Stochastic Superiority Equilibrium in Game Theory

Ali Yekkehkhany (), Timothy Murray () and Rakesh Nagi ()
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Ali Yekkehkhany: Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
Timothy Murray: Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
Rakesh Nagi: Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801

Decision Analysis, 2021, vol. 18, issue 2, 153-168

Abstract: The definition of best response for a player in the Nash equilibrium is based on maximizing the expected utility given the strategy of the rest of the players in a game. In this work, we consider stochastic games, that is, games with random payoffs, in which a finite number of players engage only once or at most a limited number of times. In such games, players may choose to deviate from maximizing their expected utility. This is because maximizing expected utility strategy does not address the uncertainty in payoffs. We instead define a new notion of a stochastic superiority best response. This notion of best response results in a stochastic superiority equilibrium in which players choose to play the strategy that maximizes the probability of them being rewarded the most in a single round of the game rather than maximizing the expected received reward, subject to the actions of other players. We prove the stochastic superiority equilibrium to exist in all finite games, that is, games with a finite number of players and actions, and numerically compare its performance to Nash equilibrium in finite-time stochastic games. In certain cases, we show the payoff under the stochastic superiority equilibrium is 70% likely to be higher than the payoff under Nash equilibrium.

Keywords: stochastic game theory; stochastic superiority equilibrium; risk aversion; prospect theory (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ordeca:v:18:y:2021:i:2:p:153-168

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