IDEAS home Printed from https://ideas.repec.org/a/bpj/bejtec/v11y2011i1n10.html
   My bibliography  Save this article

Stochastic Stability in Finitely Repeated Two Player Games

Author

Listed:
  • Robles Jack

    (Victoria University of Wellington)

Abstract

We apply stochastic stability to undiscounted finitely repeated two player games without common interests. We prove an Evolutionary Feasibility Theorem as an analog to the Folk Theorem (Benoit and Krishna, 1985 and 1987). Specifically, we demonstrate that as repetitions go to infinity, the set of stochastically stable equilibrium payoffs converges to the set of individually rational and feasible payoffs. This derivation requires stronger assumptions than the Nash Folk Theorem (Benoit and Krishna, 1987). It is demonstrated that the stochastically stable equilibria are stable as a set, but unstable as individual equilibria. Consequently, the Evolutionary Feasibility Theorem makes no prediction more specific than the entire individually rational and feasible set.

Suggested Citation

  • Robles Jack, 2011. "Stochastic Stability in Finitely Repeated Two Player Games," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-24, April.
    • Handle: RePEc:bpj:bejtec:v:11:y:2011:i:1:n:10
    DOI: 10.2202/1935-1704.1686
    as

    Download full text from publisher

    File URL: https://doi.org/10.2202/1935-1704.1686
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.2202/1935-1704.1686?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. Kreps, David M. & Milgrom, Paul & Roberts, John & Wilson, Robert, 1982. "Rational cooperation in the finitely repeated prisoners' dilemma," Journal of Economic Theory, Elsevier, vol. 27(2), pages 245-252, August.
    2. Glenn Ellison, 2000. "Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(1), pages 17-45.
    3. James W. Friedman, 1971. "A Non-cooperative Equilibrium for Supergames," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(1), pages 1-12.
    4. Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-396, March.
    5. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    6. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    7. 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..
    8. Radner, Roy, 1980. "Collusive behavior in noncooperative epsilon-equilibria of oligopolies with long but finite lives," Journal of Economic Theory, Elsevier, vol. 22(2), pages 136-154, April.
    9. Robles, Jack, 2001. "Evolution in Finitely Repeated Coordination Games," Games and Economic Behavior, Elsevier, vol. 34(2), pages 312-330, February.
    10. Friedman, James W., 1985. "Cooperative equilibria in finite horizon noncooperative supergames," Journal of Economic Theory, Elsevier, vol. 35(2), pages 390-398, August.
    11. Sobel, Joel, 1993. "Evolutionary stability and efficiency," Economics Letters, Elsevier, vol. 42(2-3), pages 301-312.
    12. Griffin, James M & Xiong, Weiwen, 1997. "The Incentive to Cheat: An Empirical Analysis of OPEC," Journal of Law and Economics, University of Chicago Press, vol. 40(2), pages 289-316, October.
    13. 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)

    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. Thijssen, J.J.J., 2003. "Investment under uncertainty, market evolution and coalition spillovers in a game theoretic perspective," Other publications TiSEM 672073a6-492e-4621-8d4a-0, Tilburg University, School of Economics and Management.
    2. Matthias Blonski & Giancarlo Spagnolo, 2015. "Prisoners’ other Dilemma," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 61-81, February.
    3. Jean J. Gabszewicz & Jacques-François Thisse, 2000. "Microeconomic theories of imperfect competition," Cahiers d'Économie Politique, Programme National Persée, vol. 37(1), pages 47-99.
    4. Aumann, Robert J., 1997. "Rationality and Bounded Rationality," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 2-14, October.
    5. Etro, Federico, 2017. "Research in economics and game theory. A 70th anniversary," Research in Economics, Elsevier, vol. 71(1), pages 1-7.
    6. Chaim Fershtman, 1987. "Cooperation Through Delegation," Discussion Papers 731, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    7. 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.
    8. Shota Fujishima, 2015. "The emergence of cooperation through leadership," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 17-36, February.
    9. Paul Seabright, 1993. "Managing Local Commons: Theoretical Issues in Incentive Design," Journal of Economic Perspectives, American Economic Association, vol. 7(4), pages 113-134, Fall.
    10. Anderlini, Luca & Sabourian, Hamid, 2001. "Cooperation and computability in n-player games," Mathematical Social Sciences, Elsevier, vol. 42(2), pages 99-137, September.
    11. García, Julián & van Veelen, Matthijs, 2016. "In and out of equilibrium I: Evolution of strategies in repeated games with discounting," Journal of Economic Theory, Elsevier, vol. 161(C), pages 161-189.
    12. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    13. Mason, Charles F. & Polasky, Stephen, 2005. "What motivates membership in non-renewable resource cartels?: The case of OPEC," Resource and Energy Economics, Elsevier, vol. 27(4), pages 321-342, November.
    14. Kalai, Ehud & Ledyard, John O., 1998. "Repeated Implementation," Journal of Economic Theory, Elsevier, vol. 83(2), pages 308-317, December.
    15. 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.
    16. Zhang, Huanren, 2018. "Errors can increase cooperation in finite populations," Games and Economic Behavior, Elsevier, vol. 107(C), pages 203-219.
    17. Jean-Pierre Benoît & Vijay Krishna, 1996. "The Folk Theorems for Repeated Games - A Synthesis," Discussion Papers 96-03, University of Copenhagen. Department of Economics.
    18. Jindani, Sam, 2022. "Learning efficient equilibria in repeated games," Journal of Economic Theory, Elsevier, vol. 205(C).
    19. Vincenzo Scoppa, 2003. "Contratti incompleti ed enforcement endogeno. Una rassegna della letteratura," Economia politica, Società editrice il Mulino, issue 3, pages 391-440.
    20. Jackson, Matthew O. & Kalai, Ehud, 1997. "Social Learning in Recurring Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 102-134, October.

    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:bpj:bejtec:v:11:y:2011:i:1:n:10. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    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.