IDEAS home Printed from https://ideas.repec.org/a/bla/ijethy/v6y2010i1p167-187.html

Mixed strategy equilibria in repeated games with one‐period memory

Author

Listed:
  • Prajit K. Dutta
  • Paolo Siconolfi

Abstract

Infinitely repeated games is the pre‐dominant paradigm within which economists study long‐term strategic interaction. The standard framework allows players to condition their strategies on all past actions; that is, assumes that they have unbounded memory. That is clearly a convenient simplification that is at odds with reality. In this paper we restrict attention to one‐period memory and characterize all totally mixed equilibria. In particular, we focus on strongly mixed equilibria. We provide conditions that are necessary and sufficient for a game to have such an equilibrium. We further demonstrate the exact set of payoffs that can be generated by such equilibria.

Suggested Citation

  • Prajit K. Dutta & Paolo Siconolfi, 2010. "Mixed strategy equilibria in repeated games with one‐period memory," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(1), pages 167-187, March.
    • Handle: RePEc:bla:ijethy:v:6:y:2010:i:1:p:167-187
    DOI: 10.1111/j.1742-7363.2009.00128.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1742-7363.2009.00128.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1742-7363.2009.00128.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. 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..
    2. 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.
    3. Abreu, Dilip & Rubinstein, Ariel, 1988. "The Structure of Nash Equilibrium in Repeated Games with Finite Automata," Econometrica, Econometric Society, vol. 56(6), pages 1259-1281, November.
    4. Benoit, Jean-Pierre & Krishna, Vijay, 1985. "Finitely Repeated Games," Econometrica, Econometric Society, vol. 53(4), pages 905-922, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Barlo, Mehmet & Carmona, Guilherme & Sabourian, Hamid, 2016. "Bounded memory Folk Theorem," Journal of Economic Theory, Elsevier, vol. 163(C), pages 728-774.
    2. Artem Baklanov, 2021. "Reactive Strategies: An Inch of Memory, a Mile of Equilibria," Games, MDPI, vol. 12(2), pages 1-28, May.

    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. Roman, Mihai Daniel, 2008. "Entreprises behavior in cooperative and punishment‘s repeated negotiations," MPRA Paper 37527, University Library of Munich, Germany, revised 05 Jan 2009.
    2. Kimmo Berg & Mitri Kitti, 2013. "Computing Equilibria in Discounted 2 × 2 Supergames," Computational Economics, Springer;Society for Computational Economics, vol. 41(1), pages 71-88, January.
    3. Anderlini, Luca & Sabourian, Hamid, 2001. "Cooperation and computability in n-player games," Mathematical Social Sciences, Elsevier, vol. 42(2), pages 99-137, September.
    4. Roman, Mihai Daniel, 2010. "A game theoretic approach of war with financial influences," MPRA Paper 38389, University Library of Munich, Germany.
    5. Olivier Compte & Andrew Postlewaite, 2007. "Effecting Cooperation," PIER Working Paper Archive 09-019, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 29 May 2009.
    6. van Damme, E.E.C., 1995. "Game theory : The next stage," Other publications TiSEM 7779b0f9-bef5-45c7-ae6b-7, Tilburg University, School of Economics and Management.
    7. Spagnolo, Giancarlo, 2005. "Managerial incentives and collusive behavior," European Economic Review, Elsevier, vol. 49(6), pages 1501-1523, August.
    8. Stähler, Frank, 1995. "Profits in pure Bertrand oligopolies," Kiel Working Papers 703, Kiel Institute for the World Economy.
    9. Hörner, Johannes & Lovo, Stefano & Tomala, Tristan, 2011. "Belief-free equilibria in games with incomplete information: Characterization and existence," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1770-1795, September.
    10. Glover, Jonathan & Xue, Hao, 2023. "Accounting conservatism and relational contracting," Journal of Accounting and Economics, Elsevier, vol. 76(1).
    11. Contou-Carrère, Pauline & Tomala, Tristan, 2011. "Finitely repeated games with semi-standard monitoring," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 14-21, January.
    12. Joyee Deb, 2008. "Cooperation and Community Responsibility: A Folk Theorem for Repeated Matching Games with Names," Working Papers 08-24, New York University, Leonard N. Stern School of Business, Department of Economics.
    13. Miller, John H., 1996. "The coevolution of automata in the repeated Prisoner's Dilemma," Journal of Economic Behavior & Organization, Elsevier, vol. 29(1), pages 87-112, January.
    14. 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.
    15. Jehiel, Philippe & Samuelson, Larry, 2023. "The analogical foundations of cooperation," Journal of Economic Theory, Elsevier, vol. 208(C).
    16. Yutaka Kayaba & Hitoshi Matsushima & Tomohisa Toyama, 2019. "Accuracy and Retaliation in Repeated Games with Imperfect Private Monitoring: Experiments (Revised version of CARF-F-433)," CARF F-Series CARF-F-466, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    17. Kalai, Ehud & Ledyard, John O., 1998. "Repeated Implementation," Journal of Economic Theory, Elsevier, vol. 83(2), pages 308-317, December.
    18. Yangbo Song & Mofei Zhao, 2023. "Cooperative teaching and learning of actions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(4), pages 1289-1327, November.
    19. van Damme, Eric, 1989. "Renegotiation-proof equilibria in repeated prisoners' dilemma," Journal of Economic Theory, Elsevier, vol. 47(1), pages 206-217, February.
    20. Zhang, Huanren, 2018. "Errors can increase cooperation in finite populations," Games and Economic Behavior, Elsevier, vol. 107(C), pages 203-219.

    More about this item

    Statistics

    Access and download statistics

    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:bla:ijethy:v:6:y:2010:i:1:p:167-187. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=1742-7355 .

    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.