Sequential Majoritarian Blotto Games

Abstract

We study Colonel Blotto games with sequential battles and a majoritarian objective. For a large class of contest success functions, the equilibrium is unique and characterized by an even split: Each battle that is reached before one of the players wins a majority of battles is allocated the same amount of resources from the player's overall budget. As a consequence, a player's chance of winning any particular battle is independent of the battlefield and of the number of victories and losses the player accumulated in prior battles. This result is in stark contrast to equilibrium behavior in sequential contests that do not involve either fixed budgets or a majoritarian objective. We also consider the equilibrium choice of an overall budget. For many contest success functions, if the sequence of battles is long enough the payoff structure in this extended games resembles an all-pay auction without noise.

Power indices, claims games and core selection

“…These have been and are studied in the literature, but usually as a series of simultaneous Blotto games or more generally, contests. See, e.g., Klumpp and Konrad [39] and the references therein. Section 4.2 is devoted to definitions and a few preliminary results, Section 4.3 to myopic play as a Nash equilibrium, and Section 4.4 mainly to myopic play with punishment as a subgame perfect equilibrium.…”