Risk Aversion Pays in the Class of 2 x 2 Games with No Pure Equilibrium

Simulations indicated that, in the class of 2 x 2 games which only have a mixed equilibrium, payoffs are increased by risk aversion compared to risk neutrality. In this paper I show that the total expected payoff to a player over this class in equilibrium is indeed higher if this player is risk averse than if he is risk neutral provided that all games are played with the same probability. Furthermore, I show that for two subclasses of games more risk aversion is always better, while for a third subclass an intermediate level of risk aversion is preferable.