Recent Developments in Game Theory.
In the preface to this book the authors write "There has been an enormous amount of interest . . . in the analysis of strategic behaviour . . . reflected in . . . articles . . . in specialist journals. It was therefore felt that a collection of special surveys of recent developments in a variety of areas of game theory would be useful not only to specialists and graduate students, but to non-specialists . . ." On the whole, the book is of high quality and is quite current in coverage; however, in terms of the goals quoted above, it is much more successful on the level of the specialist than the non-specialist. Chapter 1 by Larry Samuelson explains the basics of normal (strategic) form and extensive form games. Then it explains and motivates subgame perfect equilibrium, perfect equilibrium, and sequential equilibrium. Other refinements are briefly mentioned. The nature and role of rationality is intelligently discussed, as is the dispute over whether the normal or extensive form is to be preferred. Finally, evolutionary games are briefly mentioned to explain their role within game theory. Chapter 2 by Robert Marks mainly reviews the work on repeated games that is done using automata theory. Moore machines, the most popular form of automaton used in the game theory literature, are explained. Repeated game results in the conventional full rationality context are reviewed and then many finite automaton results relating to repeated games are sketched. Chapter 3 by George Mailath provides a very good review of signalling games, starting from the basics and then focusing mainly on the refinements of Nash equilibrium that have been used in the signalling literature to select a unique equilibrium. In Chapter 4 Jurgen Eichberger first notes that Nash equilibrium can be regarded as the result of an agreement, reached during pre-play negotiation by the players, or that Nash equilibrium can be the result of each player putting herself in the position of the other players and figuring out what is rational for them to do. Regarding the latter, he notes that this sort of introspection is insufficient to bring about equilibrium play when equilibrium is not unique. He then discusses games in which players will play repeatedly, giving them a chance to learn about the behavior to expect from other players. Various approaches to show how such games can converge on Nash equilibria are explained. Then the tracing procedure of Harsanyi and Selten is briefly described as a means to find a unique equilibrium and evolutionary game theory as another selection mechanism is mentioned. Chapter 5 by Presont McAfee and John McMillan exposits principal-agent problems in which the agent has private information and the principal acts first. Two particular problems are examined. The first is when the principal will be selling to one of several agents and must decide on the way to conduct the process. The second is when the principal will be hiring one agent and must design a contract to offer. Chapter 6 by Jeff Borland takes up the second of the McAfee and McMillan topics, a principal hiring a single agent, and looks at generalizations with multiple agents. Chapter 7 briefly describes Maynard Smith's ESS and then goes on to describe a variant game in which a mutant strategy can recognize when it is paired with itself and can behave differently to its clone than it does to another strategy. The last chapter, by Leonard Mirman, is concerned with endogenous learning in monopolistic and duopolistic markets. Four models are explored of which the first is a monopoly in which the firm does not know the parameters of its demand function and demand is subject to a random disturbance with a known distribution. The firm will be active for two periods and will, in the first period, choose an output level to both enhance its first period profit and provide information about its demand parameters. In the second model there are two firms with other details like the monopoly model. Each firm will know its own output and will observe the market price, but neither will observe the other's output. Each firm has an incentive to choose output in a way that reduces the usefulness of the price information for the rival firm. The third and fourth models are variations on the second. In all cases, the way the output decision is changed by the informational content of price and by the other structural details of the model is studied.Perhaps only Chapter 5 would be intelligible to a genuinely non-specialist reader; however, most of the chapters could be successfully used in a graduate survey course in which the students had a modest background in game theory and had seen a few modern applications of game theory previously. In the main, the papers are well written, correct, and sensible. Overall, the volume is quite worthwhile; however, judging by the handsome price for this book, the publisher seems to think that "specialists, graduate students, and non-specialists" refers either to librarians or millionaires.
James W. Friedman University of North Carolina at Chapel Hill
 Printer friendly
 Cite/link
 Email
 Feedback
| |
| Author: | Friedman, James W. |
|---|---|
| Publication: | Southern Economic Journal |
| Article Type: | Book Review |
| Date: | Jan 1, 1994 |
| Words: | 833 |
| Previous Article: | International Economic Sanctions. |
| Next Article: | The Experience of Free Banking. |
| Topics: | |