IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v117y2019icp479-498.html
   My bibliography  Save this article

The truth behind the myth of the Folk theorem

Author

Listed:
  • Halpern, Joseph Y.
  • Pass, Rafael
  • Seeman, Lior

Abstract

We study the problem of computing an ϵ-Nash equilibrium in repeated games. Earlier work by Borgs et al. (2010) suggests that this problem is intractable. We show that if we make a slight change to their model—modeling the players as polynomial-time Turing machines that maintain state—and make a standard cryptographic assumption (that public-key cryptography can carried out), the problem can actually be solved in polynomial time. Our algorithm works not only for games with a finite number of players, but also for constant-degree graphical games (where, roughly speaking, which players' actions a given player's utility depends on are characterized by a graph, typically of bounded degree). As Nash equilibrium is a weak solution concept for extensive-form games, we additionally define and study an appropriate notion of subgame-perfect equilibrium for computationally bounded players, and show how to efficiently find such an equilibrium in repeated games (again, assuming public-key cryptography).

Suggested Citation

  • Halpern, Joseph Y. & Pass, Rafael & Seeman, Lior, 2019. "The truth behind the myth of the Folk theorem," Games and Economic Behavior, Elsevier, vol. 117(C), pages 479-498.
    • Handle: RePEc:eee:gamebe:v:117:y:2019:i:c:p:479-498
    DOI: 10.1016/j.geb.2019.04.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825619300582
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2019.04.008?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
    ---><---

    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. Borgs, Christian & Chayes, Jennifer & Immorlica, Nicole & Kalai, Adam Tauman & Mirrokni, Vahab & Papadimitriou, Christos, 2010. "The myth of the Folk Theorem," Games and Economic Behavior, Elsevier, vol. 70(1), pages 34-43, September.
    2. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    3. 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..
    4. Ron Peretz, 2013. "Correlation through bounded recall strategies," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(4), pages 867-890, November.
    5. Amparo Urbano & Jose E. Vila, 2002. "Computational Complexity and Communication: Coordination in Two-Player Games," Econometrica, Econometric Society, vol. 70(5), pages 1893-1927, September.
    6. Bavly, Gilad & Peretz, Ron, 2019. "Limits of correlation in repeated games with bounded memory," Games and Economic Behavior, Elsevier, vol. 115(C), pages 131-145.
    7. Bavly, Gilad & Neyman, Abraham, 2014. "Online concealed correlation and bounded rationality," Games and Economic Behavior, Elsevier, vol. 88(C), pages 71-89.
    8. GOSSNER, Olivier, 1998. "Repeated games played by cryptographically sophisticated players," LIDAM Discussion Papers CORE 1998035, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
    10. Urbano, A. & Vila, J. E., 2004. "Unmediated communication in repeated games with imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 46(1), pages 143-173, January.
    11. Tim Roughgarden, 2010. "Computing equilibria: a computational complexity perspective," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 193-236, January.
    12. Lehrer, Ehud, 1991. "Internal Correlation in Repeated Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(4), pages 431-456.
    13. Rubinstein, Ariel, 1979. "Equilibrium in supergames with the overtaking criterion," Journal of Economic Theory, Elsevier, vol. 21(1), pages 1-9, August.
    14. O. Gossner, 2000. "Sharing a long secret in a few public words," THEMA Working Papers 2000-15, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    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. Jakub Dargaj & Jakob Grue Simonsen, 2020. "A Complete Characterization of Infinitely Repeated Two-Player Games having Computable Strategies with no Computable Best Response under Limit-of-Means Payoff," Papers 2005.13921, arXiv.org, revised Jun 2020.
    2. Dargaj, Jakub & Simonsen, Jakob Grue, 2023. "A complete characterization of infinitely repeated two-player games having computable strategies with no computable best response under limit-of-means payoff," Journal of Economic Theory, Elsevier, vol. 213(C).

    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. Drew Fudenberg & David K. Levine, 2008. "An Approximate Folk Theorem with Imperfect Private Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 14, pages 309-330, World Scientific Publishing Co. Pte. Ltd..
    2. O. Gossner, 2000. "Sharing a long secret in a few public words," THEMA Working Papers 2000-15, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    3. Olivier Gossner & Tristan Tomala, 2007. "Secret Correlation in Repeated Games with Imperfect Monitoring," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 413-424, May.
    4. Kalai, E & Neme, A, 1992. "The Strength of a Little Perfection," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(4), pages 335-355.
    5. Olivier Gossner & Tristan Tomala, 2006. "Empirical Distributions of Beliefs Under Imperfect Observation," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 13-30, February.
    6. Heng Liu, 2017. "Correlation and unmediated cheap talk in repeated games with imperfect monitoring," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 1037-1069, November.
    7. Luca Lambertini, 2000. "Technology and Cartel Stability under Vertical Differentiation," German Economic Review, Verein für Socialpolitik, vol. 1(4), pages 421-442, November.
    8. Bavly, Gilad & Neyman, Abraham, 2014. "Online concealed correlation and bounded rationality," Games and Economic Behavior, Elsevier, vol. 88(C), pages 71-89.
    9. Luca Anderlini & Dino Gerardi & Roger Lagunoff, 2007. "Social Memory and Evidence from the Past," Working Papers gueconwpa~07-07-01, Georgetown University, Department of Economics.
    10. Douglas Davis & Asen Ivanov & Oleg Korenok, 2014. "Aspects of Behavior in Repeated Games: An Experimental Study," Working Papers 727, Queen Mary University of London, School of Economics and Finance.
    11. Urbano, A. & Vila, J. E., 2004. "Unmediated communication in repeated games with imperfect monitoring," Games and Economic Behavior, Elsevier, vol. 46(1), pages 143-173, January.
    12. Douglas Davis & Asen Ivanov & Oleg Korenok, 2014. "Aspects of Behavior in Repeated Games: An Experimental Study," Working Papers 727, Queen Mary University of London, School of Economics and Finance.
    13. Asen Ivanov & Douglas D. Davis & Korenok Oleg, 2011. "A Simple Approach for Organizing Behavior and Explaining Cooperation in Repeated Games," Working Papers 1101, VCU School of Business, Department of Economics.
    14. Gilli, Mario, 1999. "On Non-Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 27(2), pages 184-203, May.
    15. Ashkenazi-Golan, Galit & Lehrer, Ehud, 2019. "What you get is what you see: Cooperation in repeated games with observable payoffs," Journal of Economic Theory, Elsevier, vol. 181(C), pages 197-237.
    16. Carlos Pimienta & Jianfei Shen, 2014. "On the equivalence between (quasi-)perfect and sequential equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 395-402, May.
    17. Bergin, James, 1989. "A characterization of sequential equilibrium strategies in infinitely repeated incomplete information games," Journal of Economic Theory, Elsevier, vol. 47(1), pages 51-65, February.
    18. Dargaj, Jakub & Simonsen, Jakob Grue, 2023. "A complete characterization of infinitely repeated two-player games having computable strategies with no computable best response under limit-of-means payoff," Journal of Economic Theory, Elsevier, vol. 213(C).
    19. Spagnolo, Giancarlo, 2005. "Managerial incentives and collusive behavior," European Economic Review, Elsevier, vol. 49(6), pages 1501-1523, August.
    20. Hannu Vartiainen, 2009. "A Simple Model of Secure Public Communication," Theory and Decision, Springer, vol. 67(1), pages 101-122, July.

    More about this item

    Keywords

    Equilibrium Computation; Folk theorem; Repeated games; Bounded rationality;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • A12 - General Economics and Teaching - - General Economics - - - Relation of Economics to Other Disciplines

    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:eee:gamebe:v:117:y:2019:i:c:p:479-498. 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/622836 .

    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.