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An Approach to Bounded Rationality

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Author Info

  • Eli Ben-Sasson
  • Adam Tauman Kalai
  • Ehud Kalai

Abstract

A central question in game theory and artificial intelligence is how a rational agent should behave in a complex environment, given that it cannot perform unbounded computations. We study strategic aspects of this question by formulating a simple model of a game with additional costs (computational or otherwise) for each strategy. First we connect this to zero-sum games, proving a counter-intuitive generalization of the classic min-max theorem to zero-sum games with the addition of strategy costs. We then show that potential games with strategy costs remain potential games. Both zero-sum and potential games with strategy costs maintain a very appealing property: simple learning dynamics converge to equilibrium.

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Bibliographic Info

Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1439.

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Date of creation: Nov 2006
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Handle: RePEc:nwu:cmsems:1439

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Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014
Phone: 847/491-3527
Fax: 847/491-2530
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Web page: http://www.kellogg.northwestern.edu/research/math/
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Keywords: bounded rationality; zero sum games; potential games; strategic complexity.;

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References

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  1. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
  2. Foster, Dean P. & Vohra, Rakesh, 1999. "Regret in the On-Line Decision Problem," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 7-35, October.
  3. Sergiu Hart & Andreu Mas-Colell, 1999. "A general class of adaptative strategies," Economics Working Papers 373, Department of Economics and Business, Universitat Pompeu Fabra.
  4. Ehud Kalai, 1987. "Bounded Rationality and Strategic Complexity in Repeated Games," Discussion Papers 783, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. Abreu, Dilip & Rubinstein, Ariel, 1988. "The Structure of Nash Equilibrium in Repeated Games with Finite Automata," Econometrica, Econometric Society, vol. 56(6), pages 1259-81, November.
  6. Ariel Rubinstein, 1997. "Finite automata play the repeated prisioners dilemma," Levine's Working Paper Archive 1639, David K. Levine.
  7. Herbert A. Simon, 1996. "The Sciences of the Artificial, 3rd Edition," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262691914.
  8. Ben-Porath Elchanan, 1993. "Repeated Games with Finite Automata," Journal of Economic Theory, Elsevier, vol. 59(1), pages 17-32, February.
  9. Ewerhart, Christian, 2000. "Chess-like Games Are Dominance Solvable in at Most Two Steps," Games and Economic Behavior, Elsevier, vol. 33(1), pages 41-47, October.
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Citations

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Cited by:
  1. Jiang, Albert Xin & Leyton-Brown, Kevin & Bhat, Navin A.R., 2011. "Action-Graph Games," Games and Economic Behavior, Elsevier, vol. 71(1), pages 141-173, January.
  2. Waters, George A., 2009. "Chaos in the cobweb model with a new learning dynamic," Journal of Economic Dynamics and Control, Elsevier, vol. 33(6), pages 1201-1216, June.

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