Game-Theoretic Methods in General Equilibrium Analysis.

This volume contains seventeen articles (together with one introduction chapter and one addendum) written by a bona fide group of distinguished game-theorists whose names frequently appeared in leading "dry" journals such as Econometrica, Journal of Economic Theory, Review of Economic Studies, Journal of Mathematical Economics, International Journal of Game Theory, and Economic Theory. Given such an impressive list of contributors (among whom many are serving on the editorial boards of the aforementioned journals), the quality of papers is uniformly high, which might explain why the editorial introduction written by Mertens takes only three pages. This book presents a systematic (and obviously axiomatic!) exposition of the use of game-theoretic methods in general equilibrium analysis. Three quarters of the themes are confined to cooperative games; the use of non-cooperative approach is spread over topics including Shapley-Shubik mechanism, Cournot-Nash equilibrium, Bertrand-Edgeworth equilibrium, correlated equilibrium, communication equilibrium, and sunspot equilibrium. It mainly brings readers to the forefront of research fields from which most of us have shied away ever since we were pursuing doctoral degrees in economics.

Most articles are based on advanced lecture notes taken by students and consequently revised by authors presenting them during a workshop held at Long Island for a two-week period in 1991. They are technical survey papers (not published elsewhere) and rigorously written for those who are no strangers to concepts like Lebesgue measure and sigma-algebra. Since it is impossible, in light of the elegant link set forth by Mertens, to discuss all articles at equal length, I will simply follow my biased taste to report some comparisons made with two seemingly close substitutes on the market without getting into the technicality.

First, I am comparing this volume to Frontiers of Game Theory (edited by Ken Binmore, Alan Kirman and Piero Tani, MIT Press, 1993). Luckily enough topics in both volumes do not overlap. (Incidentally, if no chapter in either volume interests you, then you most likely will not find the game-theoretic approach interesting at all.) One common feature is that readers of both volumes might have to dig deep just to find out that the former is the proceedings of the NATO Advanced Study Institute on Game-Theoretic Methods in General Equilibrium Analysis, while the latter was produced by a game theory workshop at Florence. Reading might be more enjoyable should this volume contain the reference and index sections. Some have argued that the notion of players is not quite clear in Frontiers of Game Theory; in this volume a clarifying entry addressing notions of "general" equilibrium, equilibrium, and various solution concepts, if added, might be quite desirable. For instance, as Mertens emphasized, both core and bargaining set describe cooperative arrangements that are ex-post stable, yet the Shapley value characterizes what can be expected ex-ante. Why must we treat the Shapley value as a solution concept?

It is good to know that two volumes of Handbook of Game Theory (edited by Robert Aumann and Sergiu Hart, 1992 and 1994) also have not much overlap with this book. The bad news is that topics such as noncooperative games with many players, Shapley value, values of large games, values of non-transferable utility functions, and values of perfectly competitive economies have been planned for the forthcoming volume three. Generally speaking, authors in the two volumes of the Handbook are unfortunately left with little room for furnishing rigorous proof, while this is not the case in this book. Nevertheless, I will recommend Myerson's chapter 24 in the Handbook (vol. 2) to readers who have problems with reading the chapter on correlated and communication equilibria in this volume.

For the benefits of readers of this journal, I highly recommend: chapter 1 on general equilibrium and core equivalence (by Allen and Sorin), chapter 2 on core convergence (by Anderson), chapter 5 on Shapley value (by Aumann), chapter 8 on Harsanyi value (by Hart), chapter 10 illustrating economic applications of the Shapley value (by Aumann), and Peck's chapter 16 dealing with correlated equilibrium and sunspot equilibrium. Those who enjoyed reading Debreu's 1959 classic piece, Theory of Value, will delightfully go through the first-half of chapter one for sure. Chapter two reserves the excellent writing style of Robert Anderson who, among the few others, thoughtfully makes some cross references to other chapters in this volume. Aumann's two chapters are extremely clear and well organized. Chapter 14 is a plus for readers who are interested in the theory of industrial organization and familiar with the Novshek-Sonnenschein framework. The long chapter by Wooders has everything in it - concepts, model-building, and examples. Editors did a splendid job in sorting out these papers into four parts: core and bargaining set, value, cooperative approach to large games/markets, as well as non-cooperative approach. To justify my longing for a reference section (for the entire volume), the "Chap. I.B.4" cited by Mertens in chapter three was meant to be section 2.4 in chapter one.

If a potential buyer has a strong feeling about an intriguing and entertaining paper entitled "Axiomatics in Economics" written by Robert Clower published in the October 1995 issue of this journal, then he/she might rather keep $117 and wait for the arrival of the volume 3 of the Handbook of Game Theory. Someone who reads this volume with extra care will find it inspiring, informative, and living up to the reputations of contributors.

Jong-Shin Wei Feng Chia University, Taiwan