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Playing off-line games with bounded rationality

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  • Renault, Jérôme
  • Scarsini, Marco
  • Tomala, Tristan

Abstract

We study a two-person zero-sum game where players simultaneously choose sequences of actions, and the overall payoff is the average of a one-shot payoff over the joint sequence. We consider the maxmin value of the game played in pure strategies by boundedly rational players and model bounded rationality by introducing complexity limitations. First we define the complexity of a sequence by its smallest period (a nonperiodic sequence being of infinite complexity) and study the maxmin of the game where player 1 is restricted to strategies with complexity at most n and player 2 is restricted to strategies with complexity at most m. We study the asymptotics of this value and a complete characterization in the matching pennies case. We extend the analysis of matching pennies to strategies with bounded recall.

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Bibliographic Info

Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 56 (2008)
Issue (Month): 2 (September)
Pages: 207-223

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Handle: RePEc:eee:matsoc:v:56:y:2008:i:2:p:207-223

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Web page: http://www.elsevier.com/locate/inca/505565

Related research

Keywords: C72 C73 primary Games/group decisions Noncooperative Zero-sum games Periodic sequences Bounded recall de Bruijn graphs Oblivious strategy;

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References

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  1. Renault, Jérôme & Scarsini, Marco & Tomala, Tristan, 2007. "A minority game with bounded recall," Economics Papers from University Paris Dauphine 123456789/6381, Paris Dauphine University.
  2. Ben-porath, Elchanan, 1990. "The complexity of computing a best response automaton in repeated games with mixed strategies," Games and Economic Behavior, Elsevier, vol. 2(1), pages 1-12, March.
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  7. Michele Piccione & Ariel Rubinstein, 2010. "Modeling the Economic Interaction of Agents with Diverse Abilities to Recognize Equilibrium Patterns," Levine's Working Paper Archive 506439000000000108, David K. Levine.
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  13. Lehrer Ehud, 1994. "Finitely Many Players with Bounded Recall in Infinitely Repeated Games," Games and Economic Behavior, Elsevier, vol. 7(3), pages 390-405, November.
  14. O'Connell, Thomas C. & Stearns, Richard E., 2003. "On finite strategy sets for finitely repeated zero-sum games," Games and Economic Behavior, Elsevier, vol. 43(1), pages 107-136, April.
  15. Gilad Bavly & Abraham Neyman, 2003. "Online Concealed Correlation by Boundedly Rational Players," Discussion Paper Series dp336, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  16. Neyman, Abraham & Okada, Daijiro, 2000. "Repeated Games with Bounded Entropy," Games and Economic Behavior, Elsevier, vol. 30(2), pages 228-247, February.
  17. Neyman, Abraham & Okada, Daijiro, 1999. "Strategic Entropy and Complexity in Repeated Games," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 191-223, October.
  18. Liaw, Sy-Sang & Liu, Ching, 2005. "The quasi-periodic time sequence of the population in minority game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 351(2), pages 571-579.
  19. Olivier Gossner & Penélope Hernández, 2005. "Coordination Through De Bruijn Sequences," Working Papers. Serie AD 2005-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  20. Sabourian, Hamid, 1998. "Repeated games with M-period bounded memory (pure strategies)," Journal of Mathematical Economics, Elsevier, vol. 30(1), pages 1-35, August.
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Cited by:
  1. Peretz, Ron, 2012. "The strategic value of recall," Games and Economic Behavior, Elsevier, vol. 74(1), pages 332-351.

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