IDEAS home Printed from https://ideas.repec.org/a/sae/miceco/v11y2023i1p101-127.html
   My bibliography  Save this article

A Method to Select Best Among Multi-Nash Equilibria

Author

Listed:
  • M. Punniyamoorthy
  • Sarin Abraham
  • Jose Joy Thoppan

Abstract

A non-zero sum bimatrix game may yield numerous Nash equilibrium solutions while solving the game. The selection of a good Nash equilibrium from among the many options poses a dilemma. In this article, three methods have been proposed to select a good Nash equilibrium. The first approach identifies the most payoff-dominant Nash equilibrium, while the second method selects the most risk-dominant Nash equilibrium. The third method combines risk dominance and payoff dominance by giving due weights to the two criteria. A sensitivity analysis is performed by changing the relative weights of criteria to check its effect on the ranks of the multiple Nash equilibria, infusing more confidence in deciding the best Nash equilibrium. JEL Codes: C7, C72, D81

Suggested Citation

  • M. Punniyamoorthy & Sarin Abraham & Jose Joy Thoppan, 2023. "A Method to Select Best Among Multi-Nash Equilibria," Studies in Microeconomics, , vol. 11(1), pages 101-127, April.
    • Handle: RePEc:sae:miceco:v:11:y:2023:i:1:p:101-127
    DOI: 10.1177/23210222211024388
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/23210222211024388
    Download Restriction: no
    File URL: https://libkey.io/10.1177/23210222211024388?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. 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. Cooper, Russell, et al, 1990. "Selection Criteria in Coordination Games: Some Experimental Results," American Economic Review, American Economic Association, vol. 80(1), pages 218-233, March.
    3. Harsanyi John C., 1995. "A New Theory of Equilibrium Selection for Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 10(2), pages 318-332, August.
    4. Matsui Akihiko & Matsuyama Kiminori, 1995. "An Approach to Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 65(2), pages 415-434, April.
    5. Andrew Colman & Michael Bacharach, 1997. "Payoff Dominance And The Stackelberg Heuristic," Theory and Decision, Springer, vol. 43(1), pages 1-19, July.
    6. Ravi Kannan & Thorsten Theobald, 2010. "Games of fixed rank: a hierarchy of bimatrix games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 157-173, January.
    7. Sarfaraz Hashemkhani Zolfani & Reza Maknoon & Edmundas Kazimieras Zavadskas, 2015. "Multiple nash equilibriums and evaluation of strategies. New application of MCDM methods," Journal of Business Economics and Management, Taylor & Francis Journals, vol. 16(2), pages 290-306, April.
    8. Cooper, Russell & De Jong, Douglas V. & Forsythe, Robert & Ross, Thomas W., 1992. "Forward induction in coordination games," Economics Letters, Elsevier, vol. 40(2), pages 167-172, October.
    9. McLennan, Andrew & Park, In-Uck, 1999. "Generic 4 x 4 Two Person Games Have at Most 15 Nash Equilibria," Games and Economic Behavior, Elsevier, vol. 26(1), pages 111-130, January.
    10. Fevrier, Philippe & Linnemer, Laurent, 2006. "Equilibrium selection: Payoff or risk dominance?: The case of the "weakest link"," Journal of Economic Behavior & Organization, Elsevier, vol. 60(2), pages 164-181, June.
    11. Saaty, Thomas L., 1994. "Highlights and critical points in the theory and application of the Analytic Hierarchy Process," European Journal of Operational Research, Elsevier, vol. 74(3), pages 426-447, May.
    12. Andrea Saltelli, 2002. "Sensitivity Analysis for Importance Assessment," Risk Analysis, John Wiley & Sons, vol. 22(3), pages 579-590, June.
    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. Parilina, Elena M. & Zaccour, Georges, 2024. "Payment schemes for sustaining cooperation in dynamic games played over event trees," European Journal of Operational Research, Elsevier, vol. 313(3), pages 1200-1216.

    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. Rui SILVA, 2018. "Equilibrium Selection in n-Person Static Games with Complete Information," Departmental Working Papers 2018-04, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    2. Colman, Andrew M. & Stirk, Jonathan A., 1998. "Stackelberg reasoning in mixed-motive games: An experimental investigation," Journal of Economic Psychology, Elsevier, vol. 19(2), pages 279-293, April.
    3. Jun Honda, 2015. "Games with the Total Bandwagon Property," Department of Economics Working Papers wuwp197, Vienna University of Economics and Business, Department of Economics.
    4. Konstantinos Georgalos & Indrajit Ray & Sonali SenGupta, 2020. "Nash versus coarse correlation," Experimental Economics, Springer;Economic Science Association, vol. 23(4), pages 1178-1204, December.
    5. Bodoff, David, 2020. "The Power of Focal Points is Strong: Coordination Games with Labels and Payoffs," MPRA Paper 102213, University Library of Munich, Germany.
    6. Kenneth Clark & Stephen Kay & Martin Sefton, 2001. "When are Nash equilibria self-enforcing? An experimental analysis," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(4), pages 495-515.
    7. Philippe Février & Laurent Linnemer, 2002. "Strengths of the "Weakest Link"?," Working Papers 2002-24, Center for Research in Economics and Statistics.
    8. Mielke, Jahel & Steudle, Gesine A., 2018. "Green Investment and Coordination Failure: An Investors' Perspective," Ecological Economics, Elsevier, vol. 150(C), pages 88-95.
    9. Colman, Andrew M. & Pulford, Briony D. & Bolger, Fergus, 2007. "Asymmetric dominance and phantom decoy effects in games," Organizational Behavior and Human Decision Processes, Elsevier, vol. 104(2), pages 193-206, November.
    10. Thomas Neumann & Bodo Vogt, 2009. "Do Players’ Beliefs or Risk Attitudes Determine The Equilibrium Selections in 2x2 Coordination Games?," FEMM Working Papers 09024, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    11. Zhang, Boyu, 2016. "Quantal response methods for equilibrium selection in normal form games," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 113-123.
    12. Andreas Blume & Peter H. Kriss & Roberto A. Weber, 2017. "Pre-play communication with forgone costly messages: experimental evidence on forward induction," Experimental Economics, Springer;Economic Science Association, vol. 20(2), pages 368-395, June.
    13. Jan Libich & Dat Thanh Nguyen & Hubert Janos Kiss, 2023. "Running Out of Bank Runs," Journal of Financial Services Research, Springer;Western Finance Association, vol. 64(1), pages 1-39, August.
    14. Georgalos, Konstantinos & Ray, Indrajit & Gupta, Sonali Sen, 2019. "Nash vs. Coarse Correlation," Cardiff Economics Working Papers E2019/3, Cardiff University, Cardiff Business School, Economics Section.
    15. Jun Honda, 2018. "Games with the total bandwagon property meet the Quint–Shubik conjecture," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 893-912, September.
    16. Jia Liu & Yohanes E. Riyanto, 2017. "Information transparency and equilibrium selection in coordination games: an experimental study," Theory and Decision, Springer, vol. 82(3), pages 415-433, March.
    17. 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.
    18. Simai He & Jay Sethuraman & Xuan Wang & Jiawei Zhang, 2017. "A NonCooperative Approach to Cost Allocation in Joint Replenishment," Operations Research, INFORMS, vol. 65(6), pages 1562-1573, December.
    19. Ennis, Huberto M. & Keister, Todd, 2005. "Government policy and the probability of coordination failures," European Economic Review, Elsevier, vol. 49(4), pages 939-973, May.
    20. Dieter Balkenborg & Rosemarie Nagel, 2016. "An Experiment on Forward vs. Backward Induction: How Fairness and Level k Reasoning Matter," German Economic Review, Verein für Socialpolitik, vol. 17(3), pages 378-408, August.

    More about this item

    Keywords

    Game theory; two-person non-zero-sum game; risk dominance; payoff dominance; mixed Nash equilibrium selection;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    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:sae:miceco:v:11:y:2023:i:1:p:101-127. 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: SAGE Publications (email available below). General contact details of provider: .

    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.