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Two-person repeated games with finite automata


Author Info

  • Abraham Neyman

    (Institute of Mathematics, The Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904, ISRAEL and SUNY at Stony Brook, Stony Brook, NY 11794-4384, USA)

  • Daijiro Okada

    (Department of Economics, SUNY at Stony Brook, Stony Brook, NY 11794-4384, USA)


We study two-person repeated games in which a player with a restricted set of strategies plays against an unrestricted player. An exogenously given bound on the complexity of strategies, which is measured by the size of the smallest automata that implement them, gives rise to a restriction on strategies available to a player. We examine the asymptotic behavior of the set of equilibrium payoffs as the bound on the strategic complexity of the restricted player tends to infinity, but sufficiently slowly. Results from the study of zero sum case provide the individually rational payoff levels.

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Bibliographic Info

Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 29 (2000)
Issue (Month): 3 ()
Pages: 309-325

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Handle: RePEc:spr:jogath:v:29:y:2000:i:3:p:309-325

Note: Received February 1997/revised version March 2000
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Keywords: repeated games; finite automata;

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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. Sylvain Béal, 2010. "Perceptron versus automaton in the finitely repeated prisoner’s dilemma," Theory and Decision, Springer, vol. 69(2), pages 183-204, August.
  3. Abraham Neyman & Joel Spencer, 2006. "Complexity and Effective Prediction," Levine's Bibliography 321307000000000527, UCLA Department of Economics.
  4. Eilon Solan & Penélope Hernández, 2014. "Bounded Computational Capacity Equilibrium," Discussion Papers in Economic Behaviour 0314, University of Valencia, ERI-CES.
  5. Abraham Neyman & Daijiro Okada, 2005. "Growth of Strategy Sets, Entropy, and Nonstationary Bounded Recall," Discussion Paper Series dp411, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  6. Hernández, Penélope & Urbano, Amparo, 2008. "Codification schemes and finite automata," Mathematical Social Sciences, Elsevier, vol. 56(3), pages 395-409, November.
  7. 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.
  8. Béal, Sylvain, 2007. "Perceptron Versus Automaton∗," Sonderforschungsbereich 504 Publications 07-58, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  9. Daijiro Okada & Abraham Neyman, 2004. "Growing Strategy Sets in Repeated Games," Econometric Society 2004 North American Summer Meetings 625, Econometric Society.
  10. Renault, Jérôme & Scarsini, Marco & Tomala, Tristan, 2008. "Playing off-line games with bounded rationality," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 207-223, September.


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