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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
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    1. Duersch, Peter & Oechssler, Jörg & Schipper, Burkhard C., 2012. "Unbeatable imitation," Games and Economic Behavior, Elsevier, vol. 76(1), pages 88-96.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Voorneveld, Mark, 2000. "Best-response potential games," Economics Letters, Elsevier, vol. 66(3), pages 289-295, March.
    7. 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.
    8. Anke Gerber, 1999. "The Nash Solution and the Utility of Bargaining: A Corrigendum," Econometrica, Econometric Society, vol. 67(5), pages 1239-1240, September.
    9. 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.
    10. Babichenko, Yakov & Tamuz, Omer, 2016. "Graphical potential games," Journal of Economic Theory, Elsevier, vol. 163(C), pages 889-899.
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