IDEAS home Printed from https://ideas.repec.org/a/kap/theord/v97y2024i4d10.1007_s11238-024-09991-x.html
   My bibliography  Save this article

A connection between von Neumann-Morgenstern expected utility and symmetric potential games

Author

Listed:
  • Mehmet S. Ismail

    (King’s College London)

  • Ronald Peeters

    (University of Otago)

Abstract

This paper establishes a previously unexplored connection between expected utility theory and potential games. Starting with a decision problem with a complete preference relation over lotteries on a finite set of alternatives, we construct a two-person symmetric game using a payoff function that represents the preference relation, and show that if the preference relation satisfies the von Neumann-Morgenstern expected utility axioms then the constructed game is a potential game. Conversely, starting with a two-player symmetric game, we (uniquely) construct a (complete) preference relation over the lotteries using the first player’s payoffs in the game, and show that if the game is a potential game then the resulting preference relation satisfies the expected utility axioms.

Suggested Citation

  • Mehmet S. Ismail & Ronald Peeters, 2024. "A connection between von Neumann-Morgenstern expected utility and symmetric potential games," Theory and Decision, Springer, vol. 97(4), pages 707-720, December.
    • Handle: RePEc:kap:theord:v:97:y:2024:i:4:d:10.1007_s11238-024-09991-x
    DOI: 10.1007/s11238-024-09991-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11238-024-09991-x
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11238-024-09991-x?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. Ania, Ana B., 2008. "Evolutionary stability and Nash equilibrium in finite populations, with an application to price competition," Journal of Economic Behavior & Organization, Elsevier, vol. 65(3-4), pages 472-488, March.
    2. Duersch, Peter & Oechssler, Jörg & Schipper, Burkhard C., 2012. "Unbeatable imitation," Games and Economic Behavior, Elsevier, vol. 76(1), pages 88-96.
    3. Anke Gerber, 1999. "The Nash Solution and the Utility of Bargaining: A Corrigendum," Econometrica, Econometric Society, vol. 67(5), pages 1239-1240, September.
    4. Peter Duersch & Jörg Oechssler & Burkhard Schipper, 2012. "Pure strategy equilibria in symmetric two-player zero-sum games," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(3), pages 553-564, August.
    5. Schaffer, Mark E., 1989. "Are profit-maximisers the best survivors? : A Darwinian model of economic natural selection," Journal of Economic Behavior & Organization, Elsevier, vol. 12(1), pages 29-45, August.
    6. Dubey, Pradeep & Haimanko, Ori & Zapechelnyuk, Andriy, 2006. "Strategic complements and substitutes, and potential games," Games and Economic Behavior, Elsevier, vol. 54(1), pages 77-94, January.
    7. Babichenko, Yakov & Tamuz, Omer, 2016. "Graphical potential games," Journal of Economic Theory, Elsevier, vol. 163(C), pages 889-899.
    8. Roth, Alvin, 2012. "The Shapley Value as a von Neumann-Morgenstern Utility," Ekonomicheskaya Politika / Economic Policy, Russian Presidential Academy of National Economy and Public Administration, vol. 6, pages 1-9.
    9. Hehenkamp, Burkhard & Possajennikov, Alex & Guse, Tobias, 2010. "On the equivalence of Nash and evolutionary equilibrium in finite populations," Journal of Economic Behavior & Organization, Elsevier, vol. 73(2), pages 254-258, February.
    10. Voorneveld, Mark, 2000. "Best-response potential games," Economics Letters, Elsevier, vol. 66(3), pages 289-295, March.
    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. Takuya Iimura & Toshimasa Maruta & Takahiro Watanabe, 2019. "Equilibria in games with weak payoff externalities," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 245-258, December.
    2. Duersch, Peter & Oechssler, Jörg & Schipper, Burkhard C., 2010. "Pure Saddle Points and Symmetric Relative Payoff Games," Working Papers 0500, University of Heidelberg, Department of Economics.
    3. Leininger, Wolfgang & Moghadam, Hamed M., 2014. "Evolutionary Stability in Asymmetric Oligopoly. A Non-Walrasian Result," Ruhr Economic Papers 497, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    4. Duersch, Peter & Oechssler, Joerg & Schipper, Burkhard C, 2010. "Pure Saddle Points and Symmetric Relative Payoff Games," MPRA Paper 20864, University Library of Munich, Germany.
    5. Takuya Iimura & Toshimasa Maruta & Takahiro Watanabe, 2020. "Two-person pairwise solvable games," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(2), pages 385-409, June.
    6. Duersch, Peter & Oechssler, Jörg & Schipper, Burkhard C., 2012. "Unbeatable imitation," Games and Economic Behavior, Elsevier, vol. 76(1), pages 88-96.
    7. Burkhard C. Schipper, 2021. "The evolutionary stability of optimism, pessimism, and complete ignorance," Theory and Decision, Springer, vol. 90(3), pages 417-454, May.
    8. Peter Duersch & Jörg Oechssler & Burkhard Schipper, 2012. "Pure strategy equilibria in symmetric two-player zero-sum games," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(3), pages 553-564, August.
    9. Konrad, Kai A. & Morath, Florian, 2016. "Bargaining with incomplete information: Evolutionary stability in finite populations," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 118-131.
    10. Wolfgang Leininger & Hamed Moghadam, 2014. "Evolutionary Stability in Asymmetric Oligopoly. A Non-Walrasian Result," Ruhr Economic Papers 0497, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
    11. Hamed Markazi Moghadam, 2020. "Price and non-price competition in an oligopoly: an analysis of relative payoff maximizers," Journal of Evolutionary Economics, Springer, vol. 30(2), pages 507-521, April.
    12. Gu, Yiquan & Hehenkamp, Burkhard & Leininger, Wolfgang, 2019. "Evolutionary equilibrium in contests with stochastic participation: Entry, effort and overdissipation," Journal of Economic Behavior & Organization, Elsevier, vol. 164(C), pages 469-485.
    13. repec:zbw:rwirep:0497 is not listed on IDEAS
    14. Robert Philipowski, 2016. "Spiteful behavior can make everybody better off," Evolutionary and Institutional Economics Review, Springer, vol. 13(1), pages 113-116, June.
    15. Abheek Ghosh & Paul W. Goldberg, 2023. "Best-Response Dynamics in Lottery Contests," Papers 2305.10881, arXiv.org.
    16. repec:ebl:ecbull:v:3:y:2007:i:19:p:1-8 is not listed on IDEAS
    17. Christian Ewerhart, 2020. "Ordinal potentials in smooth games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 1069-1100, November.
    18. Ania, Ana B. & Wagener, Andreas, 2009. "The Open Method of Coordination (OMC) as an Evolutionary Learning Process," Hannover Economic Papers (HEP) dp-416, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    19. Martimort, David & Stole, Lars, 2012. "Representing equilibrium aggregates in aggregate games with applications to common agency," Games and Economic Behavior, Elsevier, vol. 76(2), pages 753-772.
    20. Uno, Hiroshi, 2011. "Strategic complementarities and nested potential games," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 728-732.
    21. Hehenkamp, Burkhard & Possajennikov, Alex & Guse, Tobias, 2010. "On the equivalence of Nash and evolutionary equilibrium in finite populations," Journal of Economic Behavior & Organization, Elsevier, vol. 73(2), pages 254-258, February.
    22. Olivier Tercieux & Mark Voorneveld, 2010. "The cutting power of preparation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(1), pages 85-101, February.

    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:kap:theord:v:97:y:2024:i:4:d:10.1007_s11238-024-09991-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.