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Finite Rationality and Interpersonal Complexity in Repeated Games

  • Kalai, Ehud
  • Stanford, William

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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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 56 (1988)
Issue (Month): 2 (March)
Pages: 397-410

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Handle: RePEc:ecm:emetrp:v:56:y:1988:i:2:p:397-410
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  1. Drew Fudenberg & David K. Levine, 1983. "Subgame-Perfect Equilibria of Finite- and Infinite-Horizon Games," Levine's Working Paper Archive 219, David K. Levine.
  2. Smale, Steve, 1980. "The Prisoner's Dilemma and Dynamical Systems Associated to Non-Cooperative Games," Econometrica, Econometric Society, vol. 48(7), pages 1617-34, November.
  3. 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.
  4. Friedman, James W, 1971. "A Non-cooperative Equilibrium for Supergames," Review of Economic Studies, Wiley Blackwell, vol. 38(113), pages 1-12, January.
  5. 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, vol. 17(3), pages 177-86.
  6. 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.
  7. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
  8. 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.
  9. Futia, Carl, 1977. "The complexity of economic decision rules," Journal of Mathematical Economics, Elsevier, vol. 4(3), pages 289-299, December.
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