Experimental studies with the "multilateral bargaining model": a strategic analysis.

ABSTRACT

This paper examines the Multilateral Bargaining mode/of Rausser and Simon (1991), using the Uruguay Round Uruguay provides but one data point, limiting the possibilities for field testing, pilot experiments are conducted whereby the mode/can be behaviorally tested in a laboratory setting. In the lab a controlled negotiation environment is created and repeated a significant number of times, employing payoff parameters that are empirically estimated with a genera/equilibrium model The game is played in strategic form, assigning five players to each negotiating group. The players are asked to negotiate by making three strategy choices. (1) a policy proposal, (2) a feasible coalition and (3) a minimum payoff threshold at which he or she will join another's coalition. Findings from the experiments are compared to the actual negotiations, and to results that were generated in a companion set of simulation exercises. We find similar results as were found in the simulations, and find that the alternate approach from Redmond (2003), using a sector-specific scenario would more closely mimic the dynamics of the Uruguay Round. However the primary contribution of this study is to demonstrate how economic models of the impacts of policies can be integrated with bargaining models of negotiations over those policies, and then replicated in the experimental laboratory.

1. INTRODUCTION

The objective of this study is to behaviorally test the Multilateral Bargaining (MB) model, due to Rausser and Simon (1991), in an experimental laboratory setting. Previous studies have used the Rausser and Simon MB model to simulate a number of negotiation environments. Two studies, Adams, Rausser and Simon (1996) and Thoyer, Morardet, Rio, Simon, Goodhue, and Rausser (2001) examined the complexities of water negotiations, in California and South West France, respectively. Yet another, Pinto and Harrison (2003) used the model to study coalition formation in the recent environmental negotiations to reduce carbon emissions.

Redmond (2003) employed the MultiRegional Trade (MRT) computable general equilibrium model, due to Harrison, Rutherford and Tarr (1997), to empirically generate the welfare changes that would accrue to the primary players in the Uruguay Round Negotiations on Agriculture, as they reduced the levels of the targeted policy instruments. These policy instruments are export subsidies, production subsidies, and import tariffs. With this information, empirical estimates of the primary negotiators' preferred policies were calculated. Subsequently Redmond (2004) uses those preferred policies to calibrate the MB model, thus tying the impact of the economic policies with the negotiation process in which the final policies were determined. Of special interest were the coalition formation and the policy results.

Our goal in this study is to take these empirical results, and use the experimental laboratory to create a controlled negotiation environment that can be recreated and repeated a significant number of times. There is a general lack of long time-series data on negotiation outcomes under stationary institutional conditions, as well as a limited quantity of cross-section data on multilateral negotiation environments. For example, the outcome of our targeted study, the Uruguay Round Negotiations on Agriculture, provides only a single data point in the strategy space. Therefore Redmond (2003), and then Redmond (2004) showed how economic models that quantify the impacts of policies can be integrated with bargaining models of the negotiations over those policies. In this study the primary contribution is to demonstrate how these results can be replicated in the experimental laboratory.

We will proceed in the following manner. In Section Two we give a description of the MB model. Section Three presents modifications on our previous research. In Section Four we summarize previous experimental work in the area. Section Five addresses the design and significance of our experiments, explaining our primary concerns and the relevance to actual negotiation environments. Finally in Section Six we discuss some preliminary findings from our study.

2. THE RAUSSER AND SIMON MULTILATERAL BARGAINING MODEL

The Multilateral Bargaining model is a sequential, non-cooperative game in extensive form, with a finite number of players, n+1, and a finite but arbitrarily large number of rounds, T. The player set consists of n+1 members because it is dictated that a central (essential) player must belong to every admissible coalition. The central player is the '0 th" player, and the 1 though n players operate peripherally. The provision for the essential player is a critical restriction on the applicability of the model.

The model is of the class of spatial games, where instead of proposing the division of a predetermined pie, as in the Stahl (1972) and the Rubinstein (1982) games, it is assumed that the size of the pie is determined by the policy outcome. This is an important note in our present application, as the total net returns to the governmental agents in the Negotiations on Agriculture, differ according to the degree of liberalization.

The proposals in the model take the form of admissible policies, whose attributes are summarized by points on a horizontal plane, over which the negotiators' preferences are ordered. For example, in a very simple two issue setting, we may model issue A on the x-axis and issue B on the y-axis. A player's ideal preference can be represented by a coordinate, such as (6,5), and his payoff is decreasing as the Euclidean distance from that point increases. This approach, utilized in Harrison and Simon (1991), is extended in this study in order to "three dimensionally" model the three issue proposals that were debated in the Negotiations on Agriculture as admissible policies.

The MB game is set up with the following assumptions. The players in the game convene to choose a policy from a set, X, of admissible policies. Each representative player i will receive the payoff [u.sub.i](x)if the policy vector x is chosen. There is also a vector, [empty set] , representing the disagreement outcome that will be the default policy in the event that an agreement is unable to be reached. This disagreement payoff is exogenous. The vector, u, defined on [X.sup.*] (X U [empty set]) is designated the payoff function for the game.

Each player has an ideal preference. (a bliss point) in X, and the vector of the players' bliss points is given as. If we allow d(x,y)to represent the Euclidean distance between xand y, the utility that/derives from a policy x is a decreasing function of d(x,i). The model is then used to analyze games that are produced by varying either, the payoff function, LI, or the number of bargaining rounds, T, holding all other parameters constant.

In a formal bargaining process there inevitably has to be some procedure by which a policy can be chosen from the set of admissible policies. This model solves this issue by allowing nature to make this determination. Although this is a random choice, the model recognizes that there may be some asymmetry in the relative bargaining powers of the players. Therefore, nature's choice is ruled by a vector of access probabilities. As it is plausible to assume that each player's policy is more likely to be singled out as his relative negotiating power increases within the group, these access probabilities will be weighted accordingly. The game itself consists of a finite number of negotiating rounds, with each round consisting of three stages:

* Each player chooses a policy and an admissible coalition. (Assuming that all of the players have the same voting power, a coalition is admissible if it contains a majority of the voters. If there is asymmetric voting power among the players, whereby some have more votes than others, an admissible coalition consists of a set of players who have the most votes.)

* Nature chooses one of the proposals at random, with probabilities differing according to the access probabilities

* Each member of the proposer's coalition decides whether to accept or reject the proposer's policy. If all accept, it is implemented and the game ends. If one member rejects, the procedure is repeated. If the last round of the game is reached and there is no agreement the game ends and the players earn a disagreement payoff

In an intuitive interpretation, the model is characterized as "the backroom negotiations which emerge from the influential, inner circle of a complex organization." (Rausser and Simon, 1991) Prior to the full meeting of the organization, coalitions will be formed, deals will be struck and compromises will be made in meetings between the members of this inner circle.

The policy which is ultimately accepted is called the solution to the multilateral bargaining game. In a game where there is a finite set of negotiating rounds, an equilibrium outcome is a probability distribution over the policies that are implemented when equilibrium strategies are played. In contrast to the usual sub-game perfection solution concept, Rausser and Simon (1991) use a SEDS (Sequential Elimination of Dominated Strategies) criterion, through which strategies that involve inadmissible play are eliminated round by round beginning with the concluding round. Given a payoff function u, a bargaining model is a sequence of T-round bargaining games which are different only in the actual number of bargaining rounds. If the sequence of equilibrium outcomes for the model converges to some limit measure, [??], then [??] is called the solution to the model. Therefore if [??] exists, it will be a proxy for the outcome of any T-round bargaining game. Also a necessary condition for this policy to be a solution is that it resides in the core of the bargaining game, in that there is no admissible coalition whose members unanimously favor some other policy. Specifically, a vector is said to be in the core if it is feasible for some coalition and there is no other vector that is weakly preferred by each member of the coalition, and strictly preferred by one member. Finally, if a solution cannot be reached, the payoffs will not be the status quo, as there will be some credible default reform.

3. THE MULTILATERAL BARGAINING GAME WITH A FIXED NUMBER OF ROUNDS

Redmond (2004) conducted numerical simulations with the MB model and set no upper bound on the number of rounds in the game. This approach was taken because the goal in that study was not only to assess the depths of the reductions, but also the speed in which the players reached a solution. However in the laboratory experiments, as we wish to create a controlled environment, we impose a finite horizon on the games. In this section we report the findings from a simulation where the number of rounds is restricted to five, so that there is a direct comparison to the experimental sessions.

This simulation, reported in Table 1, is analogous to the simulations in Redmond (2004) where the power of the players is equal. This power is manifested as the access probability (the probability that a player gets to make a proposal) and the voting power (the percentage of votes that one player has in relation to the other players). The only difference in this simulation is that the game is restricted to five rounds. The total expected payoff of "2.401" is less than the "2.404" of the unbounded game where convergence was reached in ten rounds. This is consistent with the pattern that we found in the earlier study where the expected payoffs to the group tended to increase, as the rounds increase (i.e., we allow them to reach their point of convergence). The above analysis suggests that operating with an infinite (or arbitrarily large) horizon would be advantageous, in terms of expected payoffs, as opposed to one that is bounded. However, in the experimental laboratory it is not always feasible to operate under such conditions due to time constraints, monetary constraints, etc., so a controlled environment is necessary. It is for this reason that in this introductory work, we constrained our experimental sessions to a fixed number of (five) rounds. As we noted, we will refer to these findings when we discuss the results of the experiments. See Redmond (2004) for the "real world" interpretation of these payoffs, as well as a more robust description of the model.

4. EXPERIMENTAL LITERATURE

Previous experimental research with the MB model has been documented in Harrison and McCabe (1991). This study proposes a basic design that contains three primary features. The first of these features is to furnish players with unpaid training against simulated opponents. This is a common feature of many experiments, by which players are given a rehearsal period to familiarize themselves with the operation of the particular institution with which they will be performing, without learning anything about the behavior of the other players.

The second common feature in the design involves the manner of compensating the players. The authors use a duplicate cardinal tournament method that grants the players a share of a fixed pie based on their performance relative to others in comparable positions. This method of payment motivates the player to sustain rational behavior all the way to the end of the exercise, thus limiting the payoff dominance problem that is chronicled in Harrison (1989). Also, instead of the direct payment method where the total payment is endogenous to the experiment, this method serves to predetermine the total amount of money that is paid out per session. Therefore the experimenter can plan a series of experiments that satisfy budget restrictions and guarantee that incentives are comparable for all players.

The third common feature is the number of agents per game. The authors proposed a preliminary benchmark of five agents, though their ultimate goal was to assess institutions that have many more participants.

5. OUR MULTILATERAL BARGAINING EXPERIMENTS

As we stated earlier, the purpose of these experiments is to test the predictive powers of the MB model in the laboratory. We incorporate the basic design framework of the MB experiments to date. However, we introduce several key extensions. First, we propose to test the MB model in the laboratory by calibrating it to actual negotiation circumstances. We do this ex-post with the Uruguay Round Negotiations on Agriculture by evaluating proxies for the actual policy options introduced in the Round, and using the utility parameters calculated in Redmond (2004) with the MultiRegional Trade CGE model. Second, as three primary issues were under discussion in the Agricultural Negotiations, we expand the scope of the literature to include three-dimensional choices, instead of the two dimensions of the previous work. The integration of these characteristics into our design aids us in addressing our research questions:

* How closely do the strategies as proposed by the laboratory players approximate the strategies as prescribed by the model?

* Which strategy choices have greater impacts on the final payoffs in the game?

We are primarily interested in how self-interested players, who are provided with a suitable incentive structure, will perform in our negotiation environments. In our treatment we examine a scenario where the players are assigned the roles of the four principal agents of the Uruguay Round Negotiations on Agriculture.

Each player is assigned a point in the (0,0,0) to (100, 100, 100) vector space of admissible policies, that represents her idea/point, or most highly ranked alternative. We instruct them that as this is their ideal point, this is the policy that yields the highest payoff. It also follows that they prefer points that are closer to this ideal point, as their payoff decreases as the distance away from this point increases. Closer is defined as having a lower absolute, Euclidean distance from the ideal point, relative to alternate points. It is therefore a simple task to rank the alternative policies cardinally.

One person is randomly chosen to be the proposer at the beginning of the first day. (In this context a day could be construed as a round of the game. We discuss the design using day as this is the context that was presented to the players). The likelihood that a player will be chosen as the proposer is contingent on the access probability that she is assigned in that session. In all of our sessions, this likelihood is the same for each player. This proposer is then assigned two tasks. First this individual invites members to join him to form an admissible coalition. Next the proposer submits a policy alternative to the coalition. The coalition members now have the option of accepting or rejecting the proposed policy. If all members of the coalition accept the policy, the game ends. However if any member rejects, the game goes to the next day. Each player in the game is rewarded by receiving points relative to the proximity of the accepted policy to their ideal points.

5.1 Experimental Design

The sequence of the game is analogous to the Harrison et al. games. The design is patterned to mimic a multiparty negotiating scenario, by having players propose policies and propose coalitions that could pass the proposals. We impose an upper bound of five days to the game, assuming that an agreement has not been reached within this time.

The 12 human players in each session are randomly assigned a player type (B-E). These types are set to correspond to the chief negotiating parties from the Redmond (2004) analysis where: B = the Cairns Group, C = the United States, D = Japan, and E = the European Union. Additionally, the computer, in three incarnations, simulates the play of (A) the "essential" GATT agent. Therefore as we have 15 players (12 human and 3 simulated) and 5 player types, we can simultaneously produce three replications of the game. Each player is assigned a preferred alternative (idea/point) that is unique to his particular player type. For example each player "B" will be assigned an identical ideal point and be matched in a game against randomly selected, players of the other types, "A, C, D, and E" However as we later explain in more detail, the earnings of the player will be compared with those of the same player type, and not against those with whom he is negotiating. The players are also assigned a maximum payoff (intercept), which is the payoff that a player receives if her ideal point is the chosen alternative. The rate at which this payoff decreases, as chosen alternatives move away from the ideal point (coefficient), is also reported. This relationship is illustrated in the following equation, although our computer program very conveniently does this calculation for the players:

U(i) = [alpha](i) - [beta][(i).sup.*] [square root of [3.summation over j=1] [(X(j) - A(i,j)).sup.2]

Where:

* U(1) is the payoff for each player/following a policy change from the status quo.

* .(i) is the payoff that player/receives if her ideal policy is chosen (INTERCEPT).

* .(i) is the rate that player is utility decreases as the chosen policy vector moves away from her ideal policy (COEFFICIENT).

* A(i,j) denote the coordinates of player/s ideal point (most preferred policy). In this study, these ideal points are depicted as three-dimensional vectors.

* A(j) represent the coordinates of any proposed policy.

In the game, each player has full information on the preferences and payoffs of each of the other players. The basic design features of this game are noted in Table 2. Again, note that these are empirical estimates derived from the Redmond (2004) simulations. The intercepts and coefficients have been scaled up by a multiple of 1000 for these experimental sessions. This does not change the relative positions of the players. However it does aid in making the numbers more operative for the players in the laboratory to manipulate, as it eliminates the use of fractions that are carried out to three decimal places.

5.2 The Sessions

For each of the three pilot sessions, 12 players were recruited from the student population. Recruitment was performed with e-mail announcements to persons who had previously participated in unrelated experiments, and mass e-mail announcements that were sent to all business students on campus. We conducted the experiments after the end of the spring semester, a time of year when more graduate students are on campus. This is reflected in the mean age of 26.5 and the fact that the median player was a graduate student. We hope that the use of graduate business students adds strength to the results, as the game is relatively complex. Each of the three sessions lasted approximately two hours. As the players entered the room they were asked to choose a card that randomly assigned a Player ID number. That number directed them to a computer terminal that contained an instruction packet with the same number. This process further administered the random assignment of Player Type, as the packet (and the pre-programmed computer) contained instructions that were specific to that player.

After signing the "Information Sheet and Consent Form," the players were given the rules of the game. They were provided written instructions that the session monitor read as they followed along. They were also provided a Parameter Sheet that detailed their own preferences (the ideal point and utility parameters), and the preferences of the other four players in the game. At this time the players were instructed on the method of payment, explicitly being informed that although they were bargaining against others who had asymmetric payoffs, their final payment was determined by comparing them with players of their own type. A simple numerical example was presented on the chalkboard to aid in their understanding.

The instructions were read, and initial questions were answered, and next the players were given a practice period in which they received training on the computer by playing against simulated opponents. The monitor of the session first went through this process while showing it on a screen at the front of the room, and then the players were allowed to practice on their own. In this way, at their own paces, the players can familiarize themselves with the sequence of the game, the role of the proposer, the role of the coalition invitees, and the calculation of payoffs for each player. Following this training session the players were instructed that they would play five, 5-day periods and be randomly shuffled to play against different opponents (though of course against the same opposing Player Types) in each period. Then the actual game then began.

The first real task that the players were given was to give the computer guidelines on how to play the game on their behalf, starting with Day One. This was facilitated by using the preference and payoff information (of all of the players) that was readily accessible from the computer. First, the player must specify the coalition that he would favor in each day of the game, should he randomly be selected as the proposer. As in the earlier study, we restricted minimal winning coalitions to include 4 of the 5 players, in the instances where voting power is equal. In this game, Player A is designated as the essential player, and must be a member of each coalition. Therefore, this requirement is satisfied in this five-player game by the selection of two of the other players to join him and the essential player. Table 3 lists the possible coalitions in the game.

Next, the player must specify the policy alternative that he would propose to this coalition, again contingent on him being selected as the proposer. In these experiments the choice set is from a 3-space and is restricted to the range (0,0,0) to (100,100,100), inclusive. An appealing feature of the computer program is that on the screen it prints the payoff that each player will receive from any alternative that is entered, and allows for modifications if the payoff is not to the player's liking. Players can therefore experiment with different proposals and judge them based on their payoff consequences before submitting them. These payoffs are calculated by assessing the proximity of the proposed policies (eventually the accepted policy) to the ideal points of the players.

Finally, the player must specify the lowest payoff (point value) that he would be willing to accept to give an affirmative vote to another player's policy alternative. This value will determine whether a policy is accepted or rejected, conditional on the player being invited to join another player's coalition. If the point value of any coalition member does not reach this threshold, the policy is rejected and the game moves to the next day. The players then go on and make these three decisions for Day 2, with the understanding that if someone from the proposed coalition rejects the proposal in the first day, the game goes on to the second day, with the decision variables from day two. This continues for the subsequent days, and if no agreement is reached in the 5th day, each player receives a zero payoff. Between the selection process for each day, the players are offered the opportunity to reevaluate the payoffs for any proposal, further aiding this process.

When all players have entered their strategies for Period One, the program performs simulations using these strategies. First 1000 simulations are run, starting with the strategies of Day 1. Then assuming that the Day 1 meeting was not held, 1000 simulations are run starting with the strategies of Day,?. This scenario is repeated three additional times with 1000 simulations starting with the Day3, the Day4, and the Day S strategies.

This entire process takes about 5 seconds, so the players are immediately able to get feedback on the average payoff that they earned in each of these 5 days. From this a total payoff for the period is calculated, which is simply the sum of the daily averages. Next at the press of a key, the players are provided other key information on their performance. For each scenario they are told "you were selected as the proposer--times" and "your proposal was accepted--times." Additionally they are told "you were asked to join a coalition--times" and "you rejected this offer--times."

The above information is useful to the players because they can change their strategies for the next period. However, they are explicitly informed in the instructions that, since their bargaining partners change from one period to the next, they are not strictly playing a repeated game. This process is repeated for each of the five periods, so that at the end of the session we can total the payoffs from all of the periods, and record each player's total payoff for the experiment. As the players are filling out their socio-demographic questionnaire, we compute the earning in the following manner.

Each player begins with an initial endowment of $15, $5 for showing up to the experiment and $10 for completing the experiment. Additionally, a variable allotment of 12 additional dollars per person is allocated to be divided among the participants according to their performance, giving an average earning of $27 per player.

Using a duplicate cardinal tournament method consistent with Harrison et al. (1991), players are rewarded according to their performance relative to others of the same player type. After the experiments have been completed, we total the points that each player has accumulated in the session. This is designated as the player score. We compare player scores only in relation to the same player type. Therefore the score of [B.sub.1] will only be compared with the scores of [B.sub.2] and [B.sub.3], and likewise for the Cs, Ds, and Es. We subtract the lowest score from each of the other two scores, to reach the adjusted score. The fraction of the total pie of $36 ($12 per person variable allotment) that player [B.sub.i] receives is the ratio of his adjusted score to the sum of the adjusted scores of the other Type B players.

As a simple example, assume that the Type [B.sub.1,2,3] players have player scores of 210, 215, and 220, respectively. We subtract the lowest score (210) from each of the player scores to obtain the adjusted scores of 0, 5, and 10. As the adjusted scores sum to 15, their performance endowments are 0/15 x $36, 5/15 x $36, and 10/15 x $36, or $0, $12, and $24 respectively. When we add the initial endowment of $15 to the performance endowments, [B.sub.1] earns $15, [B.sub.2] earns $27, and [B.sub.3] earns $39.

Each experimental session consists of 5 periods. In each period we first identify the players by their ID numbers and their corresponding player type, and then index their preferred policy alternatives along with their maximum feasible point values. Then we compile data related to the decisions that are made during the period, including the player's proposed alternative, their proposed coalition, their minimum acceptable point value, and the actual points that were earned during the period.

6. RESULTS

In Section 6 we use the data compiled on proposed alternatives, the proposed coalitions, the mimmum acceptable points, and earnings to report preliminary results from the experiments. We will take two approaches in our analysis of the results. First we will report the strategies that were tallied by the players in the interactive part of the experiment, namely the choices of policy and coalition. The vast decision space of these experiments creates a sizable set of possible strategies, and these strategies are subsequently applied in a non-repeated, interactive setting. This obviously makes it a challenge to form a prescribed set of equilibrium strategies for one to follow. Additionally, previous bargaining experiments have shown that an obvious focal strategy centers on a decision that will generate an equal division of monetary payoffs, and that this equal split is more probable when the earning opportunities are symmetric (Davis and Holt 1993). The payment procedure (the duplicate cardinal method) of these experiments and the asymmetry of the players' payoffs within a game, both make it difficult to form any such focal strategy in our experiments.

We present descriptive statistics for the final round proposals to provide an initial summary of the policy decisions and then we summarize our findings on the coalition choices. The results from this evaluation are provided in Section 6.1. Additionally, in Section 6.2 we evaluate the strategies on the basis of the payoffs that the players accumulated in the game. In this approach, following Harrison et al. (1991), we define fully rational and minimally rational strategies, and compare the players' actual performances to these standards in order to ascertain the relative importance of the individual strategy choices.

6.1 An Analysis of "Strategies"

In this section we report descriptive statistics from the experimental sessions. One objective of this experimental study is to compare the strategies of the experimental players with the derived strategies from the simulation exercise. The results from this analysis are presented in Table 4.

In this table, the proposals from the final round of each game are presented. As there were three sessions of five rounds, and 3 of each "player type" in each session, we have 45 observances for each policy. For example, examining the "policy" decisions for the type "B" player, the mean policy proposal was 76.56 (Policy 1), 73.69 (Policy 2) and 80.82 (Policy 3). One of our goals in this study was to compare the policies that the experimental players proposed with the policies from the simulation exercise. Our preliminary results show these to be relatively close. Looking at the average final round policy proposal of the players in the "Mean" column with the prediction of the model in the "Model Prediction" column (both in the "All" row), we find Policy 1 to be 67.03 vs. 74.47 respectively, Policy 2 to

However just as we found in the simulation exercise, these predicted reductions are greater than the actual reductions that were adopted in the Uruguay Round negotiations (36% export subsidies, 24% production subsidies, 36% import tariffs). As Redmond (2003) maintains, it is due to the disproportional political power of the agricultural lobbying groups (relative to the non-agricultural groups) that this method of measuring utility with Equivalent Variation appears to not fully represent the true dynamic of the negotiations. In that study, a Political Preference function was used to model this interaction. Therefore in subsequent work, as an extension to the present analysis, focus will be given to the sub-game at the domestic level by dividing each region into competing (but cooperative) sectors. The payoff to the region would be influenced by the payoffs to each sector, and consequently this sub-game would be played before the parties meet to negotiate. Again however, these particular policies from the experimental laboratory do approximate the simulated policies from the same incentive structure.

The last strategy choice on which we wish to comment is the selection of coalitions. The Redmond (2004) simulations showed a consistent pattern of coalition selection and we will now determine if it carries over to the experimental session. Table 5 summarizes the coalition selection from the experimental sessions. In each of the 3 sessions we have pooled the selections of the corresponding player types, the three Bs, the three Cs, etc.

The first column indicates the player type of the player in question. The 2nd, 3rd, and 4th columns indicate the session from which we are getting the players' decision. These values that are in these columns show the frequency that the other players (from column #5, Player) are included in that column 1 player's coalition choice. A "1.0" indicates that a player type was unanimously chosen by another player type, and a "0.75" would indicate 75% inclusion, etc. Column #6, Predicted, indicates the model predictions that were derived from the simulations.

As an example, the B players in Session 1 included "A" (the essential player) and "B" (themselves) in all of the coalitions. They selected C to be in 0.65 (65%), D in 0.47, and E in 0.88 of the coalitions. Therefore a majority of the chosen coalitions, by the B players, included A, B, C, and E, which according to the check marks, follows the prediction of the simulations.

Promising results are contained in the data from Table 5. First we find that for each of the players, in each of the sessions, the predicted coalitions, were the most frequently selected by the experimental players. The model predicted that the "B" and "C" players would exclude "D" from their proposed coalition and that the "D" and "E" players would likewise exclude "B". This is consistent with the proximity of the players' ideal points and consistent with the original empirical results from Redmond (2004) where the C and E players, the U.S. and the EU respectively, were included in most of the coalitions and even later went on to negotiate solely amongst themselves.

6.2 The Strategies Evaluated by their "Contributions to the Payoffs"

An alternate approach to this evaluation is to evaluate the strategies of the players in terms of the impact on their payoffs, following Harrison et al. (1991). We conduct this analysis by constructing a numerical model of behavior in which the players' choices are simulated, following prescribed strategies. We first define minimally rational or zero intelligence (ZI) strategies to form a lower boundary on the rational behavior of the players. Next we define fully rational or full intelligence (Fl) strategies to form an upper bound on rational behavior. These full intelligence strategies are the strategies that are prescribed by the MB model and thus are the strategies that were followed in the numerical simulations of Redmond (2004). The actual results from the experiments can then be compared to the payoffs from the zero intelligence and the full intelligence simulations (and of rational, strategy combinations in between) to measure the impact of each strategy.

This practice of taking an efficiency measurement to evaluate the performance of an institution is common to the experimental literature. Davis and Holt (1993) in their discussion of double-auction market experiments, define efficiency as the percentage of the maximum possible surplus that is extracted. In this study, the same approach is taken, and this maximum possible surplus is defined as the payoff from the full intelligence scenario.

build this numerical model by first defining the message space over which each player formulates a decision. Table 6 lists the profiles for each of the strategies, in increasing order of rationality. The strategies [C.sup.0], [P.sup.0], and [M.sup.0] comprise the baseline (ZI) strategy whereby the player makes the minimum rational decision on each of the parameters. It is emphasized that these are the minimum rational choices. There are obviously choices that are irrational, and inferior to these. For example, given the rules of the game, a rational player would not exclude herself from her own coalition ... or suggest a policy alternative that is greater (less) than, the highest (lowest) ideal point of any player.... or ask for a minimum threshold value that is greater than her own proposal would imply, etc. Conversely the strategies [C.sup.*], [P.sup.*] and [M.sup.*] form the full intelligence (FI) strategy. We have also defined several strategy combinations that fall between these extremes, reflecting increasing levels of rational responses to the three decision variables. However, in this study we will concentrate on the respective ZI and the FI strategies, as we examine the overall effects that the three principal decisions have on the ultimate payoffs to the players To complete the numerical analysis the actual performances of the players are pooled. In order to isolate the effects of the individual, coalition (C), policy (P), and minimum threshold (M) strategy choices, Table 7 presents a set of strategies that deviates one decision at a time from these extreme ZI and FI strategies. For example, those strategies labeled "W" are the same as the ZI strategy except in WI the actual (from the experimental sessions) minimum threshold is implemented, in [W.sub.2] the actual policy is implemented, and in [W.sub.3] the actual coalition choice is implemented. Likewise the strategies labeled "X", are the same as the FI (fully rational) strategy, except that in [X.sub.1], the ZI minimum threshold is implemented, in [X.sub.2] the ZI policy is implemented, and in [X.sub.3] the ZI coalition choice is implemented. Finally the strategies labeled "Y", are the same as the FI, fully rational strategy, except that in [Y.sub.1], the actual minimum threshold is implemented, in [Y.sub.2] the actual policy is implemented, and in [Y.sub.3] the actual coalition choice is implemented.

In order to quantify the effects of these individual choices we introduce an efficiency index, which expresses the actual payoff as a percentage of the payoff that is derived from a particular strategy choice. This index is calculated by dividing the actual average payoff that the players received from the game, by the expected payoff that would be earned by some other strategy chosen from our list of strategies (and then multiplying by 100 to index it). For example, assume that the players received 75 actual points from a particular round in the game, and the payoff from the FI strategy would have been 100. The FI Efficiency Index would then be 75 [(75/100)*100].

Alternately assume that this actual payoff of 75 is compared to the payoff from another strategy in Table 7, for example, [W.sub.1], that has an expected payoff of 50. This [W.sub.1] Efficiency Index would then be 150 [(75/50)*100] Note: As we are working with the same actual payoff throughout the analysis, a higher index would imply a "less rational" strategy choice.

These efficiency indices can help us to assess the relative importance that a particular decision (C, P, or M) may have on the ultimate payoffs. Again, we have isolated several of these indices, each time manipulating one key variable, in an attempt to illustrate this point. In Table 8 we form a comparison that highlights the difference between the FI and the ZI decisions. Column 2 (FI) presents the efficiency index that is derived from comparing the payoffs from the actual choices that were made in the experimental sessions, with the payoffs as prescribed by the FI strategies. The indices in the next three columns are the same as this column except that in the [X.sub.1] column we use the ZI (instead of FI) minimum threshold strategy, in the [X.sub.2] column we use the ZI (instead of FI) policy choice, and in the [X.sub.3] column we use the ZI (instead of FI) coalition choice. Using the notation from Table 7 and allowing the strategies ([C.sup.i], [P.sup.i], [M.sup.i]) to represent the payoffs that are earned from particular strategies, the computations for these columns are:

FI [right arrow] [C.sup.a], [P.sup.a], [M.sup.a]/[C.sup.*], [P.sup.*], [M.sup.*] * 100

[X.sub.1] [right arrow] [C.sup.a], [P.sup.a], [M.sup.a]/[C.sup.*], [P.sup.*], [M.sup.0] * 100

[X.sub.2] [right arrow] [C.sup.a], [P.sup.a], [M.sup.a]/[C.sup.*], [P.sup.0], [M.sup.0] * 100

[X.sub.3] [right arrow] [C.sup.a], [P.sup.a], [M.sup.a]/[C.sup.0], [P.sup.*], [M.sup.0] * 100

The substantially higher index for [X.sub.1] indicates that there is a significant reduction in the payoff when a minimally rational choice is made for the minimal threshold. There is obviously some reduction in the payoff when the other parameters are changed, but these are not nearly as great.

To further examine this relationship, we conducted a similar analysis in Table 9, where again the second column, FI, represents the optimal efficiency. Now however, in the third, fourth, and fifth columns ([Y.sub.1], [Y.sub.2], and [Y.sub.3]), we change the minimal threshold, policy and coalition choice, respectively, to reflect the actual choices that were observed in the sessions. Again the figures that are in these columns are interpreted as follows.

FI [right arrow] [C.sup.a], [P.sup.a], [M.sup.a]/[C.sup.*], [P.sup.*], [M.sup.*] * 100

[Y.sub.1] [right arrow] [C.sup.a], [P.sup.a], [M.sup.a]/[C.sup.*], [P.sup.*], [M.sup.a] * 100

[Y.sub.2] [right arrow] [C.sup.a], [P.sup.a], [M.sup.a]/[C.sup.*], [P.sup.a], [M.sup.*] * 100

[Y.sub.3] [right arrow] [C.sup.a], [P.sup.a], [M.sup.a]/[C.sup.a], [P.sup.*], [M.sup.*] * 100

We find comparable results as before. The [Y.sub.1] column, where the sub-optimal choice is the minimum threshold, produces the largest increases in the index, reflecting larger decreases in the payoff. This point is further illustrated in column two of Table 10, where we now list the ZI indices in column 2, and indicated by the representations below. As these indices represent the payoffs from the minimally rational choices across all of the parameters, these indices naturally should be higher than the indices from any other combination of rational strategy choices. However the high value (382) in the first period of the column [Y.sub.1] indicates that there was in fact "sub-zero" rational decision making in this round. A closer look at the data from the experiments reveals that two of the players, in this period only, entered minimum thresholds that were greater that the payoffs that they would have received from their own proposed policies. Obviously these were not rational decisions.

ZI [right arrow] [C.sup.a], [P.sup.a], [M.sup.a]/[C.sup.0], [P.sup.0], [M.sup.0] * 100

[W.sub.1] [right arrow] [C.sup.a], [P.sup.a], [M.sup.a]/[C.sup.0], [P.sup.0], [M.sup.a] * 100

[W.sub.2] [right arrow] [C.sup.a], [P.sup.a], [M.sup.a]/[C.sup.0], [P.sup.a], [M.sup.0] * 100

[W.sub.3] [right arrow] [C.sup.a], [P.sup.a], [M.sup.a]/[C.sup.a], [P.sup.0], [M.sup.0] * 100

Otherwise, the earlier pattern still holds. In this case as we move from the minimum rational strategies to the actual strategies, we would expect the decreases in the efficiency indices (indicating increases in the payoff, in this instance) to be greater when the minimum threshold is changed. This is true, if we allow for the "less than rational" decision in period one.

A look at the mean FI index (70) of Tables 8 and 9, along with the mean ZI index (328) of Table 10 reinforces this point. It appears that the choice of the minimum threshold (M) is the most important of the three variables, as far as efficiency is concerned. When the rationality of the C or P variable is reduced, but the optimal choice of M is taken, as in strategies [X.sub.2&3] and [Y.sub.2&3], the efficiency index does not stray far from the optimal value, increasing by 21-27%. However as the M changes from optimal to actual as in Table 9, column [Y.sub.1], or optimal to ZI as in Table 10, column [X.sub.1] the percentage change in the efficiency index increases by 74% and 205%, respectively.

Intuitively, the selection of M is quite important. In the game, minimum threshold choices that are above the payoff that a chosen policy yields, send the game into later rounds (days) and can potentially result in the default, zero payoff at the end of the last period. Likewise the selection of a minimum threshold value that is low in the earlier rounds can potentially cause a player to end the game early with an arbitrarily low payoff (instead of holding out for a more favorable policy in the later rounds). As it was shown in Tables 4 and 5, the experimental players performed rather well in their choices of P and C, respectively. Therefore, although the Fl choices may not be immediately recognizable, this analysis indicates that the experimental players would be well served to focus on the choice of minimum threshold (M) in order to maximize their payoffs.

7. CONCLUSIONS AND EXTENSIONS

The objective of this study was to behaviorally test the Multilateral Bargaining model in the experimental laboratory. These experiments were calibrated from the Uruguay Round incentive structure that was established in Redmond (2003), and compared to the MB simulations that were conducted in Redmond (2004). With this methodology we wish to demonstrate how economic models concerning the impacts of policies, can be integrated with bargaining models concerning the negotiations over those policies, and then replicated in the experimental laboratory.

Our experiments follow the overall design of previous multilateral bargaining experiments, but incorporate changes to include a three-dimensional issue space. This extension broadens the policy relevance of the model to more closely mimic real world international negotiating scenarios that increasingly incorporate numerous policy issues under one negotiation heading.

We find that the experimental results lead to reductions in the policy instruments that are consistent with the results from the simulations. Likewise the coalition choices that were developed in the experimental sessions closely mimicked those from the simulations. Finally we found that the choices on "minimum threshold" were quite important to the level of payoffs that a player may achieve. We then contended that our alternate approach from Redmond (2003), using the sector-specific scenario would more closely mimic the dynamics of the Uruguay Round. This is analogous to the findings of Rutstrom and Redmond (1997) in a study of EU Common Agricultural Policy reform.

As we use the same calibration technique for our experimental analysis as we did for the simulations, and the primary focus of this study was on testing the model, our policy reductions are skewed to higher levels of reduction. Therefore we propose an extension to these experiments that will consider the effect of political rent-seekers with different political influence weights given to sectors within each negotiating entity. While these sub-game players strive to maximize the returns to their sector, they have the dual objective of placating the other player of the same player type. We hope that this type of an approach will contribute to the political preference, as well as the bargaining literatures.

We also plan to revise the computer code for another series of experiments to allow the players to interactively change their decisions from day to day, within a period. This is obviously different from our current requirement that one enters a complete strategy at the beginning of the period. It will be interesting to compare the results from the new environment with those from the current model.

There is increased relevance to this study, as the WTO at the 2001 Doha Ministerial Conference, set an agenda for a new set of negotiations on agriculture with a proposed date of completion set at January 2005. However there have again been stalemates, most notably early 2003 in Cancun. U.S. State Department official Charles Ries (2003) commenting on these failures remarked, "The trade negotiation environment today is far more complex than in the past. There are more actors that have to be accommodated and more issues on the table." It is therefore logical to further develop a bargaining institution with which these realities could be examined. This area yields a research agenda that is topical and relevant to numerous realistic, collective decision-making areas.

TABLE 1: FINAL (5TH) ROUND OF THE MB GAME, PLAYERS HAVE EQUAL
"POWER"

Coa     ES       PS       IT       CG      US
#5    77.294   68.581   84.037   0.919    0.158
#5    74.327   69.481   86.981   0.913    0.160
#2    73.270   70.124   85.038   0.905    0.158
#2    72.114   72.529   86.215   0.903    0.158
#3    75.348   73.167   85.331   0.916    0.158

expected payoff          0.911   0.158    0.415

Coa    JPN     EU     GATT

#5    0.415   0.908   2.400 - CG
#5    0.415   0.912   2.400 - US
#2    0.416   0.921   2.400 - JPN
#2    0.415   0.924   2.400 - EU
#3    0.413   0.917   2.404 - GATT

expected payoff   0.916   2.401

Where:

Coa = the coalition # ... See Table 3

ES = Export subsidy % reduction       (Policy 1) *

PS = Production subsidy % reduction   (Policy 2)

IT = Import tariff % reduction        (Policy 3)

GATT = the GATT/WTO Secretariat       (Player A)

CG = the Cairns Group                 (Player B)

US = the United States                (Player C)

JPN = Japan                           (Player D)

EU = the European Union               (Player E)

* The designations from the experiments are in parentheses

TABLE 2: EXPERIMENTAL DESIGN--PARAMETERS IN THE EXPERIMENTAL
SESSIONS

Player Type   # of Players    Ideal Point    Intercept   Coefficient

     A *           3         (100,100,100)        0           1
     B             3           (94,73,94)        1018         5
     C             3           (78,68,98)         172         1
     D             3           (28,43,45)         483         1
     E             3           (58,78,72)        1006         4

Table 3: Winning Coalitions

Coalition #   A   B   C   D   E

1             1   0   1   1   1
2             1   1   0   1   1
3             1   1   1   0   1
4             1   1   1   1   0

* A "1" denotes the inclusion in the coalition

TABLE 4--FINAL ROUND PROPOSALS

             Player   N    Mean    StDev   SE     Min.   Max   Model
             Type                          Mean                Predic-
                                                               tion

             B        45   76.56   18.07   2.69   22     100
Policy 1     C        45   73.40   5.59    0.83   58     80
             D        45   55.33   15.07   2.25   25     90
Export       E        45   62.82   17.64   2.63   29     100
Subsidies    ALL           67.03                               74.47

             B        45   73.69   15.68   2.34   44     100
Policy 2     C        45   68.09   5.48    0.82   58     80
             D        45   59.64   13.32   1.99   31     89
Production   E        45   71.04   14.39   2.14   34     99
Subsidies    ALL           68.11                               70.78

             B        45   80.82   13.10   1.95   53     100
Policy 3     C        45   87.80   6.34    0.95   75     100
             D        45   69.22   15.32   2.28   45     94
Import       E        45   73.31   14.31   2.13   50     100
Tariffs      ALL           77.79                               85.52

TABLE 5: COALITION CHOICES

              Session

       1         2        3      Player    Predicted

      1.00     1.00      1.00      A        [check]
      1.00     1.00      1.00      B        [check]
B     0.65     0.62      0.66      C        [check]
      0.47     0.41      0.39      D
      0.88     0.96      0.96      E        [check]
      1.00     1.00      1.00      A        [check]
      1.00     1.00      1.00      B        [check]
C     0.65     0.62      0.66      C        [check]
      0.47     0.41      0.39      D
      0.88     0.96      0.96      E        [check]
      1.00     1.00      1.00      A        [check]
      1.00     1.00      1.00      B
D     0.65     0.62      0.66      C        [check]
      0.47     0.41      0.39      D        [check]
      0.88     0.96      0.96      E        [check]
      1.00     1.00      1.00      A        [check]
      1.00     1.00      1.00      B
E     0.65     0.62      0.66      C        [check]
      0.47     0.41      0.39      D        [check]
      0.88     0.96      0.96      E        [check]

TABLE 6: STRATEGY PROFILES

Coalition

* Strategy [C.sup.0]: select any coalition that includes me
* Strategy [C.sup.1]: select any of the coalitions of smallest size
  that includes me, ensuring that the coalition still constitutes a
  winning coalition
* Strategy [C.sup.*]: select one of the optimal coalitions

Policy Alternative

* Strategy [P.sup.0]: select any values from the message space that
  just includes the ideal points of all players
* Strategy [P.sup.1]: select any values from the convex hull of the
  ideal points of all of the players
* Strategy [P.sup.2]: select any values from within the convex hull
  of the ideal points of the players in the proposed coalition
* Strategy [P.sup.*]: select the optimal values for the proposed
  coalition.

Minimum Threshold

* Strategy [M.sup.*]: select the payoff to me that is associated with
  any policies taken from the rectangle that just includes the ideal
  points of all of the agents
* Strategy [M.sup.1]: select the payoff value to me of any policies
  taken from the convex hull of the ideal points of the players in the
  proposed coalition
* Strategy [M.sup.*] select the optimal value

TABLE 7: STRATEGIES

Definition    Strategy

ZI            C (O),P (O),M (O)
W1            C (O),P (O),M (A)
W2            C (O),P (A),M (O)
W3            C (A),P (O),M (O)
X1            C *,P *,M (O)
X2            C *,P (O),M *
X3            C (O),P *,M *
Y1            C *,P *,M (A)
Y2            C *,P (A),M *
Y3            C (A),P *,M *
FI            C *,P *,M *

Where:

O = Minimally Rational (ZI) Choice

A = Actual Choice

* = Fully Rational (Fl) Choice

C,P,M are coalition, policy, & minimum
threshold choices, respectively.

TABLE 8: EFFICIENCY INDICES

[FULL [right arrow] ZERO]

Period    FI     [X.sub.1]    [X.sub.2]    [X.sub.3]

1         69        219          87           83
2         66        203          85           80
3         68        182          85           81
4         74        208          94           89
5         75        257          95           91
Mean      70        214          89           85

TABLE 9: EFFICIENCY INDICES

[FULL [right arrow] ACTUAL]

Period    FI     [Y.sub.1]    [Y.sub.2]    [Y.sub.3]

1         69        106          89           83
2         66         90          82           80
3         68         90          81           81
4         74        102          89           89
5         75        106          91           91
Mean      70         99          86           85

TABLE 10: EFFICIENCY INDICES

[ZERO [right arrow] ACTUAL]

Period     ZI     [W.sub.1]    [W.sub.2]    [W.sub.3]

1         325       382           205          287
2         297       157           169          251
3         266       137           150          248
4         355       189           197          300
5         400       201           211          309
Mean      328       213 *         186          279

ACKNOWLEDGEMENTS

I would like to thank E. Elisabet Rutstrom and Glenn Harrison for many helpful comments.

REFERENCES

Adams, G., Rausser, G., and Simon, L., "Modelling Multilateral Negotiations: An Application to California Water Policy", Journal of Economic Behaviour and Orqanisation, Vol. 30, 1996, 97-111.

Davis, Douglas D. and Holt, Charles A., "Chapter 5: Bargaining and Auctions," Experimental Economics, Princeton University Press, Princeton, 1993, 241-316.

Harrison, Glenn W., "Theory and Misbehavior of First Price Auctions," American Economic Review, Vol. 79, 1989, 749-762.

Harrison, Glenn W. and, McCabe Kevin A., "Testing Non-Cooperative Bargaining Theory in Experiments," Economics Working Paper B-91-02, Department of Economics, Moore School of Business, University of South Carolina, 1991.

Harrison, Glenn W.; Rutherford, Thomas F.; and Tarr, David G., "Quantifying the Uruguay Round," The Economic Journal, Vol. 107 (444), 1997, 1405-1430.

Pinto, Ligia M., and Harrison, Glenn W., "Multilateral Negotiations Over Climate Change Policy", Journal of Policy Modeling, Vol. 25 (9), 2003, 911-930.

Rausser, Gordon C. and Simon, Leo K., "A Non-Cooperative Model of Collective Decision Making: A Multilateral Bargaining Approach", Working Paper No. 618, Department of Agricultural and Resource Economics, University of California at Berkeley, 1991.

Redmond, Willie J., "A Quantification of Policy Reform: An Application to the Uruguay Round Negotiations on Agriculture", Journal of Policy Modeling, Vol. 25 (9), 2003, 893-910.

Redmond, Willie J., "Multilateral Bargaining: An Application to the Uruguay Round Negotiations on Agriculture," Under Review, 2004.

Ries, Charles, "Speech at the Baltic Development Forum Summit", October 2003; U.S. Department of State, Bureau of International Information Programs, http://www, useu.be/Cateqories/WTO/Oct0703RiesUSEUTrade.html#text

Rutstrom, E. Elisabet and Redmond, Willie J., "A Quantification of Lobbying Benefits with an Application to the Common Agricultural Policy," Journal of Policy Modeling, Vol. 19 (6), 1997, 635-660.

Thoyer, Sophie; Moradet, Sylvie; Rio, Patrick; Simon, Leo; Goodhue, Rachel; and Rausser, Gordon, "A Bargaining Model to Simulate Negotiations between Water Users," Journal of Artificial Societies and Social Simulation, Vol. 4 (2), 2001, http://www.soc.surrey.ac.uk/ JASSS/4/2/6.html

Author Profile

Dr. Willie Redmond earned his Ph.D. at the University of South Carolina in 1999. Currently he is an Assistant Professor of Economics at Southeast Missouri State University in Cape Girardeau, Missouri.