at the confluence of the Allegheny and the Monongahela rivers, which there form the Ohio River; inc. 1816.  and Carnegie Mellon University Carnegie Mellon University, at Pittsburgh, Pa.; est. 1967 through the merger of the Carnegie Institute of Technology (founded 1900, opened 1905) and the Mellon Institute of Industrial Research (founded 1913). . Each session lasted approximately 1 1/2 h. In total, 648 subjects participated in these sessions. The number of subjects in a session ranged from a minimum of 12 subjects to a maximum of 27 with a median of 21 subjects. (11) No subject was allowed to participate more than once.

Before the beginning of each session, instructions were read aloud to all subjects. Subjects were also given a paper copy of the instructions. Each player received payoff tables for all three player positions; these were also posted on the chalkboard in the experimental lab. Any questions subjects asked were answered aloud to guarantee that all information about the game was common knowledge. Before the experiment began, subjects were asked to complete a brief quiz A quiz is a form of game or mind sport in which the players (as individuals or in teams) attempt to answer questions correctly. Quizzes are also brief assessments used in education and similar fields to measure growth in knowledge, abilities, and/or skills.  designed to ensure that all subjects understood how to read the payoff tables. Choices were framed in neutral terms. We avoided using terms such as "public good" or "contribute." Subjects were simply asked to choose between "X" and "Y" where X corresponded to a decision to contribute to the public good. As part of the instructions, a single practice round with no monetary payoffs was played.

Each subject was randomly assigned as·sign  
tr.v. as·signed, as·sign·ing, as·signs
1. To set apart for a particular purpose; designate: assigned a day for the inspection.

2.
 to be a Player 1, Player 2, or Player 3 at the beginning of the session. Player type remained unchanged over the course of the session. Although subjects knew there were an equal number of individuals in each round, they were not told the role of any subject other than themselves. Each session consisted of 40 periods of the MCS game, broken into 20-period segments. Subjects were informed before play began in period 1 that they would play 20 periods of the game after which they would receive new instructions before playing the remaining 20 periods of the game. Additional instructions were given before the second half of the experiment in all sessions. For sequential/different sessions, these instructions were minimal, informing subjects that the final 20 periods would be played the same way as the first 20 periods. For sequential/same sessions, new payoff tables were handed out, a short set of instructions was read (largely pointing out that the payoffs had changed), and all subjects completed a payoff quiz on the new payoff table payoff table

a table showing the financial returns minus costs for each of the strategies under consideration.
. Simultaneous/different sessions required more detailed instructions before the final 20 periods since the structure of the game had changed. These instructions were a shortened version of the instructions given at the beginning of a sequential/different session, with sections that subjects had already seen (such as how to read the payoff tables) removed. Subjects in the simultaneous/different sessions also played a practice round as part of the instructions before beginning the final 20 periods of play.

In each round, subjects were randomly matched in three-person groups (consisting of a Player 1, a Player 2, and a Player 3) to play the MCS game. At no point did subjects learn with whom they had been matched. These aspects of the procedures (random matching and anonymity) were designed to preserve the one-shot nature of the game and were heavily stressed in the instructions. (The payoff quiz included a question about the random matching.) After each period of play, subjects were shown the individual decisions made by each of the players in their group as well as all three players' payoffs. Subjects were provided with record sheets to write down this feedback. While subjects were not required to fill out their record sheets beyond the practice period, we observed that most did so.

At the end of the session, subjects were paid their earnings in two randomly chosen periods (one period was chosen from periods 1-20 and one from periods 21-40). Each token was worth $0.30. The average payoff was about $15 per subject, including a $5 show-up fee.

VI. RESULTS

As mentioned previously, our analysis of the results will focus on the behavior of critical third players. Throughout the results section when we refer to "contributions" or the "contribution rate," the modifier (programming) modifier - An operation that alters the state of an object. Modifiers often have names that begin with "set" and corresponding selector functions whose names begin with "get".  "by critical third players" can be assumed unless otherwise stated. We generally pool data from the 3/6/9 and 1/3/9 treatments in analyzing the results. This is done for several reasons. The foremost is convenience--results from the 3/6/9 and 1/3/9 treatments are similar enough so that little is learned by considering these two treatments separately and pooling them eliminates a great deal of repetition REPETITION, construction of wills. A repetition takes place when the same testator, by the same testamentary instrument, gives to the same legatee legacies of equal amount and of the same kind; in such case the latter is considered a repetition of the former, and the legatee is entitled  in the text. Pooling these treatments also lets us focus more on the 1/3/16 cost structure, the treatment of greatest interest since it generates the largest and most puzzling puz·zle  
v. puz·zled, puz·zling, puz·zles

v.tr.
1. To baffle or confuse mentally by presenting or being a difficult problem or matter.

2.
 changes in Player 3s' behavior. Finally, we also gain some advantage in terms of statistical power by pooling these two treatments. For regressions on the pooled data we include controls for the cost structure. While these controls are generally significant at the 5% level, the magnitude of the parameter (1) Any value passed to a program by the user or by another program in order to customize the program for a particular purpose. A parameter may be anything; for example, a file name, a coordinate, a range of values, a money amount or a code of some kind.  estimates is small and inclusion of these controls has no qualitative impact on the results.

A. Overview of the Data

Tables A1 and A2 in the online Appendix S1 give a broad overview of the decisions made by all roles across all cost structures and treatments of the experimental design.

We begin our detailed analysis of the data by confirming Conjecture 1. Figure 1 graphs the contribution rate of critical Player 3s in the first half of the experiment, broken down into five-period blocks. The left panel shows data from the 1/3/16 treatment while the right panel pools data from the 3/6/9 and 1/3/9 treatments. Data are graphed separately for the sequential/different, sequential/same, and simultaneous/different treatments. For periods 1-20, critical Player 3s have significantly different contribution rates across cells of the experiment. Regardless of the cost structure, the contribution rate for the simultaneous/different treatment is much lower in periods 1-20 than for the sequential/different treatment. For the 1/3/16 treatment, the difference between the sequential/different and sequential/same treatments is also large in periods 1-20, with the latter treatment yielding a 34% greater contribution rate in periods 16-20 (93.0% vs. 57.7%). The sequential/same treatment has less impact for the 3/6/9 and 1/3/9 cost structures. There is little difference in the contribution rates in periods 1-20 between the sequential/different and sequential/same treatments and for both cost structures the contribution rate in periods 16-20 is actually greater for the sequential/different treatment than for the sequential/same treatment, albeit by a narrow margin. These slight differences reflect a ceiling effect--contribution rates are sufficiently high in the control sessions that there is little room for higher contribution rates in the sequential/same treatment.

[FIGURE 1 OMITTED]

Figure 2 summarizes the pairs of decisions by Player l s and Player 2s over the first 20 periods. The data is broken down in ten period blocks and by cost structure, with data from the 3/6/9 and 1/3/9 cost structures pooled. Outcomes are broken into four categories based on the choices made by the first and second player: first and second player contributed; only the first player contributed; only the second player contributed; and neither the first nor second player contributed. To see how often the third players were critical, combine the two categories in which exactly one of the first two players contributed.

Player 3s in the sequential/same, sequential/ different, and simultaneous/different treatments observe very different behavior by Player 1 s and 2s in periods 1-20. Regardless of cost structure, Player 3s are more likely to observe Player 1 and Player 2 contributing in the simultaneous/different treatment and to observe Player 1 and Player 2 not contributing in the sequential/same treatment as compared to the controls (sequential/different). In other words, Player 3s were more likely to observe unambiguously kind behavior in the simultaneous/different treatment and unambiguously unkind behavior in the sequential/same treatment. Over the first 20 periods, Player 3s are also less likely to be critical in the simultaneous/different treatment, regardless of cost structure.

The pattern of decisions by Players 1 and 2 observed for periods 1-20 continues, albeit in a weaker fashion, for periods 21-25. In all cost structures Player 3s are more likely to observe Player 1 and Player 2 contributing in the simultaneous/different treatment than in the sequential/same treatment. (12) Players are more likely to be critical in the sequential/same than in the simultaneous/different treatment. (13) The preceding points are useful for testing the reference-point hypothesis since the conditions for differing beliefs in these two treatments continue following the switch to the sequential MCS game with different costs of contribution across players.

Conclusion 1: Holding the cost structure fixed, Player 3s behave differently and observe significantly different feedback in periods 1-20 of the three treatments, consistent with Conjecture 1.

Having established that Player 3s have differing experiences in periods 1-20, we now examine the effects that these differences have on the behavior of critical Player 3s in periods 21-40. As noted previously, in the second half of the experiment all subjects play the sequential MCS game with different costs of contribution across players. Figure 3 summarizes the contribution rates of critical third players in all periods for which the sequential MCS game with different costs was played (i.e., periods 1-40 of the sequential/different treatment and periods 21-40 of the sequential/same and simultaneous/different treatments) broken down into five-period blocks. Periods 1-20 and periods 21-40 of the control (sequential/different) sessions are displayed separately to ease comparison with the other two treatments.

The left panel of Figure 3 shows how contribution rates change over time with the 1/3/16 cost structure. In the control sessions, the contribution rate for critical third players drops over the first 20 periods, flattens out for the next ten periods, and then rebounds somewhat. Comparing the sequential/same and simultaneous/different sessions with the controls, experienced players in either of these two treatments have lower contribution rates than inexperienced subjects in the control treatment (66% in the sequential/same treatment and 73% in the simultaneous/different treatment for periods 21-25 versus 80% in periods 1-5 of the sequential/different treatment). However, the contribution rate for experienced players in the control treatment is yet again lower (50% in periods 21-25 of the sequential/different treatment). The contribution rate for periods 6-10 of the control sessions (68%) is quite similar to that for periods 21-25 of the treatment sessions (69%). Thus, 20 periods of experience in either the sequential/same or the simultaneous/different treatment changes the behavior of critical third players in the sequential MCS game with different costs and leads to contribution rates roughly equivalent to those following five to ten periods of experience in the control sessions.

The results for the 3/6/9 and 1/3/9 cost structures, shown in the right panel of Figure 3, reveal a similar pattern. In the control sessions there is a steady increase in contribution rates over the first half of the experiment followed by little change over the final 20 periods. As with the 1/3/16 cost structure, experience with either the sequential/same or simultaneous/different treatment moves the behavior of third players in either the 3/6/9 or 1/3/9 cost structures in the direction of experienced third players' choices in the control sessions. The contribution rate for critical third players in periods 21-25 of either treatment is greater than in periods 1-5 of the control session (83% in periods 21-25 of the sequential/same costs treatment and 89% in the simultaneous/different treatment versus 78% in periods 1-5 of the sequential/different treatment). Averaging over the two treatments, contribution rates in periods 21-25 of the treatment sessions (86%) are roughly the same as in periods 11-15 of the control sessions (85%). For the 3/6/9 and 1/3/9 cost structures, 20 periods of experience with the treatments changes contribution rates by about as much as ten periods of experience in the control sessions.

[FIGURE 2 OMITTED]

Conclusion 2: Consistent with Conjecture 2, experience with either of the two treatments, sequential/same or simultaneous/different is a substitute, albeit an imperfect imperfect: see tense.  one, for experience with the control treatment (sequential/different).

Conclusion 2 establishes that subjects are gaining something from their experiences in the first 20 periods of the experiment that affects their choices in the second half of the experiment. This is a critical point. The treatments are designed to present subjects with dramatically different experiences prior to beginning play of the sequential MCS game with different costs. However, if there was no effect from the initial 20 periods in the treatments, the obvious conclusion would be that the differences were too dramatic and that subjects were gaining nothing from the two treatments. We now turn to the central question of why third players' experiences over the first half of the experiment affect their choices in the second half. We begin by examining whether it matters that these experiences vary so widely across treatments.

For Conjecture 3 to hold as written, the contribution rates in periods 21-30 of the sequential/same and simultaneous/different treatments should bracket In programming, brackets (the [ and ] characters) are used to enclose numbers and subscripts. For example, in the C statement int menustart [4] = ; the [4] indicates the number of elements in the array, and the contents are enclosed in curly braces.  the contribution rate in the control sessions. Because experience with either treatment is only an imperfect substitute for experience with the control treatment, the control sessions actually have far lower contribution rates in these periods than either treatment contrary to Conjecture 3. (14)

[FIGURE 3 OMITTED]

Ignoring the control sessions, the implied comparison Conjecture 3 makes between the sequential/same and simultaneous/different treatments is of independent interest. The data show little evidence of any such difference. With the 1/3/16 cost structure, the contribution rate is 8% lower for periods 21-25 of the sequential/same treatment (as compared to the simultaneous/different treatment). For the 3/6/9 and 1/3/9 treatments, the contribution rate is 7% lower for periods 21-25 of the sequential/same treatment. (15) Recall that the contribution rates were conjectured to be higher in the sequential/same treatment. As will be seen in regression analysis In statistics, a mathematical method of modeling the relationships among three or more variables. It is used to predict the value of one variable given the values of the others. For example, a model might estimate sales based on age and gender.  that follows, these lower contribution rates are not statistically significant, and, in both cases, any difference between the treatments has disappeared by periods 26-30. Nonetheless, the data provide no support for any form of Conjecture 3.

Conclusion 3: Because experience with either treatment is only an imperfect substitute for experience in the control sessions, Conjecture 3 as written can be rejected. Moreover, which treatment is experienced, sequential/same or simultaneous/different, has little impact on behavior in periods 21-30.

Third players' experiences in the first half of the two treatments affect their behavior in the second half of the experiment, but in a way that varies little across the two treatments. In determining which of our three hypotheses best explains this effect, one important clue is whether the effects identified in Conclusions 2 and 3 are persistent. The data indicate they are not. Subjects in the two treatments quickly cease to differ from control session subjects with equal amounts of experience in the sequential MCS game with different costs. For the 1/3/16 cost structure, contribution rates in periods 26-30 of the two treatments are only slightly lower than in periods 6-10 of the control treatments (65% in the sequential/same treatment and 64% in the simultaneous/different treatment vs. 68% in the sequential/different treatment). With the 3/6/9 and 1/3/9 cost structures, one would again be hard pressed to distinguish periods 6-I0 of the control treatments (81% contribution rate) from periods 26 to 30 of the sequential/same and simultaneous/different sessions (84% contribution rate for either treatment). Likewise, comparing the treatments at the last possible interval, periods 36-40, reveals few differences. For the 1/3/16 treatment, contribution rates are almost identical across the three treatments in periods 36-40. There is only a 7% difference between the treatment with the highest contribution rate in this time span and that with the lowest. This similarity Similarity is some degree of symmetry in either analogy and resemblance between two or more concepts or objects. The notion of similarity rests either on exact or approximate repetitions of patterns in the compared items.  carries over to the 3/6/9 and 1/3/9 cost structures where the difference between the maximum contribution rate in periods 36-40 and the minimum is only 4%.

Conclusion 4: Any impact of varying the previous experience of Player 3s prior to playing the sequential MCS game with different costs is transitory. We therefore find no support for Conjecture 4.

In conjunction, Conclusions 3 and 4 indicate that the discovered preferences hypothesis is more consistent with the data than the constructed preferences hypothesis. The distinguishing feature of the discovered preferences hypothesis is that in the long run individuals' preferences are not history dependent. Experienced subjects facing identical decisions, in particular identical information about possible payoffs and the actions of other players, should eventually make identical decisions. This is precisely what we observe. While the behavior of third players changes over time and is temporarily affected by our manipulations of their experiences, eventually subjects in all treatments act the same.

The failure of Conjecture 3 even in its modified form is particularly damning for the reference-point hypothesis. One can argue that this hypothesis does not imply a persistent effect in our data. Given that Player 3s behave more or less identically in the sequential/same and simultaneous/different treatments, the conditions for norms to be mutually reinforcing (and hence persistent) do not exist. However, the correct conditions unambiguously exist in periods 1-20 (and continue weakly through periods 21-25) for Player 3s to have differing beliefs across the sequential/same and simultaneous/different treatments about the behavior of Player 1s and 2s. The lack of any difference in contribution rates for periods 21-25 by critical third players in the sequential/same and simultaneous/different treatments argues that the changing behavior of third players is not being driven by changes in beliefs. (16)

B. Regression Analysis

We now turn to regressions on the contribution decisions of critical third players. This analysis examines whether our conclusions are robust to controls for individual effects in the data. We also use it to identify the features of third players' experiences in periods 1-20 affect that contribution rates in periods 21-40. By giving us a more detailed picture of changes in third players' choices than can be seen from the descriptive statistics descriptive statistics

see statistics.
, this allows us to further distinguish between our three hypotheses.

Tables 3 and 4 report the results of regressions on third player data. These regressions are probits with a random effects Random effects can refer to:
  • Random effects estimator
  • Random effect model
 specification to correct for any individual effects in the data. Data is coded at the individual level, with each observation corresponding to a single decision by a critical third player. (17) The dependent variable is whether the critical third player chose to contribute (0 = do not contribute, 1 - contribute). Positive parameter estimates therefore correspond to higher contribution rates. Throughout this paper, all tests of significance for individual parameters are two-tailed Two-tailed may refer to:

In entomology:
  • Two-tailed Pasha, butterfly which can be seen only in the Mediterranean regions in August and September
  • Two-tailed Swallowtail, large North American butterfly
In other fields:
 z-tests. All tests of joint significance use a log-likelihood ratio test.

Table 3 reports results for data from the 1/3/16 cost structure sessions and Table 4 reports results for pooled data from the 3/6/9 and 1/3/9 treatments. The data have been broken down into ten period blocks. The equation for the unrestricted model is given by Equation (1). [Con.sub.it] is the latent Hidden; concealed; that which does not appear upon the face of an item.

For example, a latent defect in the title to a parcel of real property is one that is not discoverable by an inspection of the title made with ordinary care.
 dependent variable for subject i in period t. As per usual, the observed dependent variable equals 1 if the latent variable In statistics, Latent variables (as opposed to observable variables), are variables that are not directly observed but are rather inferred (through a mathematical model) from other variables that are observed and directly measured.  is greater than zero and equals 0 otherwise.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE re·pro·duce  
v. re·pro·duced, re·pro·duc·ing, re·pro·duc·es

v.tr.
1. To produce a counterpart, image, or copy of.

2. Biology To generate (offspring) by sexual or asexual means.
 IN ASCII ASCII or American Standard Code for Information Interchange, a set of codes used to represent letters, numbers, a few symbols, and control characters. Originally designed for teletype operations, it has found wide application in computers. ]

The model in Equation (1) is designed to compare periods 1-10 of the control sessions with periods 21-30 of the treatment sessions and periods 11-20 of the control sessions with periods 31-40 of the treatment sessions. The primary variables in Equation (1) are dummies for the treatment and time periods. SeqDiff, SeqSame, and SimDiff are dummies for the sequential/different, sequential/same, and simultaneous/different treatments, respectively. The numbers in parentheses refer to the periods covered. So, for example, SeqDiff(11-20) is a dummy Sham; make-believe; pretended; imitation. Person who serves in place of another, or who serves until the proper person is named or available to take his place (e.g., dummy corporate directors; dummy owners of real estate).  for periods 11-20 of the sequential/different treatment. The treatments are differenced from the control treatment with the same amount of experience in the sequential MCS game with different costs of contribution across players. Specifically, [[gamma].sub.1] captures the difference between the treatments in periods 21-30 and the controls in periods 1-10 while Y2 measures the difference between the treatments in periods 31-40 and the controls in periods 11-20. (18) Likewise, the simultaneous/different treatment is differenced from the sequential/same treatment. The parameter [[lambda].sub.1] measures the difference between the sequential/same and simultaneous/different treatments in periods 21-30 and the parameter [[lambda].sub.1] measures the analogous analogous /anal·o·gous/ (ah-nal´ah-gus) resembling or similar in some respects, as in function or appearance, but not in origin or development.

a·nal·o·gous
adj.
 difference for periods 31-40.

The continued evolution of play beyond the first 20 periods in the sequential/different treatment is captured by [delta] which measures the difference between the periods 1-10 and periods 21-40 of the sequential/different treatment. The parameters [phi] and [eta] are useful for establishing that the necessary initial conditions hold. These measure the differences between periods 1-10 of the sequential/different treatment and periods 1-20 of the simultaneous/different and sequential/same treatments respectively.

The vector of variables labeled "history" studies how Player 3s' experiences in periods 1-20 affect their decisions in periods 21-40. Player 3s can observe four possible histories for the other two players: Players 1 and 2 contribute, Player 1 contributes and Player 2 does not, Player 1 does not contribute and Player 2 does, or neither Player 1 nor Player 2 contributes. For each Player 3, we calculate the frequency with which they saw each of these four outcomes in the first 20 periods of the experiment and include this frequency as an independent variable in the final 20 periods of the experiment. To avoid colinearity, the frequency for "Player 1 does not contribute, Player 2 contributes" is dropped. The three remaining variables have been demeaned to make comparison of the models easier.

The variable "variance The discrepancy between what a party to a lawsuit alleges will be proved in pleadings and what the party actually proves at trial.

In Zoning law, an official permit to use property in a manner that departs from the way in which other property in the same locality
" takes a slightly different view of a Player 3's history in periods 1-20. Rather than focusing on the specifics of what a Player 3 saw, we instead consider how varied their experience was. In particular, for each Player 3 we calculate the variance of the frequencies of the four possible outcomes in periods 1-20. For example, suppose a Player 3 saw all four outcomes with equal frequency. The variance would equal zero, the minimum possible. Suppose a Player 3 always saw the outcome where neither Player 1 nor Player 2 contributed, then variance would equal 3/16, the maximum possible. "Variance" is included as an independent variable for periods 21-40. We demean de·mean 1  
tr.v. de·meaned, de·mean·ing, de·means
To conduct or behave (oneself) in a particular manner: demeaned themselves well in class.
 it (subtract A relational DBMS operation that generates a third file from all the records in one file that are not in a second file.  the mean) to make comparison across models easier. To ease interpretation, the "variance" variable is multiplied by negative one, so more varied experiences correspond to higher values.

It is possible that the behavior of critical third players depends on which of the two preceding players has contributed. To control for this, the variable P1con is a dummy for when Player 1 has contributed. For regressions in Table 4, where data from the 3/6/9 and 1/3/9 cost structures are pooled, the regressions include a dummy for the 1/3/9 cost structure, Pay139. The terms [micro].sub.i] and [[epsilon].sub.it] are, respectively, an individual specific and an idiosyncratic id·i·o·syn·cra·sy  
n. pl. id·i·o·syn·cra·sies
1. A structural or behavioral characteristic peculiar to an individual or group.

2. A physiological or temperamental peculiarity.

3.
 error term. We report the fitted value of the correlation between the error terms for two observations from the same subject as [rho].

Looking at the results on Tables 3 and 4, Model 1 reexamines Conjecture 2. The base is periods 1-10 of the sequential/different treatment. We difference periods 21-30 of the treatments from the base ([[gamma].sub.1]) and difference periods 31-40 of the treatments from periods 11-20 of the control sessions ([[gamma].sub.2]). For the 1/3/16 cost structure, the difference for the first ten periods of the sequential MCS game with different costs ([[gamma].sub.1]) is negative and significant at the 1% level. For the pooled 3/6/9 and 1/3/9 data, this difference is positive and statistically significant at the 5% level. These results provide statistical confirmation for Conclusion 2--experience with either the sequential/same or simultaneous/different treatment makes the behavior of critical third players significantly different than that of naive third players in the control (sequential/different) sessions. In other words, third players in the two treatments are gaining something from their experiences in the first half of the experiment that affects their behavior in the second half of the experiment. Looking at the magnitude of the estimates, the difference between periods 11-20 of the controls ([beta]) and periods 21-30 of the treatments ([[gamma].sub.1]) is small and not statistically significant for either the 1/3/16 data or the pooled 3/6/9 and 1/3/9 data. Twenty periods of experience with the treatments has roughly the same effect on contribution rates as ten periods of experience with the control sessions.

Several other points can be gleaned from Model 1. For both the 1/3/16 data and the pooled 3/6/9 and 1/3/9 data, the difference between periods 31-40 of the treatments and periods 11-20 of the controls, [[gamma].sub.2], is much smaller than [[gamma].sub.1] and not statistically significant at the 10% level. Consistent with Conclusion 4, any impact from previous experience with either the sequential/same or simultaneous/different treatment quickly vanishes. For all cost structures, the dummy for periods 1-20 of the simultaneous/different treatment is negative and significant at the 1% level. The dummy for periods 1-20 of the sequential/same treatment is positive and significant at the 1% level for the 1/3/16 data and at the 5% level for the pooled 3/6/9 and 1/3/9 data. These results provide statistical confirmation for Conclusion 1--the treatments induce in·duce
v.
1. To bring about or stimulate the occurrence of something, such as labor.

2. To initiate or increase the production of an enzyme or other protein at the level of genetic transcription.

3.
 different behavior by third players in periods 1-20.

Model 2 reexamines Conclusion 3 by adding dummies for periods 21-30 ([[lambda].sub.1]) and periods 31-40 ([[lambda].sub.2]) of the simultaneous/different treatment. For both the 1/3/16 data and the pooled 3/6/9 and 1/3/9 data, these parameter estimates are smallish and statistically insignificant. Considered together, [[lambda].sub.1] and [[lambda].sub.2] also fail to achieve joint statistical significance at even the 10% level for either data set. Consistent with Conclusion 3, any effect from which treatment subjects have previously experienced is minimal.

Digressing briefly, we have also run Model 2 with periods 21-30 of the sequential/different treatment as the base and a dummy for periods 31-40 (instead of periods 11-20) of the sequential/different treatment. Using this regression regression, in psychology: see defense mechanism.
regression

In statistics, a process for determining a line or curve that best represents the general trend of a data set.
, we can formally test whether there are any statistically significant differences between the three treatments in periods 31-40. Not surprisingly, we fail to find any such difference for either the 1/3/16 data or the pooled 3/6/9 and 1/3/9 data. In both cases the relevant parameter estimates are small and fail to be statistically significant at even the 10% level. (19) Along with the results of Model 1, this confirms Conclusion 4--any effect of the sequential/same and simultaneous/different treatments is transitory.

Conclusion 5: The regression analysis confirms Conclusions 1-4. The choices of critical third players in periods 1-20 are significantly affected by the three treatments. Third players in periods 21-30 of either the sequential/same or simultaneous/different treatment behave differently than third players in periods 1-10 of the control (sequential/different) treatment. Even in periods 21-30, we cannot statistically distinguish between the behavior of third players in the sequential/same and simultaneous/different treatments. The behavior of critical third players in periods 31-40 is statistically indistinguishable across the three treatments.

At this point, we are left with an empirical puzzle “Puzzle solving” redirects here. For the concept in Thomas Kuhn's philosophy of science, see normal science.

A puzzle is a problem or enigma that challenges ingenuity.
. Previous experience with either the sequential/same or simultaneous/different treatment affects behavior in the sequential MCS game with different costs. However, even though these two treatments give third players dramatically different experiences, subjects seem to respond identically to the two treatments. This suggests that there must be some common factor between the two treatments which is driving the changes in third players' behavior. Models 3 and 4 try to identify this factor.

Model 3 modifies Model 1 by adding the three history variables. For the 1/3/16 cost structure, only the frequency of observing neither of the preceding two players contribute is statistically significant, and then only at the 10% level. In the pooled data from the 3/6/9 and 1/3/9 cost structures none of the three history variables is statistically significant. In neither regression are the three history variables jointly significant. It seems unlikely that the three history variables are driving the changing behavior of critical third players.

To study the reference-point hypothesis more closely, we ran a variation of Model 3 that replaced the three history variables with two alternate independent variables. For each Player 3 we calculate the contribution rate they observed in periods 1-20 for Player 1s, Player 2s conditional on Player 1 contributing, and Player 2s conditional on Player 1 not contributing. We then create two new variables for each observation as a critical third player in periods 21-40: the historical contribution rate for the role that did contribute and the historical contribution rate for the role that did not contribute. (20)

If the reference-point hypothesis is correct, the parameter estimate on the contribution rate for the role that has contributed (and hence treated me kindly) should be negative, as kind behavior should seem less unusual as this contribution rate rises. Likewise, the parameter estimate on the contribution rate for the role that has not contributed (and hence treated me unkindly) should be negative, as unkind behavior should seem more unusual as this contribution rate rises. In fact, neither of these two contribution rates is statistically significant at the 10% level in either the 1/3/16 data or the pooled 3/6/9 and 1/3/9 data. (21) The individual level data provide little support for the reference-point hypothesis as an explanation for why experience in the first half of the treatments is affecting contribution rates in the second half of the experiment.

Model 4 tests an implication of the discovered preferences hypothesis. According to according to
prep.
1. As stated or indicated by; on the authority of: according to historians.

2. In keeping with: according to instructions.

3.
 this hypothesis, the experiences that Player 3s have in periods 1-20 are not changing their preferences, but instead make it possible for them to discover their preferences. As such, having a wide variety of experiences should speed up the learning process even though the final resting point is unaffected. Intuitively, consider the position of a critical third player. He considers not contributing to punish the previous player who did not contribute. Implicitly, a comparison is being made between being treated well (the first two players provide the public good) and being treated poorly (one of the first two players tries to free-fide on the third players contribution). Varied experience helps a subject know not only how he feels about the situation he is in, but also how he would have felt about other possible situations. Model 4 tests this hypothesis by adding the "variance" variable to Model 1. The results are exactly as this hypothesis predicts. For the 1/3/16 cost structure, the estimate for the "variance" variable is statistically significant at the 1% level and has a negative sign. With the 1/3/16 cost structure, contribution rates for critical third players fall over time. Having broader experiences in periods 1-20 accelerates this process. Likewise, for the pooled data from the 3/6/9 and 1/3/9 cost structures the estimate for the "variance" variable is statistically significant, albeit only at the 10% level, and has a positive sign. Once again, broader experiences in periods 1-20 serve to accelerate the learning process.

This result suggests why the sequential/different and simultaneous/same treatments have similar impact on the behavior of third players. Under both treatments subjects get to experience similar types of outcomes (the other two players are kind, unkind, etc.), but the frequency of the outcomes differs. However, if the marginal impact of experiencing each outcome is declining, what matters is having an opportunity to experience all possible outcomes rather than how often one experiences them.

Conclusion 6: Critical third players' responses to the play of Player 1s and Player 2s in periods 1-20 are inconsistent with predictions of the reference-point hypothesis. The speed of learning depends on the breadth of experience third players have rather than the depth of experience with any one particular outcome, consistent with the discovered preferences hypothesis.

C. Some Additional Results

Before concluding the results section, we briefly address some secondary issues in the data. We discuss the effect of our treatments on provision rates for the public good, establish that reputation building does not play an important role in our data, and show that declining error rates cannot explain the observed dynamics.

[FIGURE 4 OMITTED]

An interesting implication of the constructed preference hypothesis is that if social preferences could be permanently affected by interventions, this could be used to generate greater efficiency in a variety of settings. For the MCS game, this translates to an ability to manipulate the provision rate for the public good. Figure 4 illustrates provision rates in the sequential MCS game with different costs across the different treatments and cost structures. Not surprisingly given our failure to permanently alter the behavior of third players, the three treatments do not have any permanent impact on provision rates for the public good. For the 1/3/16 cost structure, the control treatment yields a higher provision rate for periods 1-5 than for periods 21-25 in either the sequential/same or simultaneous/different treatments. However, this difference has largely vanished by the next five-period block and never reappears. In the pooled data from the 3/6/9 and 1/3/9 cost structures, the control treatment yields lower provision rates in periods 1-5 than for periods 21-25 in either the sequential/same or simultaneous/different treatments. However, once again this difference vanishes almost immediately. Our treatments have no long-run impact on provision of the public good.

The upward hook observed at the end of all three treatments for the 1/3/16 treatment merits a brief discussion. One explanation for this pattern is that critical third players who do not contribute are engaged in reputation building and start contributing at the end of the session as the value of a reputation for toughness wanes. If this reputation hypothesis is correct, then the strong dynamics in the 1/3/16 treatment have nothing to do with learning about preferences in any sense, but instead reflect strategic considerations. The reputation hypothesis does not hold up on several dimensions. First, it is not clear that the late increase in contribution rates is very large. In no case do contribution rates in periods 36-40 come even close to those observed in periods 1-5. Suppose we use regressions like those reported in Table 3 to compare the contribution rates in periods 21-30 with the contribution rates in periods 31-40. Only in the control treatments do we get a statistically significant difference, and then only weakly at the 10% level. Second, if reputation building is important, contribution rates should be sensitive to session size--recall that session size varied from a minimum of 12 subjects to a maximum of 27. Larger sessions should yield higher contribution rates, since maintaining a reputation is less valuable in large sessions. If we modify Model 1 from Table 3 by adding a parameter for session size, the estimate is positive but not statistically significant at even the 10% level. Even worse, the effect of session size on contribution rates is stronger in the second half of the experiment (although still not statistically significant). Under the reputation hypothesis, the effect of group size should weaken over time. Finally, there exists a better explanation than reputation building for the late increase in contribution rates--aggregation effects. Third players are more likely to be critical in sessions where their contribution rate is high than those where it is low. This means that observations in the later periods of sessions will come disproportionately dis·pro·por·tion·ate  
adj.
Out of proportion, as in size, shape, or amount.



dispro·por
 from sessions with high contribution rates by critical third players. Thus, the contribution rate will appear to rise in late periods when it in fact is constant. This explanation is consistent with the data. Breaking down the data at the session level, the contribution rate rises from periods 31-35 to periods 36-40 in only 5 of the 12 sessions with the 1/3/16 cost structure, including 2 of 4 control sessions. The correlation between the likelihood of a third player being critical and the contribution rate for their session is quite high -0.667 for periods 36-40.22 We therefore feel confident in stating that the strong dynamics seen in the 1/3/16 cost structure cannot be attributed to reputation building.

Another alternative explanation for the observed changes in contribution rates for critical third players is that inexperienced subjects are prone to making random errors, but stop making errors as they gain experience. While such an explanation might explain changing contribution rates in the 3/6/9 and 1/3/9 cost structures, it makes little sense for the 1/3/16 cost structure where the most dramatic changes occur. If play in the last half of the experiment accurately reflects subjects' true preferences, there is approximately a 60-40 split between subjects that prefer to contribute as critical third players in the 1/3/16 cost structure and those who prefer to not contribute. Since random errors are presumably unbiased, it is equally likely that a player who intended to contribute would accidentally choose to not contribute as vice versa. Thus, a declining error rate should lead to increasing contribution rates over time, not decreasing contribution rates as is observed.

VII. DISCUSSION AND CONCLUSIONS

At the heart of this paper is an empirical puzzle. Critical third players in the sequential MCS game with differing costs of contribution do not have anything obvious to learn. They face neither strategic uncertainty nor payoff uncertainty. Nonetheless, we observe systematic changes in the behavior of critical third players. Most strikingly, in the treatment with the greatest asymmetry Asymmetry

A lack of equivalence between two things, such as the unequal tax treatment of interest expense and dividend payments.
 between roles, the 1/3/16 treatment, Player 3s appear to acquire a taste for punishing pun·ish  
v. pun·ished, pun·ish·ing, pun·ish·es

v.tr.
1. To subject to a penalty for an offense, sin, or fault.

2. To inflict a penalty for (an offense).

3.
 free-riders. The goal of this paper is to better understand why negative reciprocity by critical third players in the MCS game changes with experience. More broadly, we hope that understanding changing behavior in the MCS game will contribute to an understanding of why other-regarding behavior changes in a wide variety of settings.

As possible explanations for third players' changing behavior, we entertain three hypotheses: the constructed preferences hypothesis, the discovered preferences hypothesis, and the reference-point hypothesis. Our experimental design varies the experience subjects receive in the first half of the session, allowing us to distinguish between these hypotheses. The treatments succeed in generating very different experiences for Player 3s in periods 1-20. While subjects' experience in the first 20 periods has an impact on their play in the sequential MCS game with different costs, the surprise is that while third players change their behavior in response to experience, the particular nature of their experience matters little. This is especially true in the long run, as the behavior of critical third players in periods 31-40 is virtually indistinguishable across treatments. Thus, our treatments do not yield any evidence of persistent history dependence.

Returning to our three hypotheses, the reference-point hypothesis has the least support in the data. Not only do we not observe the persistent history dependence this hypothesis implies, we also fail to observe the predicted differences between treatments immediately following the change to the sequential MCS game with different costs. The pattern of responses to past history that the reference-point hypothesis predicts is also absent. If we failed to observe any effect of experience in the first half of the treatment sessions on play in the second half of the experiment, we could conclude that the difference between games is too large for any transfer of beliefs to take place, but this is not the case. The constructed preferences hypothesis finds little support as well. A fundamental prediction of the constructed preferences hypothesis is that subjects' preferences are malleable malleable /mal·le·a·ble/ (mal´e-ah-b'l) susceptible of being beaten out into a thin plate.

mal·le·a·ble
adj.
1. Capable of being shaped or formed, as by hammering or pressure.
, yet we observe that subjects' choice are remarkably stable in the face of markedly different experiences. Once again, arguing that the various games are too different begs the point--something must explain why play in the second half of the treatment sessions is not the same as play by naive players in the control sessions. The data is most consistent with this something being the discovered preferences hypothesis. While the behavior of critical third players changes over time and the path of play is affected by the experience third players receive, in the long-run contribution rates are not history dependent. Moreover, varied experiences accelerate third players' movement toward their long-run contribution rates. These results are consistent with a model where subjects learn stable underlying preferences.

Our results should be viewed as making a positive point rather than a negative one.

The changing behavior of third players in the MCS game indicates that learning about preferences can be an important source of change in other-regarding behavior. It does not follow that anchoring and adjustment or changing beliefs about other players' behavior never lead to changes in other-regarding behavior. As noted in the introduction, evidence from other experiments is more positive for these hypotheses, especially the reference-point hypothesis. More work is needed to determine when each of the various forces that might be driving changes in other-regarding behavior is likely to be particularly important.

Our final point is methodological. There are numerous studies from psychology and behavioral economics Behavioral Economics

A field of economics that studies how the actual decision-making process influences the decisions that are reached.

Notes:
The two most important questions in this field are:
 that find evidence in favor of the constructed preferences hypothesis, including several from the literature on social preferences (Bohnet and Huck 2004; Cookson 2000; Stahl and Haruvy 2008). This raises the question of whether some feature of our experimental design explains we are not finding evidence for constructed preferences, giving us some feeling for when stable preferences are or are not likely to be observed.

(1) Our treatments are insufficiently strong to produce a persistent impact. We have previously discussed the possibility that our manipulations are too strong, but the opposite is also possible. Specifically, either subjects are not given enough rounds of experience with the treatments prior to beginning play of the sequential MCS game with differing costs or subjects' experiences in the two treatments are not sufficiently different. This possibility cannot be completely dismissed without further experiments, but we suspect that the results would not change if the intensity of the treatments was increased. Twenty periods are more than enough time to produce large changes in the behavior of critical third players in the sequential MCS game. Whatever drives these changes must therefore work over a short time span. Moreover, the manipulation of subjects' experiences used here is far more dramatic than the framing and/or anchoring manipulations other studies have used to generate effects. It therefore seems unlikely that increasing the intensity of the manipulation without changing its nature would yield qualitatively different results.

(2) We are not relying on framing effects. Economists typically assume that an individual's preferences over two options do not depend on how those preferences are elicited e·lic·it  
tr.v. e·lic·it·ed, e·lic·it·ing, e·lic·its
1.
a. To bring or draw out (something latent); educe.

b. To arrive at (a truth, for example) by logic.

2.
, but studies that find evidence in favor of constructed preferences often do so by relying on violations of procedural invariance in·var·i·ant  
adj.
1. Not varying; constant.

2. Mathematics Unaffected by a designated operation, as a transformation of coordinates.

n.
An invariant quantity, function, configuration, or system.
 (e.g., framing effects). Our experimental treatments do not vary the procedure used to elicit e·lic·it  
tr.v. e·lic·it·ed, e·lic·it·ing, e·lic·its
1.
a. To bring or draw out (something latent); educe.

b. To arrive at (a truth, for example) by logic.

2.
 subjects' preferences. This is appropriate, since we are trying to explain changes in other-regarding behavior observed in previous experiments that did not vary how preferences are elicited, but experimental treatments that employ framing effects might find evidence in favor of the constructed preferences hypothesis in the formation of social preferences. For example, Haruvy and Stahl (2008) find that rejection rates in ultimatum games are sensitive to how the game is presented. (They do not study whether this effect is persistent.)

(3) We give subjects a relatively large amount of experience. Much of the evidence suggesting that preferences are constructed comes from psychology rather than economics. These experiments typically give subjects little opportunity to learn from feedback. For the experiments reported here, extensive experience plays a critical role in determining our conclusions. We observe subjects' initial reaction to the treatments and how their behavior evolves in the long run. Consider how this affects our comparison between the sequential/same and simultaneous/different treatments for the 1/3/16 cost structure. If we only observe the first time third players are critical following the switch to the sequential MCS game with differing costs, contribution rates are 8% higher for the sequential/same treatment. Looking at a somewhat longer time span, contribution rates are 8% lower for the sequential/same treatment over the first five rounds following the switch. Considering the full 20 rounds following the switch, differences in contribution rates between the two treatments eventually vanish. In other words, it is only because subjects play a large number of rounds following the switch to the sequential MCS game with differing costs that we clearly observe the lack of any persistent history dependence. With fewer rounds we might mistakenly have believed that the treatments have a permanent effect and therefore changed our conclusions about the formation of social preferences. We conjecture that the relatively large amount of experience our experiments give subjects is an explanation for why we find support for the discovered preferences hypothesis rather than the constructed preference hypothesis. (23) More broadly, this suggests that exercises in estimating social preferences that are based on single shot games will be flawed flaw 1  
n.
1. An imperfection, often concealed, that impairs soundness: a flaw in the crystal that caused it to shatter. See Synonyms at blemish.

2.
 given that behavior may only settle down after extensive experience.

ABBREVIATIONS

VCM: Voluntary Contribution Mechanism

MCS: Minimal Contributing Set

doi: 10.1111/j.1465-7295.2010.00325.x

SUPPORTING INFORMATION

Additional Supporting Information may be found in the online version of this article:

Appendix S1. History Dependence and the Formation of Social Preferences: An Experimental Study.

Please note: Wiley-Blackwell are not responsible for the content or functionality of any supporting materials supplied by the authors. Any queries (other than missing material) should be directed to the corresponding author for the article.

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(1.) We adopt Fehr and Fischbacher's (2002) designation for this broad class of preferences.

(2.) Eliminating strategic uncertainty as a potential explanation for changing behavior is crucial. With strategic uncertainty, changing levels of cooperation and/or punishment are unsurprising. For example, consider a standard VCM public goods game. Suppose that most individuals are conditional cooperators in the sense of Fischbacher, Gachter, and Fehr (2001), contributing more when they expect others to contribute more. With experience, such participants will change their behavior if they find that others contribute more or less often than initially expected.

(3.) See Subsection subsection
Noun

any of the smaller parts into which a section may be divided

Noun 1. subsection - a section of a section; a part of a part; i.e.
 VI.C for a detailed explanation about why the changing behavior of critical third players cannot be explained by reputation effects or decreasing error rates.

(4.) The MCS game was first introduced in a simultaneous form by Van de Kragt, Orbell, and Dawes (1983) and in a sequential form by Erev and Rapoport (1990).

(5.) A critical third player might also be motivated mo·ti·vate  
tr.v. mo·ti·vat·ed, mo·ti·vat·ing, mo·ti·vates
To provide with an incentive; move to action; impel.



mo
 by positive reciprocity toward the preceding player who contributed to the public good. This added complexity in the problem faced by critical third players is, oddly, a positive feature of using three rather than two players. The MCS game is useful for studying the formation of social preferences because of the dramatic change observed in the choices of critical third players over time. The countervailing reciprocity arguments facing critical third players make their decision nontrivial nontrivial - Requiring real thought or significant computing power. Often used as an understated way of saying that a problem is quite difficult or impractical, or even entirely unsolvable ("Proving P=NP is nontrivial"). The preferred emphatic form is "decidedly nontrivial". , which likely enhances the observed dynamics.

(6.) See also Charness, Corominas-Bosch, and Frechette (2001) for results consistent with the reference-point hypotheses. For contrary results, see Brandts and Fatas (2001).

(7.) Cooper and Stockman (2002b) find mixed evidence in favor of the reference-point hypothesis for the MCS game. They examine the effect of past play by Players 1 and 2 on current play by critical third players. Some, but not all, of the parameter estimates are consistent with the reference-point hypothesis.

(8.) Data from the control (sequential/different) sessions were previously reported in Cooper and Stockman (2002a).

(9.) In the 1/3/16 treatment, it is possible for third players to lose money. If loss aversion In prospect theory, loss aversion refers to the tendency for people strongly to prefer avoiding losses than acquiring gains. Some studies suggest that losses are as twice much psychologically powerful as gains.  is present, this makes it even less likely that third players will contribute.

(10.) An alternative path to the same prediction is pure inertia inertia (ĭnûr`shə), in physics, the resistance of a body to any alteration in its state of motion, i.e., the resistance of a body at rest to being set in motion or of a body in motion to any change of speed or change in direction of . A third player who has been contributing may continue to do so after the game is changed if subjects only re-evaluate their decisions irregularly ir·reg·u·lar  
adj.
1. Contrary to rule, accepted order, or general practice: irregular hiring practices.

2.
. This reflects bounded rationality Many models of human behavior in the social sciences assume that humans can be reasonably approximated or described as "rational" entities (see for example rational choice theory).  rather than any feature of preferences.

(11.) We have run the regression analysis reported in the results section with controls for session size. These controls are not statistically significant and do not impact the qualitative conclusions we draw from the regressions.

(12.) The difference is 34.5% versus 19.2% (28.8% vs. 8.4%) with the 1/3/16 (3/6/9 and 1/3/9) cost structure(s).

(13.) The difference is 84.2% versus 60.0% (74.4% vs. 53.8%) with the 1/3/16 (3/6/9 and 1/3/9) cost structure(s).

(14.) To clarify, Conjecture 3 implicitly assumes that subjects in the treatments get the full effect of 20 rounds in the controls plus a shift due to the treatment, leading to the bracketing A still camera technique for ensuring correct exposure. One picture is taken directly at, one slightly under and one slightly over the estimated exposure. See bracket. . Since 20 rounds in the treatment have less than half the effect of 20 rounds in the controls, this bracketing is unlikely to occur unless the shifts for the treatments effects are very large (which they are not).

(15.) A referee A judicial officer who presides over civil hearings but usually does not have the authority or power to render judgment.

Referees are usually appointed by a judge in the district in which the judge presides.
 suggests that contributing as a critical third player may seem even more unfair when subjects have previous experience with symmetric No difference in opposing modes. It typically refers to speed. For example, in symmetric operations, it takes the same time to compress and encrypt data as it does to decompress and decrypt it. Contrast with asymmetric.

(mathematics) symmetric - 1.
 costs, providing a possible explanation for the difference between the sequential/same and simultaneous/different treatments.

(16.) Suppose that the reference-point hypothesis explained changes in third player behavior, but differences between the various games are so large that subjects do not carry over beliefs from the first half of the experiment to the second. This would imply that behavior in the two treatments for periods 21-26 should be identical to behavior in periods 1-5 of the controls, which is not the case.

(17.) For periods 1-20 of the simultaneous/different treatment, Player 3s did not know if they were critical when making decisions. To be consistent, the dataset for the regressions only includes observations where the Player 3 was critical, but the parameter estimates are virtually unchanged if we include all observations for periods 1-20 of the simultaneous different treatment.

(18.) To see the latter point, compare the terms following [beta] and [[gamma].sub.2] in Equation (l)--these only differ in the inclusion of SeqDiff(11-20) following [beta].

(19.) The two treatment dummies in periods 31-40 also fail to achieve joint statistical significance.

(20.) For example, suppose Player l contributes and Player 2 does not. The first variable, the contribution rate for the role that contributed, is set equal to the observed contribution rate for Player 1s in periods 1-20. The second variable, the contribution rate for the role that has not contributed, is set equal to the observed contribution rate for periods 1-20 for Player 2s subject to Player 1 not contributing.

(21.) The two variables also fail to achieve joint significance in either regression.

(22.) The random effects specification used for the probit In probability theory and statistics, the probit function is the inverse cumulative distribution function (CDF), or quantile function associated with the standard normal distribution.  regressions controls for any aggregation effects in the data.

(23.) For example, the history effect that Bohnet and Huck (2004) report for trust games appears to have collapsed by the end of ten rounds. Based on our experimental evidence, we conjecture that no persistent effect would have been found if the experiment had been run for an additional ten rounds.

DAVID David, in the Bible
David, d. c.970 B.C., king of ancient Israel (c.1010–970 B.C.), successor of Saul. The Book of First Samuel introduces him as the youngest of eight sons who is anointed king by Samuel to replace Saul, who had been deemed a failure.
 J. COOPER and CAROL KRAKER STOCKMAN *

* The authors would like to thank the National Science Foundation for financial support. We would like to thank two anonymous referees, Eric Bettinger, Jordi Brandts, Gary Charness, Yan Chen, John Ham Ham, in the Bible
Ham, in the Bible, son of Noah. In biblical ethnography, Ham is the father of the nations Cush, Mizraim, Phut, and Canaan. In a story separate from the flood narrative, the legend related in the Book of Genesis and in the Qur'an suggests
. John Kagel, Jack Ocbs, Charles Plott Charles Plott, born in 1938, is an American economist. He currently is Edward S. Harkness Professor of Economics and Political Science at the California Institute of Technology and a pioneer in the field of experimental economics. He is a member of the National Academy of Sciences. , Marl Rege, AI Roth, and Lise Vesterlund for helpful discussions. The usual caveat applies.

Cooper: Professor, Department of Economics, Florida State University, Tallahassee, FL 32306. Phone 850 644 7097, Fax 850 644 4535, E-mail: djcooper@fsu.edu

Stockman: Graduate School of Public Health, University of Pittsburgh, Pittsburgh, PA 15261. E-mail: ckstockman@gmail.com
TABLE 1
Summary of Contribution Costs by Treatment

                       3/6/9       1/3/9     1/3/1916    Sequential/
                     Treatment   Treatment   Treatment      Same

Player l's cost of   3 tokens    1 tokens    1 tokens     6 tokens
  contribution
Player 2's cost of   6 tokens    3 tokens    3 tokens     6 tokens
  contribution
Player 3's cost of   9 tokens    9 tokens    16 tokens    6 tokens
  contribution

TABLE 2
Experimental Design

MCS game periods 1-20                      Costs of Contribution

                 Different or
Timing            Same Costs       3/6/9         1/3/9       1/3/1916

                                4 Sessions    4 Sessions    4 Sessions
Sequential        Different     75 Subjects   66 Subjects   93 Subjects
                                3 Sessions    3 Sessions    4 Sessions
Seq Sequential       Same       66 Subjects   63 Subjects   75 Subjects
                                3 Sessions    3 Sessions    4 Sessions
Simultaneous      Different     66 Subjects   57 Subjects   87 Subjects

TABLE 3
Regressions for 1/3/16 Treatment (a) (Dependent Variable: Contribution
by a Critical Third Player)

Variable                                        Model 1

Constant ([alpha])                              0.822 **
                                               (0.161)
Sequential/different x Periods 11-20           -0.766 **
  ([beta])                                     (0.192)
Simultaneous/different and sequential/same     -0.567 **
  x Periods 21-30 ([[gamma].sub.1])            (0.197)
Simultaneous/different and sequential/same     -0.250
  x Periods 31-40 ([[gamma].sub.2])            (0.187)
Sequential/different x Periods 21-40           -1.013 **
  ([delta])                                    (0.173)
Simultaneous/different x Periods 1-20          -2.601 **
  ([PHI])                                      (0.248)
Sequential/same x Periods 1-20 ([eta])          0.620 **
                                               (0.216)
Simultaneous/different x Periods 21-30
  ([[lambda].sub.1]
Simultaneous/different x Periods 31-40
  ([[lambda].sub.2]
Proportion in Periods 1-20 Players 1 and 2
  contribute ([[kappa].sub.1])
Proportion in Periods 1-20 Player 1
  contributes, Player 2 does not
  ([[kappa].sub.1])
Proportion in Periods 1-20 Players 1 and 2
  do not contribute ([[kappa].sub.1])
Variance in Periods 1-20 choices by
  Players 1 and 2 ([tau])
Current period Player 1 contributes ([psi])

p                                               0.684 **
                                               (0.032)
Log-likelihood                                 -758.88

Variable                                            Model 2

Constant ([alpha])                              0.822 **
                                               (0.161)
Sequential/different x Periods 11-20           -0.766 **
  ([beta])                                     (0.192)
Simultaneous/different and sequential/same     -0.669 **
  x Periods 21-30 ([[gamma].sub.1])            (0.227)
Simultaneous/different and sequential/same     -0.421 ([dagger])
  x Periods 31-40 ([[gamma].sub.2])            (0.237)
Sequential/different x Periods 21-40           -1.013 **
  ([delta])                                    (0.173)
Simultaneous/different x Periods 1-20          -2.511 **
  ([PHI])                                      (0.259)
Sequential/same x Periods 1-20 ([eta])          0.551 **
                                               (0.212)
Simultaneous/different x Periods 21-30          0.181
  ([[lambda].sub.1]                            (0.221)
Simultaneous/different x Periods 31-40          0.315
  ([[lambda].sub.2]                            (0.237)
Proportion in Periods 1-20 Players 1 and 2
  contribute ([[kappa].sub.1])
Proportion in Periods 1-20 Player 1
  contributes, Player 2 does not
  ([[kappa].sub.1])
Proportion in Periods 1-20 Players 1 and 2
  do not contribute ([[kappa].sub.1])
Variance in Periods 1-20 choices by
  Players 1 and 2 ([tau])
Current period Player 1 contributes ([psi])

p                                               0.684 **
                                               (0.032)
Log-likelihood                                 -758.01

Variable                                        Model 3      Model 4

Constant ([alpha])                              0.866 **      0.871 **
                                               (0.175)       (0.175)
Sequential/different x Periods 11-20           -0.774 **     -0.780 **
  ([beta])                                     (0.192)       (0.193)
Simultaneous/different and sequential/same     -0.600 **     -0.496 *
  x Periods 21-30 ([[gamma].sub.1])            (0.192)       (0.197)
Simultaneous/different and sequential/same     -0.273        -0.167
  x Periods 31-40 ([[gamma].sub.2])            (0.185)       (0.178)
Sequential/different x Periods 21-40           -1.157 **     -0.924 **
  ([delta])                                    (0.190)       (0.176)
Simultaneous/different x Periods 1-20          -2.638 **     -2.411 **
  ([PHI])                                      (0.285)       (0.243)
Sequential/same x Periods 1-20 ([eta])          0.487 *       0.558 **
                                               (0.199)       (0.211)
Simultaneous/different x Periods 21-30
  ([[lambda].sub.1]
Simultaneous/different x Periods 31-40
  ([[lambda].sub.2]
Proportion in Periods 1-20 Players 1 and 2     -0.425
  contribute ([[kappa].sub.1])                 (0.620)
Proportion in Periods 1-20 Player 1            -0.084
  contributes, Player 2 does not               (0.693)
  ([[kappa].sub.1])
Proportion in Periods 1-20 Players 1 and 2     -2.638 *
  do not contribute ([[kappa].sub.1])          (1.284)
Variance in Periods 1-20 choices by                         -10.47 **
  Players 1 and 2 ([tau])                                    (2.779)
Current period Player 1 contributes ([psi])    -0.057        -0.068
                                               (0.083)       (0.084)
p                                               0.673 **      0.694 **
                                               (0.031)       (0.030)
Log-likelihood                                 -755.76      -754.90

(a) All regressions include 1899 observations over 85 individuals.
Statistical significance at the 1%, 5%, and 10% levels are denoted
with the symbols **, *, and ([dagger]) respectively.

TABLE 4
Regressions for 3/6/9 and 1/3/9 Treatments (Dependent Variable:
Contribution by a Critical Third Player)

Variable                                  Model l         Model 2

Constant ([alpha])                        0.916 **    0.906 **
                                         (0.127)     (0.131)
Sequential/different x Periods 11-20      0.458 **    0.458 **
  ([beta])                               (0.155)     (0.155)
Simultaneous/different and                0.368 *     0.271
  sequential/same x Periods 21-30        (0.160)     (0.212)
  ([[gamma].sub.1])
Simultaneous/different and                0.047       0.035
  sequential/same x Periods 31-40        (0.173)     (0.226
  ([[gamma].sub.2])
Sequential/different x Periods 21-40      0.488 **    0.488 **
  ([delta])                              (0.130)     (0.130)
Simultaneous/different x Periods 1-20    -1.435 **   -1.420 **
  ([PHI])                                (0.159)     (0.163)
Sequential/same x Periods 1-20            0.414 *     0.370 ([dagger])
  ([eta])                                (0.172)     (0.200)
Simultaneous/different x Periods                      0.176
  21-30 ([[lambda].sub.1])                           (0.219)
Simultaneous/different x Periods                     -0.013
  31-40 ([[lambda].sub.1])                           (0.217)
Proportion in Periods 1-20 Players 1
  and 2 contribute ([[kappa].sub.1])
Proportion in Periods 1-20 Player 1
  contributes. Player 2 does not
  ([[kappa].sub.1])
Proportion in Periods 1-20 Players 1
  and 2 do not contribute
  ([[kappa].sub.1])
Variance in Periods 1-20 choices by
  Players 1 and 2 ([tau])
Current period Player I contributes
  ([psi])
1/3/9 Treatment ([xi])                   -0.306 *    -0.279+
                                         (0.134)     (0.150)
p                                         0.551 **    0.546 **
                                         (0.034)     (0.035)
Log-likelihood                           -1206.83    -1206.33

Variable                                  Model 3         Model 4

Constant ([alpha])                        0.916 **    0.909 **
                                         (0.130)     (0.130)
Sequential/different x Periods 11-20     456 **       0.458 **
  ([beta])                               (0.154)     (0.155)
Simultaneous/different and                0.399 *     0.457 **
  sequential/same x Periods 21-30        (0.195)     (0.169)
  ([[gamma].sub.1])
Simultaneous/different and                0.079       0.124
  sequential/same x Periods 31-40        (0.204)     (0.175)
  ([[gamma].sub.2])
Sequential/different x Periods 21-40      0.502 **    0.487 **
  ([delta])                              (0.134)     (0.130)
Simultaneous/different x Periods 1-20    -1.389 **   -1.370 **
  ([PHI])                                (0.173)     (0.170)
Sequential/same x Periods 1-20            0.449'      0.511 **
  ([eta])                                (0.231)     (0.184)
Simultaneous/different x Periods
  21-30 ([[lambda].sub.1])
Simultaneous/different x Periods
  31-40 ([[lambda].sub.1])
Proportion in Periods 1-20 Players 1      0.273
  and 2 contribute ([[kappa].sub.1])     (0.310)
Proportion in Periods 1-20 Player 1       0.263
  contributes. Player 2 does not         (0.484)
  ([[kappa].sub.1])
Proportion in Periods 1-20 Players 1      0.469
  and 2 do not contribute                (0.851)
  ([[kappa].sub.1])
Variance in Periods 1-20 choices by                   4.364 ([dagger])
  Players 1 and 2 ([tau])                            (2.479)
Current period Player I contributes      -0.011      -0.001
  ([psi])                                (0.068)     (0.067)
1/3/9 Treatment ([xi])                   -0.321 *    -0.286 *
                                         (0.152)     (0.129)
p                                         0.556 **    0.547 **
                                         (0.037)     (0.030)
Log-likelihood                           -1206.12    -1205.39

Note: All regressions include 3683 observations over 131 individuals.
Statistical significance at the 1%, 5%, and 10% levels are denoted
with the symbols **, *, and ([dagger]) respectively.
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Author:Cooper, David J.; Stockman, Carol Kraker
Publication:Economic Inquiry
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Date:Apr 1, 2011
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