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An Approach to Bounded Rationality

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  • 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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Keywords: bounded rationality; zero sum games; potential games; strategic complexity.;

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  1. Herbert A. Simon, 1996. "The Sciences of the Artificial, 3rd Edition," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262691914, December.
  2. 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.
  3. Ariel Rubinstein, 1997. "Finite automata play the repeated prisioners dilemma," Levine's Working Paper Archive 1639, David K. Levine.
  4. 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.
  5. Hart, Sergiu & Mas-Colell, Andreu, 2001. "A General Class of Adaptive Strategies," Journal of Economic Theory, Elsevier, vol. 98(1), pages 26-54, May.
  6. Ewerhart, Christian, 2000. "Chess-like games are dominancesolvable in at most two steps," Sonderforschungsbereich 504 Publications 00-24, Sonderforschungsbereich 504, Universit├Ąt Mannheim & Sonderforschungsbereich 504, University of Mannheim.
  7. 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.
  8. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
  9. Ben-Porath Elchanan, 1993. "Repeated Games with Finite Automata," Journal of Economic Theory, Elsevier, vol. 59(1), pages 17-32, February.
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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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