IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2205.13772.html
   My bibliography  Save this paper

Asymmetric Equilibria in Symmetric Multiplayer Prisoners Dilemma Supergames

Author

Listed:
  • Davidson Cheng

Abstract

We propose a finite automaton-style solution concept for supergames. In our model, we define an equilibrium to be a cycle of state switches and a supergame to be an infinite walk on states of a finite stage game. We show that if the stage game is locally non-cooperative, and the utility function is monotonously decreasing as the number of defective agents increases, the symmetric multiagent prisoners' dilemma supergame must contain one symmetric equilibrium and can contain asymmetric equilibria.

Suggested Citation

  • Davidson Cheng, 2022. "Asymmetric Equilibria in Symmetric Multiplayer Prisoners Dilemma Supergames," Papers 2205.13772, arXiv.org.
    • Handle: RePEc:arx:papers:2205.13772
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2205.13772
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Robert J. Aumann, 2025. "Long-Term Competition — A Game-Theoretic Analysis," World Scientific Book Chapters, in: SELECTED CONTRIBUTIONS TO GAME THEORY, chapter 8, pages 201-218, World Scientific Publishing Co. Pte. Ltd..
    2. Fey, Mark, 2012. "Symmetric games with only asymmetric equilibria," Games and Economic Behavior, Elsevier, vol. 75(1), pages 424-427.
    3. Fudenberg, Drew & Maskin, Eric, 1990. "Evolution and Cooperation in Noisy Repeated Games," American Economic Review, American Economic Association, vol. 80(2), pages 274-279, May.
    4. Rubinstein, Ariel, 1979. "Equilibrium in supergames with the overtaking criterion," Journal of Economic Theory, Elsevier, vol. 21(1), pages 1-9, 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. Andriy Zapechelnyuk & Ro'i Zultan, 2008. "Altruism, Partner Choice, and Fixed-Cost Signalling," Levine's Working Paper Archive 122247000000002199, David K. Levine.
    2. David G. Pearce, 1991. "Repeated Games: Cooperation and Rationality," Cowles Foundation Discussion Papers 983, Cowles Foundation for Research in Economics, Yale University.
    3. 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.
    4. Drew Fudenberg & David G. Rand & Anna Dreber, 2012. "Slow to Anger and Fast to Forgive: Cooperation in an Uncertain World," American Economic Review, American Economic Association, vol. 102(2), pages 720-749, April.
    5. 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.
    6. Spagnolo, Giancarlo, 2002. "Globalization and Cooperative Relations," CEPR Discussion Papers 3522, C.E.P.R. Discussion Papers.
    7. 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..
    8. 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.
    9. 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.
    10. Zhang, Huanren, 2018. "Errors can increase cooperation in finite populations," Games and Economic Behavior, Elsevier, vol. 107(C), pages 203-219.
    11. Timo Goeschl & Ole Jürgens, 2012. "Environmental quality and welfare effects of improving the reporting capability of citizen monitoring schemes," Journal of Regulatory Economics, Springer, vol. 42(3), pages 264-286, December.
    12. Piotr Swistak, 1992. "What Games? Why Equilibria? Which Equilibria?," Rationality and Society, , vol. 4(1), pages 103-116, January.
    13. Ichiro Obara, 2005. "Informational Smallness and Private Monitoring in Repeated Games (with R. McLean and A. Postlewaite)," UCLA Economics Online Papers 365, UCLA Department of Economics.
    14. Matthijs van Veelen, 2007. "Evolution of Strategies in Repeated Games with Discounting," Tinbergen Institute Discussion Papers 06-115/1, Tinbergen Institute.
    15. 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.
    16. Habu, Takuma & Lipnowski, Elliot & Ravid, Doron, 2024. "Knowing the informed player's payoffs and simple play in repeated games," Journal of Economic Theory, Elsevier, vol. 221(C).
    17. Evans, Alecia & Sesmero, Juan, 2022. "Cooperation in Social Dilemmas with Correlated Noisy Payoffs: Theory and Experimental Evidence," 2021 Annual Meeting, August 1-3, Austin, Texas 322804, Agricultural and Applied Economics Association.
    18. Bhaskar V., 1996. "On the neutral stability of mixed strategies in asymmetric contests," Mathematical Social Sciences, Elsevier, vol. 31(1), pages 56-57, February.
    19. Pedro Bó, 2007. "Social norms, cooperation and inequality," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(1), pages 89-105, January.
    20. Bhaskar, V., 1993. "Neutral Stability in Assymetric Evolutionary Games," Papers 9358, Tilburg - Center for Economic Research.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:2205.13772. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.