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Repeated games with one-memory

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  • Barlo, Mehmet
  • Carmona, Guilherme
  • Sabourian, Hamid

Abstract

We study the extent to which equilibrium payoffs of discounted repeated games can be obtained by 1-memory strategies. We establish the following in games with perfect (rich) action spaces: First, when the players are sufficiently patient, the subgame perfect Folk Theorem holds with 1-memory. Second, for arbitrary level of discounting, all strictly enforceable subgame perfect equilibrium payoffs can be approximately supported with 1-memory if the number of players exceeds two. Furthermore, in this case all subgame perfect equilibrium payoffs can be approximately supported by an [epsilon]-equilibrium with 1-memory. In two-player games, the same set of results hold if an additional restriction is assumed: Players must have common punishments. Finally, to illustrate the role of our assumptions, we present robust examples of games in which there is a subgame perfect equilibrium payoff profile that cannot be obtained with 1-memory. Thus, our results are the best that can be hoped for.

Suggested Citation

  • Barlo, Mehmet & Carmona, Guilherme & Sabourian, Hamid, 2009. "Repeated games with one-memory," Journal of Economic Theory, Elsevier, vol. 144(1), pages 312-336, January.
  • Handle: RePEc:eee:jetheo:v:144:y:2009:i:1:p:312-336
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    References listed on IDEAS

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    1. Bhaskar, V. & Vega-Redondo, Fernando, 2002. "Asynchronous Choice and Markov Equilibria," Journal of Economic Theory, Elsevier, vol. 103(2), pages 334-350, April.
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    Citations

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    Cited by:

    1. Canning, David, 1992. "Average behavior in learning models," Journal of Economic Theory, Elsevier, vol. 57(2), pages 442-472, August.
    2. Barlo, Mehmet & Carmona, Guilherme & Sabourian, Hamid, 2016. "Bounded memory Folk Theorem," Journal of Economic Theory, Elsevier, vol. 163(C), pages 728-774.
    3. Aperjis, Christina & Zeckhauser, Richard J. & Miao, Yali, 2014. "Variable temptations and black mark reputations," Games and Economic Behavior, Elsevier, vol. 87(C), pages 70-90.
    4. Barlo, Mehmet & Urgun, Can, 2011. "Stochastic discounting in repeated games: Awaiting the almost inevitable," MPRA Paper 28537, University Library of Munich, Germany.
    5. Monte, Daniel, 2013. "Bounded memory and permanent reputations," Journal of Mathematical Economics, Elsevier, vol. 49(5), pages 345-354.
    6. Liu, Qingmin & Skrzypacz, Andrzej, 2014. "Limited records and reputation bubbles," Journal of Economic Theory, Elsevier, vol. 151(C), pages 2-29.
    7. Doraszelski, Ulrich & Escobar, Juan F., 2012. "Restricted feedback in long term relationships," Journal of Economic Theory, Elsevier, vol. 147(1), pages 142-161.
    8. Benjamin Sperisen, 2016. "Bounded Memory, Reputation, and Impatience," Working Papers 1602, Tulane University, Department of Economics.
    9. Barlo, Mehmet & Carmona, Guilherme, 2004. "Time Dependent Bounded Recall Strategies Are Enough to Play the Discounted Repeated Prisoners Dilemma," FEUNL Working Paper Series wp449, Universidade Nova de Lisboa, Faculdade de Economia.
    10. V. Bhaskar & Fernando Vega-Redondo, 1998. "Asynchronous Choice and Markov Equilibria:Theoretical Foundations and Applications," Game Theory and Information 9809003, EconWPA.
    11. Sergei Kovbasyuk & Giancarlo Spagnolo, 2016. "Memory and Markets," EIEF Working Papers Series 1606, Einaudi Institute for Economics and Finance (EIEF), revised Oct 2017.
    12. Raphael Thomadsen & Pradeep Bhardwaj, 2011. "Cooperation in Games with Forgetfulness," Management Science, INFORMS, vol. 57(2), pages 363-375, February.
    13. repec:eee:gamebe:v:103:y:2017:i:c:p:185-198 is not listed on IDEAS
    14. George J. Mailath & : Wojciech Olszewski, 2008. "Folk Theorems with Bounded Recall under (Almost) Perfect Monitoring, Second Version," PIER Working Paper Archive 08-027, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 28 Jul 2008.
    15. Yves Breitmoser, 2015. "Cooperation, but No Reciprocity: Individual Strategies in the Repeated Prisoner's Dilemma," American Economic Review, American Economic Association, vol. 105(9), pages 2882-2910, September.
    16. Łukasz Balbus & Kevin Reffett & Łukasz Woźny, 2013. "Markov Stationary Equilibria in Stochastic Supermodular Games with Imperfect Private and Public Information," Dynamic Games and Applications, Springer, vol. 3(2), pages 187-206, June.
    17. Sabourian, Hamid, 1998. "Repeated games with M-period bounded memory (pure strategies)," Journal of Mathematical Economics, Elsevier, vol. 30(1), pages 1-35, August.
    18. Hilbe, Christian & Traulsen, Arne & Sigmund, Karl, 2015. "Partners or rivals? Strategies for the iterated prisoner's dilemma," Games and Economic Behavior, Elsevier, vol. 92(C), pages 41-52.

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