A Note on a Comparison of Simultaneous and Sequential Colonel Blotto Games

Abstract

Abstract Clark and Konrad (2007) introduce the weakest link against the best shot property to the Colonel Blotto game where the defendant has to win all the battle fields while the attacker only needs to win at least one battlefield. They characterize the Nash equilibrium assuming that the attacker attacks all the battlefields simultaneously. We construct a two stage model and endogenize the attacker’s attack pattern. We show that the attacker chooses a sequential attack pattern in the subgame perfect Nash equilibrium. Therefore, the game analyzed by Clark and Konrad (2007) is never realized. We also conducted experiments and found that the subjects’ behavior was inconsistent to theoretical predictions. Both players overinvested and the variances were large. In the simultaneous game, the attackers took a guerrira strategy at 30% of the time in which they invested only in one battlefield and the defenders took a surrender strategy at 11% of the time in which they invested nothing in the simultaneous game. Both players invested more in period 1 than in period 2 in the sequential game. Although all of these are inconsistent to the theoretical predictions, the winning probability of a game was consistent to the theoretical prediction in the simultaneous games, but it was lower than the theoretical prediction in the sequential games. We conclude that the subjects’ irrational behavior is mainly a rational response to his/ her opponent’s irrational behavior. Our model can explain terrorism, cyber terrorism, lobbying, and patent trolls and the huge gap between the theory and the experiments are important considering the significance of the problems.