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

Mehmet S. Ismail () and Ronald Peeters
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Mehmet S. Ismail: King’s College London

Theory and Decision, 2024, vol. 97, issue 4, No 5, 707-720

Abstract: 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.

Keywords: Expected utility; Potential games; Symmetric two-player games; SSB utility; Independence axiom (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11238-024-09991-x

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