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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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    References listed on IDEAS

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