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Finite Rationality and Interpersonal Complexity in Repeated Games

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  • Ehud Kalai
  • William Stanford

Abstract

Finite complexity strategies suffice for approximating all subgame perfect equ ilibrium payoffs of repeated games. Generically, at such equilibria, no player's complexity exceeds the product of his opponents' complexi ties. Also, no player's memory exceeds the maximal memory of his oppo nents. The complexity of a strategy is defined here to equal the numb er of distinct strategies it induces in the various subgames. It equa ls the size (number of states) of the smallest automaton describing i t and also the number of states of the smallest information system ne eded for the implementation of the strategy. Copyright 1988 by The Econometric Society.
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Suggested Citation

  • Ehud Kalai & William Stanford, 1986. "Finite Rationality and Interpersonal Complexity in Repeated Games," Discussion Papers 679, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:679
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    References listed on IDEAS

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    1. Drew Fudenberg & David Levine, 2008. "Subgame–Perfect Equilibria of Finite– and Infinite–Horizon Games," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 1, pages 3-20, World Scientific Publishing Co. Pte. Ltd..
    2. James W. Friedman, 1971. "A Non-cooperative Equilibrium for Supergames," Review of Economic Studies, Oxford University Press, vol. 38(1), pages 1-12.
    3. Stanford, William G., 1986. "Subgame perfect reaction function equilibria in discounted duopoly supergames are trivial," Journal of Economic Theory, Elsevier, vol. 39(1), pages 226-232, June.
    4. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
    5. 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.
    6. Futia, Carl, 1977. "The complexity of economic decision rules," Journal of Mathematical Economics, Elsevier, vol. 4(3), pages 289-299, December.
    7. Stanford, William G., 1986. "On continuous reaction function equilibria in duopoly supergames with mean payoffs," Journal of Economic Theory, Elsevier, vol. 39(1), pages 233-250, June.
    8. Smale, Steve, 1980. "The Prisoner's Dilemma and Dynamical Systems Associated to Non-Cooperative Games," Econometrica, Econometric Society, vol. 48(7), pages 1617-1634, November.
    9. Kalai, Ehud & Samet, Dov & Stanford, William, 1988. "A Note on Reactive Equilibria in the Discounted Prisoner's Dilemma and Associated Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(3), pages 177-186.
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