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Two-person repeated games with finite automata

Author

Listed:
  • 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)

Abstract

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.

Suggested Citation

  • Abraham Neyman & Daijiro Okada, 2000. "Two-person repeated games with finite automata," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(3), pages 309-325.
  • 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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    References listed on IDEAS

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    1. Lehrer, E, 1988. "An Axiomatization of the Banzhaf Value," International Journal of Game Theory, Springer;Game Theory Society, pages 89-99.
    2. Haller, Hans, 1994. "Collusion Properties of Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(3), pages 261-281.
    3. Gerard van der Laan & René van den Brink, 1998. "Axiomatization of a class of share functions for n-person games," Theory and Decision, Springer, pages 117-148.
    4. Chun, Youngsub, 1991. "On the Symmetric and Weighted Shapley Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(2), pages 183-190.
    5. (*), Gerard van der Laan & RenÊ van den Brink, 1998. "Axiomatizations of the normalized Banzhaf value and the Shapley value," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(4), pages 567-582.
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    Citations

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    Cited by:

    1. Neyman, Abraham & Spencer, Joel, 2010. "Complexity and effective prediction," Games and Economic Behavior, Elsevier, vol. 69(1), pages 165-168, May.
    2. Hernández, Penélope & Solan, Eilon, 2016. "Bounded computational capacity equilibrium," Journal of Economic Theory, Elsevier, vol. 163(C), pages 342-364.
    3. Hernández, Penélope & Urbano, Amparo, 2008. "Codification schemes and finite automata," Mathematical Social Sciences, Elsevier, vol. 56(3), pages 395-409, November.
    4. Sylvain Béal, 2010. "Perceptron versus automaton in the finitely repeated prisoner’s dilemma," Theory and Decision, Springer, pages 183-204.
    5. Abraham Neyman, 2008. "Learning Effectiveness and Memory Size," Levine's Working Paper Archive 122247000000001945, David K. Levine.
    6. Neyman, Abraham & Okada, Daijiro, 2009. "Growth of strategy sets, entropy, and nonstationary bounded recall," Games and Economic Behavior, Elsevier, vol. 66(1), pages 404-425, May.
    7. Daijiro Okada & Abraham Neyman, 2004. "Growing Strategy Sets in Repeated Games," Econometric Society 2004 North American Summer Meetings 625, Econometric Society.
    8. 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.
    9. 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.
    10. Béal, Sylvain, 2007. "Perceptron Versus Automaton∗," Sonderforschungsbereich 504 Publications 07-58, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.

    More about this item

    Keywords

    repeated games; finite automata;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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