Incorporating risk preferences in stochastic noncooperative games

Abstract

ABSTRACTTraditional game-theoretic models of competition with uncertainty often ignore preferences and attitudes toward risk by assuming that players are risk neutral. In this article, we begin by considering how a comprehensive analysis and incorporation of expected utility theory affect players’ equilibrium behavior in a simple, single-period, sequential stochastic game. Although the literature posits that the more risk averse a first mover is, the more likely she is to compete and defend her position as the “leader”, and that the more risk seeking a “follower” is, the more likely he is willing to participate and compete, we find that this behavior may not always be true in this more general setting. Under simple assumptions on the utility function, we perform sensitivity analyses on the parameters and show which behavior changes when deviations from risk neutrality are introduced into a model. We also provide some insights on how risk preferences influence pre-emption and interdiction by looking at how these preferences affect the first mover’s advantage in a sequential setting. This article generates novel insights when a confluence of factors leads players to deviate or change their behavior in many risk analysis settings where stochastic games are used.