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The rationality/computability trade-off in finite games

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  • Prasad, Kislaya

Abstract

The computability of Nash equilibrium points of finite strategic form games is examined. When payoffs are computable there always exists an equilibrium in which all players use computable strategies, but there can be no algorithm that, given an arbitrary strategic form game, can compute its Nash equilibrium point. This is a consequence of the fact, established in this paper, that there is a computable sequence of games for which the equilibrium points do not constitute a computable sequence. Even for games with computable equilibrium points, best response functions of the players need not be computable. In contrast, approximate equilibria and error-prone responses are computable.

Suggested Citation

  • Prasad, Kislaya, 2009. "The rationality/computability trade-off in finite games," Journal of Economic Behavior & Organization, Elsevier, vol. 69(1), pages 17-26, January.
  • Handle: RePEc:eee:jeborg:v:69:y:2009:i:1:p:17-26
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    References listed on IDEAS

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    1. Jordan J. S., 1993. "Three Problems in Learning Mixed-Strategy Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 368-386, July.
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    6. Prasad, Kislaya, 1997. "On the computability of Nash equilibria," Journal of Economic Dynamics and Control, Elsevier, vol. 21(6), pages 943-953, June.
    7. Velupillai, K., 2000. "Computable Economics: The Arne Ryde Memorial Lectures," OUP Catalogue, Oxford University Press, number 9780198295273.
    8. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
    9. Prasad, Kislaya, 1991. "Computability and randomness of Nash equilibrium in infinite games," Journal of Mathematical Economics, Elsevier, vol. 20(5), pages 429-442.
    10. Lewis, Alain A., 1988. "Lower bounds on degrees of game-theoretic structures," Mathematical Social Sciences, Elsevier, vol. 16(1), pages 1-39, August.
    11. Radner, Roy, 1980. "Collusive behavior in noncooperative epsilon-equilibria of oligopolies with long but finite lives," Journal of Economic Theory, Elsevier, vol. 22(2), pages 136-154, April.
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    Blog mentions

    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. Computability of Nash Equilibrium
      by Eran in The Leisure of the Theory Class on 2011-01-05 03:31:14

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    Cited by:

    1. Hu, Tai-Wei, 2014. "Unpredictability of complex (pure) strategies," Games and Economic Behavior, Elsevier, vol. 88(C), pages 1-15.
    2. Halpern, Joseph Y. & Pass, Rafael, 2015. "Algorithmic rationality: Game theory with costly computation," Journal of Economic Theory, Elsevier, vol. 156(C), pages 246-268.

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