Contests between Players with Mean-Variance Preferences

Abstract

We study contests between players who rank uncertain outcomes using two parameters: the mean and the variance. This framework admits situations where players do not obey the axioms of expected utility maximization and represents an interesting modification of the usual assumptions in the contest literature. We demonstrate the existence of a unique equilibrium in the case of many heterogeneous players and examine a number of features of equilibrium behaviour. In a contest between two players who value the prize equally but have different strictly positive variance aversion parameters, the player with greater aversion to variance will put in less effort than the player with lower aversion to variance. If there are two identical variance averse players in the contest, we obtain an irrelevance result: even though the players are variance-averse and do not obey the axioms of expected utility theory, in equilibrium their efforts are identical to the equilibrium efforts of players who are risk neutral expected utility maximizers. Finally, we derive equilibrium efforts for the symmetric n>2 player case, and show that variance aversion unambiguously results in less rent dissipation than the risk neutral case.