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Growth of Strategy Sets, Entropy, and Nonstationary Bounded Recall

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  • Abraham Neyman
  • Daijiro Okada

Abstract

The paper initiates the study of long term interactions where players' bounded rationality varies over time. Time dependent bounded rationality, for player i, is reflected in part in the number [psi]i(t) of distinct strategies available to him in the first t-stages. We examine how the growth rate of [psi]i(t) affects equilibrium outcomes of repeated games. An upper bound on the individually rational payoff is derived for a class of two-player repeated games, and the derived bound is shown to be tight. As a special case we study the repeated games with nonstationary bounded recall and show that, a player can guarantee the minimax payoff of the stage game, even against a player with full recall, by remembering a vanishing fraction of the past. A version of the folk theorem is provided for this class of games.

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Bibliographic Info

Paper provided by UCLA Department of Economics in its series Levine's Bibliography with number 122247000000000920.

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Date of creation: 30 Dec 2005
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Handle: RePEc:cla:levrem:122247000000000920

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References

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  1. Aumann, Robert J., 1997. "Rationality and Bounded Rationality," Games and Economic Behavior, Elsevier, Elsevier, vol. 21(1-2), pages 2-14, October.
  2. Olivier Gossner & Abraham Neyman & Penélope Hernández, 2005. "Optimal Use Of Communication Resources," Working Papers. Serie AD, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) 2005-06, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  3. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, Elsevier, vol. 19(3), pages 227-229.
  4. Lehrer, Ehud, 1988. "Repeated games with stationary bounded recall strategies," Journal of Economic Theory, Elsevier, Elsevier, vol. 46(1), pages 130-144, October.
  5. O. Gossner & N. Vieille, 1999. "How to play with a biased coin ?," THEMA Working Papers 99-31, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  6. Ben-Porath Elchanan, 1993. "Repeated Games with Finite Automata," Journal of Economic Theory, Elsevier, Elsevier, vol. 59(1), pages 17-32, February.
  7. Robert J. Aumann & Lloyd S. Shapley, 2013. "Long Term Competition -- A Game-Theoretic Analysis," Annals of Economics and Finance, Society for AEF, vol. 14(2), pages 627-640, November.
  8. Neyman, Abraham & Okada, Daijiro, 2000. "Repeated Games with Bounded Entropy," Games and Economic Behavior, Elsevier, Elsevier, vol. 30(2), pages 228-247, February.
  9. Abraham Neyman & Daijiro Okada, 2000. "Two-person repeated games with finite automata," International Journal of Game Theory, Springer, Springer, vol. 29(3), pages 309-325.
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Cited by:
  1. Ron Peretz, 2007. "The Strategic Value of Recall," Discussion Paper Series, The Center for the Study of Rationality, Hebrew University, Jerusalem dp470, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  2. Abraham Neyman, 2008. "Learning Effectiveness and Memory Size," Levine's Working Paper Archive 122247000000001945, David K. Levine.
  3. Ron Peretz, 2011. "Correlation through Bounded Recall Strategies," Discussion Paper Series, The Center for the Study of Rationality, Hebrew University, Jerusalem dp579, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  4. Ron Peretz, 2013. "Correlation through bounded recall strategies," International Journal of Game Theory, Springer, Springer, vol. 42(4), pages 867-890, November.
  5. Ron Peretz, 2007. "The Strategic Value of Recall," Levine's Bibliography 122247000000001774, UCLA Department of Economics.
  6. Peretz, Ron, 2012. "The strategic value of recall," Games and Economic Behavior, Elsevier, Elsevier, vol. 74(1), pages 332-351.

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