Cooperative Microeconomics: A Game-Theoretic Introduction.
Princeton, NJ: Princeton University Press, 1995. Pp. ix, 454. $49.50.
The one and only normative notion explicitly retained in new welfare economics analysis is that expressed by the Pareto efficiency criterion. In that literature, statements abound of the sort that the economist should only tell people how to approach Pareto efficiency while unspecified others should select from the wide range of Pareto efficient allocations. We may wish to note that the very point of departure of this argument is an explicit value judgment. Normative judgments are unavoidable in economics as we know it.
The proponents of this strategy succeeded in introducing a healthy injection of rigor into welfare economics. The cost has been an impoverishment of welfare economics discourse, a development that should not be congenial to anyone who claims to be an intellectual descendant of Adam Smith, who, we remember, wrote The Theory of Moral Sentiments before The Wealth of Nations.
A problem with the avoidance of explicitly normative analysis becomes apparent when reading applied microeconomics papers. Often in that literature, specific normative principles are simplistically employed in evaluating the effects of the various policies analyzed, and the main reason for the use of such principles seems to be analytical tractability. A good example is the common practice of adding up consumer and producer surplus and using this sum as a social welfare function. This practice is hardly ever accompanied by a consideration of alternative social welfare functions or even of the implicit normative axioms that could be shown to justify it.
This is not an attack on rigor or practicality in applied economics; quite the opposite. I am firmly convinced that mathematically expressed rigorous analysis is a gift of the highest order to the economist. I also believe that it can be made to produce deep insights when dealing with issues of justice and cooperation, insights that mainstream textbooks often relegate to a few short chapter sections (some books are better than others in this respect, most notably Mas-Colell, Whinston, and Green ). The publication of Herve Moulin's Cooperative Microeconomics by Princeton University Press came as very welcome news to me, given my concerns expressed above, and I propose to convince you to share my view in the rest of this review. Moulin has written a number of books, including another one on these issues (Moulin 1988), but Cooperative Microeconomics is explicitly written as a graduate microeconomics textbook, for the first time filling this niche with a book centered on welfare economics.
Moulin takes a broad view of cooperation between selfish economic agents. He organizes the book around three modes of cooperation: (i) cooperation by direct agreements, (ii) cooperation in the justice mode, and (iii) cooperation in the decentralized mode.
The direct agreements mode is closely connected to the core. All institutional detail is endogenous in this mode, created by agreements that belong to the core. Since the core is often empty in interesting economic situations and large in other interesting situations, this discussion cannot exhaust the topic. Also, limiting our attention to the zero transaction cost story that underlies the core concept is clearly quite restrictive. (This issue is not addressed in most of the literature on welfare economics. It seems to me that we should come to terms with it [see Gilles, Diamantaras, and Ruys 1996], but I shall not criticize this book for not covering what it did not set out to cover.)
The justice mode corresponds to social contract theories of justice. Society chooses a mechanism to divide the surplus that emerges from cooperation. The choice of mechanism is morally deliberate; ethically compelling axiomatic properties of it are essential to the discussion. In this view, policy making simplifies to choosing from a menu which mechanism to put in place. Once society has chosen the most appealing collection of axioms that are known to characterize a mechanism, then the mechanism is institutionally fleshed out and allowed to run. This mode also has limitations. The axiomatic characterizations underlying it obtain for mathematically tractable domains of possible economies, and one must assume a lot to conclude that their domains include the actual economy around us. Moreover, it is typically necessary to use privately held information in the operation of the mechanism, and this opens the mechanism up to strategic manipulation by agents.
The decentralized mode is designed to respond to the latter criticism. It envisions a framework where some personification of collective authority is the referee of a game of strategy in which agents engage in noncooperative game-theoretic behavior. The equilibrium outcomes of such a game are guaranteed to be immune to selfish behavior of the type corresponding to the specific game-theoretic solution used, and so they provide another menu of mechanisms from which society may choose.
Ideally, we would like to design mechanisms that work well in all three modes. A large part of the message of the book elaborates on a negative answer to this question: Unfortunately, such a mechanism design dream is utopian. Instead of giving up, however, a superior response is to explore the frontiers of what is possible, and this book excels in the exposition of this issue. The author does this in seven chapters.
Chapter 1 elaborates on the meaning of the three modes of cooperation. It provides connections to political theory and philosophy and discusses the connection with standard treatments of welfare economics, stressing the fact that efficiency and equity issues are inseparable. At the same time, the author reassures us that he is not after a grand theory of welfare economics; he dispenses with "utopian social engineering" by citing Popper's celebrated discussion of it (Popper 1966) and the failures of utilitarianism and the Nash program to become the panaceas they were intended to be. The discussion quickly turns to a presentation of examples in order to illustrate the issues involved. The creative and widespread use of examples to illuminate abstract concepts is one of the best features of this book, one that other textbook authors have not brought to such a high degree of effectiveness yet.
In Chapter 2, Moulin presents an extended analysis of the core and competitive equilibrium in a variety of models with one good and money. By money I mean a good that enters linearly in consumers' utility functions (which are then representing quasi-linear preferences), in other words, a carrier for transferable utility. Models with only one good in addition to the money good may sound a little too restrictive, but this chapter dispels this notion by presenting in detail illuminating analyses of the Bohm-Bawerk horse market model (where the good is indivisible and each agent wants at most one unit), an oligopoly model with binary demands, a discussion of existence of competitive equilibrium, an extended discussion of the implications of decreasing marginal costs for efficiency and the core, the possibility of an empty core with nonconvex preferences, and (briefly) some trading games in the Bohm-Bawerk market.
Chapter 3 returns to the core and competitive equilibrium, this time with many goods. This chapter is quite different from the long disquisition on the technicalities of core convergence results one might expect. These get an appropriate nod in section 7 of the chapter, where Edgeworth's most famous idea receives its customary geometric treatment. Other sections cover the Shapley-Scarf model of trading of indivisible objects, matching models with and without utility money and the assignment model, the existence and efficiency of competitive equilibria in Arrow-Debreu-McKenzie economies, and Hurwicz's demonstration that Pareto efficiency and voluntary participation are incompatible with strategy-proofness. An appendix provides some proofs in detail. I would have liked more attention to the Hurwicz-related results, but Moulin has already given us more extensive expositions of these in previous books, and some tradeoffs always have to be made to save space.
An even more ground-breaking part of the book commences with Chapter 4. Here Moulin devotes considerable attention to the implications of the normative principle of no envy, which states that no individual should rather have someone else's bundle of commodities. First, Moulin situates this notion in the wider discourse about justice in economic allocation. Then he contrasts it to its main competitor, the stand alone principle, which he covers more extensively in Chapter 5. When discussing the fair division of a jointly owned endowment vector, the stand-alone principle demands that no individual end up doing better than if he or she alone were consuming the entire vector. This may sound mild (besides obviously compelling), but it can be downright incompatible with no envy, which produces morally questionable recommendations in situations with jointly owned production with decreasing marginal costs. In the rest of the chapter, Moulin discusses the application of the no envy principle to assignment economies, its close relation to competitive equilibria from equal incomes, and the alternative principle of egalitarian equivalence. He ends the chapter with discussions of the resource monotonicity axiom (if an economy acquires more resources, nobody should become worse off) and a discussion of games of the divide-and-choose variety, which are intended to result in envy-free allocations.
Chapter 5 studies the stand-alone principle on a wide variety of economic domains, such as one-input, one-output production with increasing or decreasing marginal costs and economies with public goods. For the latter, Moulin devotes sections to the stand-alone core, ratio equilibrium (first proposed by Kaneko), and the egalitarian equivalent solutions proposed by Moulin. The chapter ends with a section on public bads and other externalities and the usual long and stimulating exercise section. One of the most welcome aspects of this chapter is that it covers some issues of public economic theory that have so far been almost invisible to graduate textbooks, even those covering public finance.
In Chapter 6, Moulin shifts gears and presents a number of specific resource allocation mechanisms that operate on domains with externalities and/or public goods or bads: voting games to select levels of public goods or bads, voluntary contributions towards a public good, exploitation of a commons by means of three different mechanisms. The last of these mechanisms is the serial mechanism that Moulin has developed in collaboration with Scott Shenker. These mechanisms reach equilibrium outcomes that are not efficient but that may be considered second-best outcomes. Their strategic properties depend heavily on the presence of convexity of preferences and technology (and are undesirable in the absence of convexity). It also turns out that the stand-alone and no envy concepts play a major role in the discussion of the equilibria of these mechanisms.
Chapter 7, the last chapter of the book, provides a survey of the mathematical properties of the core and Shapley value in cooperative games in characteristic function form. This chapter is shorter and different in orientation than the previous ones, giving more attention to general mathematical results and less to examples. It is useful as a guide to how the analyses in the previous chapters relate to the more traditional (and voluminous) work on cooperative game theory.
I highly recommend the book as a complement to the main textbook used in first-year, second-semester graduate courses in microeconomics. I also feel it has a place on the shelves of every economist who does welfare economics in some form. There is no other source with such a lengthy treatment of models with indivisibilities and which gives such thoughtful consideration to issues of economic justice. Also, as I have noted above, Moulin uses exercises masterfully, and he consistently uses the simplest possible model that can illuminate an issue. He does not present competitive equilibrium as the be-all and end-all of economic analysis (which is the only way to obtain a true perspective of the real importance of competitive equilibrium in such analysis even when we don't postulate this importance a priori). There is only one reason that keeps me from making this book the main text in a graduate microeconomics course and that is the lack of coverage of the traditional topics of consumer theory, production theory, and noncooperative game theory and its applications to models with adverse selection and moral hazard. A new edition, incorporating a treatment of these issues of the same caliber as the issues already covered, could be a clear winner in the textbook game.
Gilles, Robert P., Dimitrios Diamantaras, and Pieter H. M. Ruys. 1996. Valuation, efficiency and cores in economies with costly trade. Working Paper No. 96-01, Virginia Polytechnic Institute.
Mas-Colell, Andreu, Michael D. Whinston, and Jerry R. Green. 1995. Microeconomic theory. New York: Oxford University Press.
Moulin, Herve. 1988. Axioms of cooperative decision making. Econometric Society Monograph 15. Cambridge, UK; New York: Cambridge University Press.
Popper, Karl R. 1966. The open society and its enemies. 5th edition, volume 1. Princeton, NJ: Princeton University Press.
Dimitrios Diamantaras Temple University