IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v144y2009i1p312-336.html
   My bibliography  Save this article

Repeated games with one-memory

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022-0531(08)00063-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Bhaskar, V. & Vega-Redondo, Fernando, 2002. "Asynchronous Choice and Markov Equilibria," Journal of Economic Theory, Elsevier, vol. 103(2), pages 334-350, April.
    2. Lehrer Ehud, 1994. "Finitely Many Players with Bounded Recall in Infinitely Repeated Games," Games and Economic Behavior, Elsevier, vol. 7(3), pages 390-405, November.
    3. Cho, In-Koo, 1994. "Bounded Rationality, Neural Network and Folk Theorem in Repeated Games with Discounting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(6), pages 935-957, October.
    4. Aumann, Robert J. & Sorin, Sylvain, 1989. "Cooperation and bounded recall," Games and Economic Behavior, Elsevier, vol. 1(1), pages 5-39, March.
    5. Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-396, March.
    6. Kalai, Ehud & Stanford, William, 1988. "Finite Rationality and Interpersonal Complexity in Repeated Games," Econometrica, Econometric Society, vol. 56(2), pages 397-410, March.
    7. Mailath, George J. & Morris, Stephen, 2002. "Repeated Games with Almost-Public Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 189-228, January.
    8. Cole, Harold L. & Kocherlakota, Narayana R., 2005. "Finite memory and imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 53(1), pages 59-72, October.
    9. Drew Fudenberg & David Levine & Eric Maskin, 2008. "The Folk Theorem With Imperfect Public Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 12, pages 231-273, World Scientific Publishing Co. Pte. Ltd..
    10. , J. & ,, 2006. "Coordination failure in repeated games with almost-public monitoring," Theoretical Economics, Econometric Society, vol. 1(3), pages 311-340, September.
    11. Drew Fudenberg & Eric Maskin, 2008. "The Folk Theorem In Repeated Games With Discounting Or With Incomplete Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 11, pages 209-230, World Scientific Publishing Co. Pte. Ltd..
    12. Neyman, Abraham & Okada, Daijiro, 1999. "Strategic Entropy and Complexity in Repeated Games," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 191-223, October.
    13. Fudenberg, Drew & Maskin, Eric, 1991. "On the dispensability of public randomization in discounted repeated games," Journal of Economic Theory, Elsevier, vol. 53(2), pages 428-438, April.
    14. Lehrer, Ehud, 1988. "Repeated games with stationary bounded recall strategies," Journal of Economic Theory, Elsevier, vol. 46(1), pages 130-144, October.
    15. Sabourian, Hamid, 1998. "Repeated games with M-period bounded memory (pure strategies)," Journal of Mathematical Economics, Elsevier, vol. 30(1), pages 1-35, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Barlo, Mehmet & Carmona, Guilherme & Sabourian, Hamid, 2016. "Bounded memory Folk Theorem," Journal of Economic Theory, Elsevier, vol. 163(C), pages 728-774.
    2. Mailath, George J. & Olszewski, Wojciech, 2011. "Folk theorems with bounded recall under (almost) perfect monitoring," Games and Economic Behavior, Elsevier, vol. 71(1), pages 174-192, January.
    3. Mehmet Barlo & Guilherme Carmona, 2007. "One - memory in repeated games," Nova SBE Working Paper Series wp500, Universidade Nova de Lisboa, Nova School of Business and Economics.
    4. 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.
    5. Marco Battaglini & Stephen Coate, 2008. "A Dynamic Theory of Public Spending, Taxation, and Debt," American Economic Review, American Economic Association, vol. 98(1), pages 201-236, March.
    6. repec:dau:papers:123456789/6381 is not listed on IDEAS
    7. Renault, Jérôme & Scarsini, Marco & Tomala, Tristan, 2008. "Playing off-line games with bounded rationality," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 207-223, September.
    8. Jérôme Renault & Marco Scarsini & Tristan Tomala, 2007. "A Minority Game with Bounded Recall," Mathematics of Operations Research, INFORMS, vol. 32(4), pages 873-889, November.
    9. Gossner, Olivier & Hörner, Johannes, 2010. "When is the lowest equilibrium payoff in a repeated game equal to the minmax payoff?," Journal of Economic Theory, Elsevier, vol. 145(1), pages 63-84, January.
    10. repec:dau:papers:123456789/6127 is not listed on IDEAS
    11. Barlo, Mehmet & Urgun, Can, 2011. "Stochastic discounting in repeated games: Awaiting the almost inevitable," MPRA Paper 28537, University Library of Munich, Germany.
    12. Cole, Harold L. & Kocherlakota, Narayana R., 2005. "Finite memory and imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 53(1), pages 59-72, October.
    13. Olivier Gossner & Jöhannes Horner, 2006. "When is the individually rational payoff in a repeated game equal to the minmax payoff?," Discussion Papers 1440, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    14. Kimmo Berg & Gijs Schoenmakers, 2017. "Construction of Subgame-Perfect Mixed-Strategy Equilibria in Repeated Games," Games, MDPI, vol. 8(4), pages 1-14, November.
    15. Ely, Jeffrey C. & Valimaki, Juuso, 2002. "A Robust Folk Theorem for the Prisoner's Dilemma," Journal of Economic Theory, Elsevier, vol. 102(1), pages 84-105, January.
    16. Richard McLean & Ichiro Obara & Andrew Postlewaite, 2001. "Informational Smallness and Private Monitoring in Repeated Games," PIER Working Paper Archive 05-024, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 20 Jul 2005.
    17. Yamamoto, Yuichi, 2009. "A limit characterization of belief-free equilibrium payoffs in repeated games," Journal of Economic Theory, Elsevier, vol. 144(2), pages 802-824, March.
    18. Jimmy Chan, 2000. "On the Non-Existence of Reputation Effects in Two-Person Infinitely-Repeated Games," Economics Working Paper Archive 441, The Johns Hopkins University,Department of Economics.
    19. Jehiel, Philippe & Samuelson, Larry, 2023. "The analogical foundations of cooperation," Journal of Economic Theory, Elsevier, vol. 208(C).
    20. Abreu, Dilip & Dutta, Prajit K & Smith, Lones, 1994. "The Folk Theorem for Repeated Games: A NEU Condition," Econometrica, Econometric Society, vol. 62(4), pages 939-948, July.
    21. Dasgupta, Ani & Ghosh, Sambuddha, 2022. "Self-accessibility and repeated games with asymmetric discounting," Journal of Economic Theory, Elsevier, vol. 200(C).
    22. Ueda, Masahiko, 2023. "Memory-two strategies forming symmetric mutual reinforcement learning equilibrium in repeated prisoners’ dilemma game," Applied Mathematics and Computation, Elsevier, vol. 444(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jetheo:v:144:y:2009:i:1:p:312-336. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.