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Growth of strategy sets, entropy, and nonstationary bounded recall

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  • Neyman, Abraham
  • Okada, Daijiro

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

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 66 (2009)
Issue (Month): 1 (May)
Pages: 404-425

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Handle: RePEc:eee:gamebe:v:66:y:2009:i:1:p:404-425

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Web page: http://www.elsevier.com/locate/inca/622836

Related research

Keywords: Bounded rationality Strategy set growth Strategic complexity Nonstationary bounded recall Repeated games Entropy;

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References

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  1. Neyman, Abraham & Okada, Daijiro, 2000. "Repeated Games with Bounded Entropy," Games and Economic Behavior, Elsevier, vol. 30(2), pages 228-247, February.
  2. Lehrer, Ehud, 1988. "Repeated games with stationary bounded recall strategies," Journal of Economic Theory, Elsevier, vol. 46(1), pages 130-144, October.
  3. Gossner, O. & Vieille, N., 1999. "How to play with a biased coin?," Papers 99-31, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
  4. Ben-Porath Elchanan, 1993. "Repeated Games with Finite Automata," Journal of Economic Theory, Elsevier, vol. 59(1), pages 17-32, February.
  5. Abraham Neyman & Daijiro Okada, 2000. "Two-person repeated games with finite automata," International Journal of Game Theory, Springer, vol. 29(3), pages 309-325.
  6. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
  7. Olivier Gossner & Penélope Hernández & Abraham Neyman, 2006. "Optimal Use of Communication Resources," Econometrica, Econometric Society, vol. 74(6), pages 1603-1636, November.
  8. Robert J. Aumann & Lloyd S. Shapley, 1992. "Long Term Competition-A Game Theoretic Analysis," UCLA Economics Working Papers 676, UCLA Department of Economics.
  9. Aumann, Robert J., 1997. "Rationality and Bounded Rationality," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 2-14, October.
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Citations

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Cited by:
  1. Abraham Neyman, 2008. "Learning Effectiveness and Memory Size," Discussion Paper Series dp476, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  2. Peretz, Ron, 2012. "The strategic value of recall," Games and Economic Behavior, Elsevier, vol. 74(1), pages 332-351.
  3. Ron Peretz, 2013. "Correlation through bounded recall strategies," International Journal of Game Theory, Springer, vol. 42(4), pages 867-890, November.
  4. Ron Peretz, 2011. "Correlation through Bounded Recall Strategies," Discussion Paper Series dp579, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  5. Ron Peretz, 2007. "The Strategic Value of Recall," Levine's Bibliography 122247000000001774, UCLA Department of Economics.
  6. Ron Peretz, 2007. "The Strategic Value of Recall," Discussion Paper Series dp470, The Center for the Study of Rationality, Hebrew University, Jerusalem.

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