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Rationality, Computability, and Nash Equilibrium

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  • Canning, David

Abstract

Suppose two agents play a game, each using a computable algorithm to decide what to do, these algorithms being common knowledge. The author shows that it is possible to act rationally provided he limits his attention to a natural subset of solvable games and to opponents who use rational algorithms; the outcome is a Nash equilibrium. Going further, the author shows that rationality is possible on many domains of games and opposing algorithms but each domain requires a particular solution algorithm; no one algorithm is rational on all possible domains. Copyright 1992 by The Econometric Society.

Suggested Citation

  • Canning, David, 1992. "Rationality, Computability, and Nash Equilibrium," Econometrica, Econometric Society, vol. 60(4), pages 877-888, July.
  • Handle: RePEc:ecm:emetrp:v:60:y:1992:i:4:p:877-88
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    Cited by:

    1. Kumabe, Masahiro & Mihara, H. Reiju, 2008. "Computability of simple games: A characterization and application to the core," Journal of Mathematical Economics, Elsevier, vol. 44(3-4), pages 348-366, February.
    2. Anderlini, Luca, 1998. "Forecasting errors and bounded rationality: An example," Mathematical Social Sciences, Elsevier, vol. 36(2), pages 71-90, September.
    3. Horaguchi, Haruo, 1996. "The role of information processing cost as the foundation of bounded rationality in game theory," Economics Letters, Elsevier, vol. 51(3), pages 287-294, June.
    4. Richter, Marcel K. & Wong, Kam-Chau, 1999. "Computable preference and utility," Journal of Mathematical Economics, Elsevier, vol. 32(3), pages 339-354, November.
    5. David Levine & Balázs Szentes, 2006. "Can A Turing Player Identify Itself?," Economics Bulletin, AccessEcon, vol. 1(1), pages 1-6.
    6. Koppl, Roger, 2010. "Some epistemological implications of economic complexity," Journal of Economic Behavior & Organization, Elsevier, vol. 76(3), pages 859-872, December.
    7. repec:ebl:ecbull:v:1:y:2006:i:1:p:1-6 is not listed on IDEAS
    8. Nachbar, John H & Zame, William R, 1996. "Non-computable Strategies and Discounted Repeated Games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 103-122, June.
    9. Siegfried Berninghaus & Werner G³th & Hartmut Kliemt, 2003. "Reflections on Equilibrium: Ideal Rationality and Analytic Decomposition of Games," Homo Oeconomicus, Institute of SocioEconomics, vol. 20, pages 257-302.
    10. Mihara, H. Reiju, 1999. "Arrow's theorem, countably many agents, and more visible invisible dictators1," Journal of Mathematical Economics, Elsevier, vol. 32(3), pages 267-287, November.

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