Budget and Effort Choice in Sequential Colonel Blotto Campaigns

Abstract

Military campaigns are studied as dynamic best-of-three contests, where final victory is attributed to the first player who wins a critical number of battles. The article studies how overall budget constraints and different assumptions about the destruction of military resources used in a given battle affect the dynamics and overall equilibrium resources in a best-of-three contest. Discouragement effects for players who lag behind and the showdown effect when the campaign reaches a more decisive state vanish if players have to choose an overall budget and can draw on what is left from this budget in the course of the campaign. This is true both in a context in which the resources allocated to a battle are used up there as well as if player’s battle resources carry over to future battles. If only the winner’s contest resources carryover, this generates precautionary behavior of the leading player and all-in behavior for the player lagging behind.