Risk Aversion Pays int he class of 2 £ 2 Games with No Pure Equilibrium

Simulations indicated that in the class of 2 £ 2 games which only have a mixed equilibrium payo¤s are increased by risk aversion compared to risk neutrality. In this note I show that the total expected payo¤ to a player over this class in equilibrium is indeed higher if this player is risk averse than if he is first 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.