Majoritarian contests with asymmetric battlefields: An experiment

We investigate a version of the classic Colonel Blotto game in which individual battles may have different values. Two players allocate a fixed budget across battlefields and each battlefield is won by the player who allocates the most to that battlefield. The winner of the game is the player who wins the battlefields with highest total value. We focus on the case where there is one large and several small battlefields, such that a player wins if he wins the large and any one small battlefield, or all the small battlefields. We compute the mixed strategy equilibrium for these games and compare this with choices from a laboratory experiment. The equilibrium predicts that the large battlefield receives more than a proportional share of the resources of the players, and that most of the time resources should be spread over more battlefields than are needed to win the game. We find support for the main qualitative features of the equilibrium. In particular, strategies that spread resources widely are played frequently, and the large battlefield receives more than a proportional share in the treatment where the asymmetry between battlefields is stronger.