This two-day Short Course on Game-theoretic Modeling: Techniques and Applications is organized by Michael A. Jones, Montclair State University, and will take place on Tuesday and Wednesday, July 29 and 30 in Madison, WI, as a prelude to MathFest 2008.

 

Anytime one person’s decision can affect another person, that situation can be modeled by game theory. This cocktail party description hints at how game theory can be considered a collection of tools and techniques for modeling diverse applications. The object of this short course is to study both the mathematical techniques and the range of applications they model. Techniques will include simultaneous and sequential move games under different information assumptions, cooperative games, mechanism design, theory of moves – a dynamic extension of game theory – and a qualitative approach to evolutionary game theory. Applications will be drawn from biology, economics, environmental science, literature, political science, and popular culture.

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9:15am – 10:30am

Why was Nash awarded the Nobel Prize in Economics? I will discuss how Nash’s solution concept generalizes both optimization (from decision theory) and Von Neumann’s Minimax Theorem (for zero-sum games). Decision theory (or games in which players have identical preferences) and zero-sum games (or games in which players have opposite preferences) form the two endpoints of the spectrum of two-player, simultaneous move games.  Nash’s equilibrium allows the games in this spectrum, as well as others, to be analyzed. I will conclude with an overview of the short course to demonstrate how game theory has evolved from these historic roots.

 

10:30am – 11:00am
Break

 

11:00am – 12:15pm

Besides sharing an adjective, what do game shows have to do with game theory? I will introduce concepts and well-known games (e.g., the Prisoner’s Dilemma) from non-cooperative game theory by using actual games from television game shows including the Price is Right and Friend or Foe, among other sources. Optimal behavior for these games will demonstrate different solution concepts for both simultaneous and sequential move games.

 

 

12:15pm – 2:15pm
Lunch

2:15pm – 3:30pm

I will highlight the difference between Nash and subgame-perfect equilibria for games in which players move sequentially and explain how subgame-perfect equilibria use a stronger criterion of rationality to refine Nash equilibria to a more compelling (or demanding) solution. I will extend subgame-perfect equilibria to games of imperfect information and incomplete information. Applications will include models of deterrence and truels (3-person duels).

 

3:30pm – 4:00pm
Break

 

4:00pm – 5:15pm

Cooperative game theory models situations in which players form coalitions whose value is greater than the sum of their parts.  In this talk, I will discuss several well-known methods, including the core and Shapley value, which assign players values based on the coalitions that they can join. Applications include sharing the cost of building an airport runway and cleaning up a polluted river, as well as determining power in voting games. I will discuss recent extensions of these ideas to multi-choice and fuzzy games.

 

 

5:15pm – 6:45pm
Reception

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9:00am – 10:15am
Game Theory and Auctions
Robert J. Weber, The Kellogg School of Management at Northwestern University
Sealed bid, ascending price, descending clock, and other types of auctions are used in various economic settings. Why? If one format were better for sellers than the others, wouldn’t it be the only one in common use? In order to compare alternative auction procedures from the perspective of a seller’s revenues, we need to begin by considering how bidders will bid. Assuming that the bidder’s strategies constitute an equilibrium point of the auction “game,” we’ll compare a seller’s expected revenue across auction formats. Indeed, using the “revelation principle” (central to the work cited by the most recent Nobel Prize in Economics), we’ll be able to draw conclusions about auction procedures that no one has yet invented!
 
References:

1.    Milgrom, Paul R. and Weber, Robert J. (1982) “A Theory of Auctions and Competitive Bidding,” Econometrica 50(5):1089-1122.
2.    Klemperer.Paul (ed.), The Economic Theory of Auctions, Edward Elgar, Cheltenham, UK, 2000.
3.    Krishna, Vijay, Auction Theory, Academic Press, San Diego, 2002.

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10:45am – 12:00pm

Game Theory and Emotions
Steven J. Brams, New York University
Emotions such as anger, jealousy, and love would seem to be spontaneous feelings that overtake us suddenly and hence not the product of careful means-ends analysis that we normally associate with rational choice.  On the contrary, I argue that the passionate pursuit of certain ends may be eminently rational in expressing strong commitment, extreme frustration, and the like, which in turn affect the responses of others in gamelike situations.  I will use "theory of moves," a dynamic extension of game theory, to illustrate this thesis, focusing on frustration and its most common manifestation in anger.  My principal sources will be literary, from the Bible to Shakespeare to such modern authors as William Faulkner and Joseph Heller.

1. Brams, S.J. Biblical Games: Game Theory and the Hebrew Bible. MIT Press, 1980, 2003.
2. Brams, S.J. Theory of Moves. Cambridge University Press, 1994.

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2:00pm – 3:15pm

Donald G. Saari, University of California Irvine
Evolutionary game theory has proved to be popular in explaining different social and biological behavior.  Unfortunately the approach is too difficult for most to use and it is very difficult to accept the "behavioral dynamics."  A new, easily understood approach is introduced to avoid these problems.

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3:45pm – 5:00pm

Not only has game theory been successfully taught in economics and political science departments, game theory has been an integral part of non-major, general education math courses and has been a popular, yet infrequent math major elective. We will discuss how game theory can also be introduced in math major courses like calculus, combinatorics, probability, and differential equations. Further, we will discuss areas of open research that would be suitable for faculty and for faculty/student collaborations.

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