IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v144y2024icp378-394.html
   My bibliography  Save this article

Beyond dominance and Nash: Ranking equilibria by critical mass

Author

Listed:
  • Kalai, Adam Tauman
  • Kalai, Ehud

Abstract

Strategic interactions pose central issues that are not adequately explained by the traditional concepts of dominant strategy equilibrium (DSE), Nash equilibrium (NE), and their refinements. A comprehensive analysis of equilibrium concepts within the von Neumann-Nash framework of n-person optimization reveals a decreasing hierarchy of n nested concepts ranging from DSE to NE. These concepts are defined by the “critical mass,” the number of players needed to adopt and sustain the play of a strategy profile as an equilibrium. In games with n>2 players, the n−2 intermediate concepts explain strategic issues in large social systems, implementation, decentralization, as well as replication studied in economics, operations management, and political games.

Suggested Citation

  • Kalai, Adam Tauman & Kalai, Ehud, 2024. "Beyond dominance and Nash: Ranking equilibria by critical mass," Games and Economic Behavior, Elsevier, vol. 144(C), pages 378-394.
    • Handle: RePEc:eee:gamebe:v:144:y:2024:i:c:p:378-394
    DOI: 10.1016/j.geb.2024.01.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825624000113
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2024.01.011?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. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, April.
    2. Gradwohl, Ronen & Reingold, Omer, 2014. "Fault tolerance in large games," Games and Economic Behavior, Elsevier, vol. 86(C), pages 438-457.
    3. Crawford, Vincent P, 1995. "Adaptive Dynamics in Coordination Games," Econometrica, Econometric Society, vol. 63(1), pages 103-143, January.
    4. 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.
    5. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    6. Duk Gyoo Kim & Daehong Min & John Wooders, 2022. "Viable Nash Equilibria: An Experiment," CESifo Working Paper Series 9913, CESifo.
    7. Kfir Eliaz, 2002. "Fault Tolerant Implementation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(3), pages 589-610.
    8. Bernheim, B. Douglas & Peleg, Bezalel & Whinston, Michael D., 1987. "Coalition-Proof Nash Equilibria I. Concepts," Journal of Economic Theory, Elsevier, vol. 42(1), pages 1-12, June.
    9. Marina Halac & Ilan Kremer & Eyal Winter, 2020. "Raising Capital from Heterogeneous Investors," American Economic Review, American Economic Association, vol. 110(3), pages 889-921, March.
    10. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
    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. Kets, Willemien & Kager, Wouter & Sandroni, Alvaro, 2022. "The value of a coordination game," Journal of Economic Theory, Elsevier, vol. 201(C).
    2. Willemien Kets & Alvaro Sandroni, 2021. "A Theory of Strategic Uncertainty and Cultural Diversity," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 88(1), pages 287-333.
    3. Nax, Heinrich Harald & Newton, Jonathan, 2022. "Deep and shallow thinking in the long run," Theoretical Economics, Econometric Society, vol. 17(4), November.
    4. Dal Bó, Pedro & Fréchette, Guillaume R. & Kim, Jeongbin, 2021. "The determinants of efficient behavior in coordination games," Games and Economic Behavior, Elsevier, vol. 130(C), pages 352-368.
    5. Battalio,R. & Samuelson,L. & Huyck,J. van, 1998. "Risk dominance, payoff dominance and probabilistic choice learning," Working papers 2, Wisconsin Madison - Social Systems.
    6. Pedro Dal Bo & Guillaume R. Frochette, 2011. "The Evolution of Cooperation in Infinitely Repeated Games: Experimental Evidence," American Economic Review, American Economic Association, vol. 101(1), pages 411-429, February.
    7. Cabrales, Antonio & Garcia-Fontes, Walter & Motta, Massimo, 2000. "Risk dominance selects the leader: An experimental analysis," International Journal of Industrial Organization, Elsevier, vol. 18(1), pages 137-162, January.
    8. Alexander Funcke & Daniel Cownden, 2015. "A Mechanism for Optimal Enforcement of Coordination: Sidestepping Theory of Mind," PPE Working Papers 0003, Philosophy, Politics and Economics, University of Pennsylvania.
    9. Goeree, Jacob K. & Holt, Charles A., 2005. "An experimental study of costly coordination," Games and Economic Behavior, Elsevier, vol. 51(2), pages 349-364, May.
    10. Flavio M. Menezes & Paulo K. Monteiro & Akram Temimi, 1998. "Equilibrium Selection and the Rate of Convergence in Coordination Games with Simultaneous Play," Discussion Papers 98-14, University of Copenhagen. Department of Economics.
    11. Pilwon Kim & Dongryul Lee, 2019. "Repeated minimum-effort coordination games," Journal of Evolutionary Economics, Springer, vol. 29(4), pages 1343-1359, September.
    12. Masiliūnas, Aidas, 2019. "Overcoming inefficient lock-in in coordination games with sophisticated and myopic players," Mathematical Social Sciences, Elsevier, vol. 100(C), pages 1-12.
    13. Bosch-Domènech, Antoni & Vriend, Nicolaas J., 2013. "On the role of non-equilibrium focal points as coordination devices," Journal of Economic Behavior & Organization, Elsevier, vol. 94(C), pages 52-67.
    14. Maarten C.W. Janssen, 1997. "Focal Points," Tinbergen Institute Discussion Papers 97-091/1, Tinbergen Institute.
    15. Michael Kosfeld, 2002. "Stochastic strategy adjustment in coordination games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(2), pages 321-339.
    16. Sanjeev Goyal & Fernando Vega-Redondo, 2000. "Learning, Network Formation and Coordination," Econometric Society World Congress 2000 Contributed Papers 0113, Econometric Society.
    17. Jun Honda, 2015. "Games with the Total Bandwagon Property," Department of Economics Working Papers wuwp197, Vienna University of Economics and Business, Department of Economics.
    18. , & , & ,, 2008. "Monotone methods for equilibrium selection under perfect foresight dynamics," Theoretical Economics, Econometric Society, vol. 3(2), June.
    19. 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.
    20. Norman, Thomas W.L., 2009. "Rapid evolution under inertia," Games and Economic Behavior, Elsevier, vol. 66(2), pages 865-879, July.

    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:144:y:2024:i:c:p:378-394. 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.