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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



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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


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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.


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