Mixed Equilibrium: When Burning Money is Rational

We discuss the rationality of burning money behavior from a new perspective: the mixed Nash equilibrium. We support our argument analyzing the first-order derivatives of the mixed equilibrium expected utility of the players with respect to their own utility payoffs in a 2x2 normal form game. We establish necessary and sufficient conditions that guarantee the existence of negative derivatives. In particular, games with negative derivatives are the ones that create incentives for burning money behavior since such behavior in these games improves the player’s mixed equilibrium expected utility. We show that a negative derivative for the mixed equilibrium expected utility of a given player i occurs if, and only if, he has a strict preference for one of the strategies of the other player. Moreover, negative derivatives always occur when they are taken with respect to player i’s highest and lowest game utility payoffs.