Generalizations of the General Lotto and Colonel Blotto games

Abstract

In this paper, we generalize the General Lotto game (budget constraints satisfied in expectation) and the Colonel Blotto game (budget constraints hold with probability one) to allow for battlefield valuations that are heterogeneous across battlefields and asymmetric across players and for the players to have asymmetric resource constraints. We completely characterize Nash equilibrium in the generalized version of the General Lotto game and find that there exist sets of nonpathological parameter configurations of positive Lebesgue measure with multiple payoff nonequivalent equilibria. Across equilibria each player achieves a higher payoff when he more aggressively attacks battlefields in which he has lower relative valuations. Hence, the best defense is a good offense. We, then, show how this characterization can be applied to identify equilibria in the Colonel Blotto version of the game.