Risk aversion in game theory is usually modeled using expected utility, which was criticized early on, leading to an extensive literature on generalized expected utility. In this paper we are the first to apply Âµâ€“Ïƒ theory to the analysis of (static) games. Âµâ€“Ïƒ theory is widely accepted in the finance literature; using it allows us to study the effect on uncertainty endogenous to the game, i.e., mixed equilibria. In particular, we look at the case of linear Âµâ€“Ïƒ utility functions and determine the best response strategy. In the case of 2 Ã— 2 and N Ã— M games, we are able to characterize all mixed equilibria.