MANAGERIAL AND DECISION ECONOMICS, VOL. 13, 369 (1992)

BOOK REVIEW

GAME THEORY: ANALYSIS OF CONFLICT, by Myerson, R. B., Cambridge: Harvard University Press.

Roger Myerson needs no introduction as a major con- tributor to recent developments in game theory. It is often a joy to see one of the leaders in a field write a text and this is no exception. The book elegantly summarizes the greater part of modern game theory and is almost self- contained. It will reward anyone who takes the effort to work through the book extensively.

Unfortunately, the book is not easily approachable for a novice in game theory or for a researcher wishing to learn about a particular topic. There is also too little discussion of the strengths and weaknesses of game theory--Myerson’s task here is to preach to the conver- ted. Thus, it may not be an ideal textbook to use in graduate courses for nonspecialists in economics or man- agement science. For intensive users of game theory, however, it will be a valuable and often-consulted re- source.

The problem for the student new to game theory is that the subject is treated as a nut to crack, not as an onion to peel. The reader learns all the tools and then the nut is cracked in an elegant, intellectually rigorous manner. Myerson does not start with the simple and build to the complex, but jumps head-first into general models. Once readers get completely through a topic, they will have learned quite a bit. But one must digest the whole topic just to learn the simpler ideas. While such a treatment has a certain logic and aesthetic, it may not be the best way to introduce difficult ideas to students. Less general notions can develop intuition for more general concepts. Two topics where the general approach imposes barriers are treating pure and mixed strategies in finite games to- gether, instead of first explaining Nash equilibria in pure strategies, and developing the subgame perfection refine- ment briefly as a sideline to sequential equilibrium.

This concern is only meant as a warning of what not to expect from a fine book. The text will serve well any student who has first learned the rudiments of game theory elsewhere. Fine points are developed nicely and the general level of rigor is appropriate for the serious student of game theory.

The book contains many topics not easily found else- where. A variety of normal forms-reduced, purely re- duced, multi-agent-are defined and their usefulness is illustrated in simple examples. The difficulty with iter- ative elimination of weakly dominated strategies is shown through a simple example. Sequential equilibrium has an excellent chapter all to itself. Given the importance of the concept in modern economic theory and its inherent difficulties, I must applaud the author for his success here in making it understandable. Co-operative game theory and recent developments in that field also receive con- siderable attention, in contrast to other recent books.

The past 15 years have seen an explosion of research in

refinements of nonco-operative equilibrium. Economists not familiar with the details of this research often only know some applications of these refinements. With so many concepts around, what is one to make of all of them? Is there a single best refinement, for example? This text explains why refinements are important and what one should search for in refinements. One criticism is that this literature may not be directed at serving applied game theorists. Myerson makes clear that existence is a desirable property for a refinement of Nash equilibrium. The commonly used refinements exist for all finite games. Refinements that do not satisfy this property, such as strictly perfect equilibrium (Okada, 198 I), have quickly fallen out offavor with game theorists and in applications of game theory. This emphasis on existence may be misplaced. Myerson gives a clue to this by delineating three types of solutions to games--exact, upper, and lower solutions. An upper solution to a game includes all outcomes we cannot rule out as a solution that might arise in some environment. A lower solution includes all outcomes that would be an accurate prediction of be- havior in some environment. The set of Nash equilibria is probably best thought of as an upper solution, although refinements are an attempt to work toward an exact solution. We now know that the search for a unique exact solution will be futile, as argued by Kohlberg and Mer- tens (1986). Another approach would be to consider refinements that are, instead, lower solutions. What would this gain? A lower solution need not always exist to be useful. But a refinement that existed in only a large subsgt of games could still serve as an excellent prediction of behavior for that class of games. In a sense, Myerson may instead be classifying these lower-solution refine- ments as selection devices. Selection devices, however, vary with the environment in which a game is played. My suggestion is to consider refinements, ideally based on decision-theoretic arguments, without necessarily re- quiring existence for all finite games.

In sum, this is an excellent book for those who know some game theory and wish to increase their understand- ing of recent developments. Advanced students of game theory will find it invaluable in expanding their horizons.

REFERENCES

E. Kohlberg and J.-F. Mertens (1986). On the strategic stability

A. Okada (1981). On the stability of perfect equilibrium points. of equilibria. Econornetrica 54, 1003-39.

lnternutional Journal of Game 7heory 10, 67-73.

JONATHAN HAMILTON Department of Economics, University of Florida,

Gainesville, FL, and Department of Economics, Duke University,

Durham. N C , U S A

0 1992 by John Wiley & Sons, Ltd.