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Evolutionary Stability in the Traveler's Dilemma

Award: George Pólya

Year of Award: 2010

Publication Information: College Mathematics Journal, vol. 40, no. 1, January 2009, pp. 33-38

Summary: This paper begins with a brief survey of three game-theoretic tools -- dominated and undominated strategies, Nash equilibrium, and the more familiar Prisoner's Dilemma -- using each of them to explain why the counterintuitive strategy of claiming only two dollars is actually the rational option. Human subjects normally do not take this rational option, but their "irrationality" is usually rewarded with higher payoffs. The rest of this paper uses evolutionary game theory to help reconcile the dichotomy between how people should play this game and how they actually do play it.

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About the Author: (From Prizes and Awards, MathFest 2010) Andrew T. Barker is a postdoctoral researcher at Louisiana State University, where he works under Susanne Brenner. He received his Ph.D. in Applied Mathematics from the University of Colorado at Boulder in 2009, doing his dissertation under Xiao-Chuan Cai. He has research interests are in the areas of numerical analysis, finite element methods, domain decomposition methods, pre-conditioning, high-performance computing, and game theory. Outside of work he enjoys playing the piano, hiking, cycling, and reading. He lives in Baton Rouge with his wife Katie, where they drink lots of coffee and eat too much unhealthy Cajun food.

MSC Codes: 
91-XX
Author(s): 
Andrew Barker (University of Colorado)
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Publication Date: 
Saturday, August 14, 2010
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Summary: 

This paper begins with a brief survey of three game-theoretic tools -- dominated and undominated strategies, Nash equilibrium, and the more familiar Prisoner’s Dilemma -- using each of them to explain why the counterintuitive strategy of claiming only two dollars is actually the rational option. Human subjects normally do not take this rational option, but their "irrationality" is usually rewarded with higher payoffs. The rest of this paper uses evolutionary game theory to help reconcile the dichotomy between how people should play this game and how they actually do play it.

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