A class of risk-sensitive noncooperative games

Abstract

Risk sensitivity is studied in connection to a class of noncooperative games with incomplete information. Specifically, we consider a two-player noncooperative stochastic game where each player maximizes the expected value of a utility function with constant absolute risk aversion. The approach generalizes more traditional models for economic policy evaluation, including the linear-quadratic stochastic Nash game studied by Papavassilopoulos (1981) and the exponential-quadratic function studied, in the context of single decision making, by Van der Ploeg (1984). Conditions for the existence of noncooperative equilibria are derived. The paper offers new insight on the influence of risk attitudes on equilibrium. It is shown, among other results, that in the assumption of Gaussian distribution of the random variables a Nash equilibrium may not exist when players risk attitudes are too conservative. The main results are illustrated with an example.