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Strategic complexity in repeated extensive games

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  • Muto, Nozomu

Abstract

This paper studies a machine (finite automaton) playing a two-player repeated game of a simple extensive-form game with perfect information. We introduce a new complexity measure called multiple complexity which incorporates a strategyʼs responsiveness to information in the stage game as well as the number of states of the machine. We completely characterize the Nash equilibrium of the machine game. In the sequential-move prisonerʼs dilemma, cooperation can be sustained as an equilibrium.

Suggested Citation

  • Muto, Nozomu, 2014. "Strategic complexity in repeated extensive games," Games and Economic Behavior, Elsevier, vol. 83(C), pages 45-52.
    • Handle: RePEc:eee:gamebe:v:83:y:2014:i:c:p:45-52
    DOI: 10.1016/j.geb.2013.10.007
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    References listed on IDEAS

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    1. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
    2. Piccione Michele & Rubinstein Ariel, 1993. "Finite Automata Play a Repeated Extensive Game," Journal of Economic Theory, Elsevier, vol. 61(1), pages 160-168, October.
    3. Binmore, Kenneth G. & Samuelson, Larry, 1992. "Evolutionary stability in repeated games played by finite automata," Journal of Economic Theory, Elsevier, vol. 57(2), pages 278-305, August.
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    7. Yuval Salant, 2011. "Procedural Analysis of Choice Rules with Applications to Bounded Rationality," American Economic Review, American Economic Association, vol. 101(2), pages 724-748, April.
    8. Lee, Jihong & Sabourian, Hamid, 2007. "Coase theorem, complexity and transaction costs," Journal of Economic Theory, Elsevier, vol. 135(1), pages 214-235, July.
    9. Douglas Gale & Hamid Sabourian, 2005. "Complexity and Competition," Econometrica, Econometric Society, vol. 73(3), pages 739-769, May.
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    Cited by:

    1. Oren Bar-Gill & Christoph Engel, 2020. "Property is Dummy Proof: An Experiment," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2020_02, Max Planck Institute for Research on Collective Goods.

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    More about this item

    Keywords

    Strategic complexity; Finite automaton; Repeated game; Extensive game; Prisonerʼs dilemma; Multiple complexity;
    All these keywords.

    JEL classification:

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

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