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Game Theory: 5 Questions Vincent F. Hendricks and Pelle G. Hansen, editors, Automatic Press, 2007, 233 + vi pp., index, ISBN 87-991013-4-3, US$ 26.00. Did you know that the bad weather in the English Channel is to some extend responsible for Ken Binmore being a game theorist? Or did you know that Ehud Kalai is not only a great game theorist but also a business consultant who finds game theoretic concepts useful for thinking about specific business projects? Moreover, if you don't agree with Robert Aumann' statement “I don't think that behavioral economics is going to last” (p. 5) then perhaps your prior is different from Aumann's prior. These sorts of things you can learn from the book. The editors present statements by nineteen prominent game theorists and users of game theory based on following five questions: 1. Why were you initially drawn to game theory? 2. What example(s) from your work (or the work of others) illustrates the use of game theory for foundational studies and/or applications? 3. What is the proper role of game theory in relation to other disciplines? 4. What do you consider the most neglected topics and/or contributions in late 20th century game theory? 5. What are the most important open problems in game theory and what are the prospects for progress? It is interesting to observe that the answers do not only convey autobiographical information (questions 1 and 2) and thoughts on the present state of game theory (questions 3 to 5) but also the different personalities of the contributors. Apart from a one-and-a-half-page preface, the editors refrain from any editorial introduction. I wished that such introduction would have answered the following three questions that came to my mind while reading the book: I. Why were those five questions selected and not others? For instance, questions 4 and 5 are rather closely related. Indeed, eight out of nineteen contributors somehow combined the answers to the two questions. Were these questions motivated by analogous books on mathematics, formal philosophy etc. edited by Hendricks and others? As expected, answers to questions 4 and 5 do not provide a ready-made list for PhD students seeking dissertation topics. As Rubinstein (p. 163) remarks, the term ‘open problem’ is perhaps not relevant for game theory. II. The editors do not give a motivation for their selection of the nineteen contributors. How about other prominent game theorists like Shapley, Selten, Myerson, Nash, Maschler, Samet, Fudenberg, Mertens, Sorin, Wilson etc.? Were they asked but declined to contribute? III. Why do the formats differ slightly between contributors? I.e., both Aumann and Hart were interviewed by one of the editors. Kreps replaced answers to questions 3 to 5 by a manuscript of a speech. Samuelson provided a very interesting and readable essay on game theory. All others stayed more or less in the 5 question format.1 An editorial synopsis of the rich information in the book would be tempting. It is interesting to note that five contributors mentioned the book by Luce and Raiffa (1957) as an important influence 1 The styles of references differ among contributors. Sometimes references are incomplete. (while four mentioned directly or indirectly von Neumann and Morgenstern, 1944) for why they were drawn to game theory. Table 1 provides a concise cross-author comparison of answers to the first question. Name, Age, Affiliation Why were you initially drawn to game theory? Aumann "a problem about defending a city from air attack." 77, The Hebrew University of Jerusalem van Benthem Luce and Raiffa (1957), Lorenzen's "Logische Propädeutik" 58, University of Amsterdam, Stanford University Bicchieri An interest in Bayesian decision theory when the outcome depends also on what University of Pennsylvania other people choose Binmore A lack of alternatives to reading von Neumann and Morgenstern (1944) while being 67, University College London trapped in a harbor in the English Channel due to bad weather, Nash's work on bargaining Brandenburger A lecture by Frank Hahn at Cambridge University New York University Camerer Colleagues at my first academic job at Northwestern University, Luce and Raiffa 47, California Institute of (1957), suitability for doing experiments Technology Grafen Admission interview at Oxford University, Richard Dawkins Oxford University Hammerstein John Maynard Smith and Reinhard Selten Humboldt Universität zu Berlin Hart "Aumann" 58, The Hebrew University of Jerusalem Kalai As a PhD student in the mathematics department at Cornell University in the 1960s 64, Northwestern University Kreps As a graduate student at Stanford University Stanford University Moulin As a student of mathematics interested in applications to the social sciences, von 57, Rice University Neumann's Minimax theorem, Schelling's "Strategic of Conflict", Owen's textbook on game theory Parikh The connection between "rational" and "logical", Aumann's "Agreeing to disagree", City University of New York thesis advice, logic of games Rubinstein Hebrew University of Jerusalem, ingenious name of the field, wanted to improve my 56, Tel Aviv University, New strategic skills, vague notion that mathematics has some connection to real life York University Samuelson "swept up by the strategic revolution in the 1980s", bargaining theory Yale University Schelling International negotiations in late 1940s and early 1950s, coordination of 86, University of Maryland expectations, Luce and Raiffa (1957), reciprocal fear of surprise attack Skyrms "Because it makes rational deliberation more interesting when deliberators University of California at interact." Irvine Sugden Hume's Treatise of Human Nature as well as work by Sen, Rawls, Harsanyi University of East Anglia Young Teaching a course on "Mathematics in the Social Sciences", legislative John Hopkins University, apportionment, strategic aspects of voting Oxford University Table 1 2 There seems to be some disagreement about the practical usefulness of game theory. Some contributors like Binmore, Kalai, Kreps, Samuelson, Schelling, and Young find game theory useful for solving practical problems, while Rubinstein appears to dismiss the practical use of game theory altogether. Perhaps a compromise would be to acknowledge that while game theory can not generate advice on how to play in a particular strategic situation in real life, game theoretic concepts might nevertheless be useful to think about and structure strategic situations in real life. In fact, this is probably how game theory is used more formally in sciences: As a useful modeling language. At least eight contributors agreed that game theory is a modeling language or a tool without necessarily having substantive content. Table 2 provides a more comprehensive yet brief synopsis of answers to the third question across authors. Name What is the proper role of game theory in relation to other disciplines? Aumann An umbrella, a unified field theory van Benthem Logic and game theory have similar academic roles Bicchieri Game theory is an autonomous discipline despite being used extensively in other fields. It gives us formal models of phenomena we study. Binmore Game theory is a tool without substantive content Brandenburger Game theory is used to explore, clarify, sharpen and communicate intuitive observations Camerer Game theory is a useful general common language for describing social interaction in many disciplines Grafen Game theory acts as a repository of ideas for other subjects, assists in transmitting ideas between different subjects, biology contributes to game theory and vice versa Hammerstein Game theory is a set of tools that need to be adjusted and perhaps added to in applications Hart "Game theory is universal.", "we game theorists learn from biologists", "Game theory provides the tool for analyzing interactive situations" in computer science, philosophy, social sciences in general etc. Kalai Analogous to probability theory and statistics (used in various fields), game theory offers a language and rules to deal with strategic interaction wherever it arises Kreps Game theory has proved to be a fairly flexible and yet precise modeling language. Moulin Game theory is a modeling tool box or language in all disciplines where it is used. It does not provide a ready-made template for a context-free analysis of a game. Parikh Example: Existential and universal quantifier in first order logic interpreted as moves by two players respectively Rubinstein Game theory provides a limited set of formal and conceptional tools to formulate and to clearly state problems involving strategic interaction Samuelson Normative: designing auctions, allocation of places in schools, access to railroad tracks, payload priority on space shuttles, allocation of airport take-off and landing slots, medical residents and kidneys; Positive: evolutionary stability useful to analyze behavior of spiders, game theory helps to explain examples in the Talmud, evolutionary explanations of share- cropping contracts among farmers, behavior in auctions; Analytical implications: game theory allows us to make precise and hence evaluate and revise our intuition about behavior; Conceptional: identify a few key ideas that recur as fundamental in a variety of interactions Schelling Game theory should inform economics, sociology, social psychology, law and anthropology, should be accepted as potentially descriptive, rationality requirements should be relaxed Skyrms A mathematical theory of evolution, rational and irrational interactive decisions Sugden Game theory depends on other disciplines for corroboration Young Invaded social sciences, now colonizing biology, computer science and philosophy; rationality plays a less prominent role for computer science and biology Table 2 At least four contributors felt that cooperative game theory is unjustly neglected. Another set of four contributors agreed that the connection between computer science and game theory is promising. Two contributors, Kalai and Samuelson, mentioned that game theory is challenged by how to 3 balance additional complexity against enhanced applicability. At least eight authors thought that game theory could benefit from more empirical content. What to make of all the answers? I think the following facts about game theory emerge throughout the book: Game theory is a ‘ripe’ field. In the past, much of its success derived from its applicability to various fields studying interaction such as economics, evolutionary biology, political science, philosophy, and computer science. As a mathematical theory it served those non-mathematical fields as a formal modeling language enabling a clear statement of (more or less) real-world problems and the transfer of solutions across those fields. The future of game theory is unclear. One can conjecture that it will depend on how it will embrace (further) computer science, neuroscience, logic, ideas of bounded rationality, and any fields in which interaction plays a role, and how it will cope with limits to its applicability posed by the increased modeling complexity.2 Altogether I believe the book is an important document on the history and the current state of game theory. I very much enjoyed reading it. References Luce, R. D., Raiffa, H., 1957. Games and Decisions. John Wiley, New York. von Neumann, J., Morgenstern, O., 1944. Theory of Games and Economic Behavior. Princeton University Press, Princeton. Burkhard C. Schipper3 Department of Economics University of California, Davis One Shields Avenue Davis, CA 95616 USA Phone: +1-530-752 6142 Email: bcschipper@ucdavis.edu 2 A synopsis of answers to all questions in form of a table with excerpts is provided under http://www.econ.ucdavis.edu/faculty/schipper/5questions.pdf 3 I thank Giacomo Bonanno and Roger Koppl for helpful comments. 4

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