Colonel Blotto games with a head start

Leopold Aspect, Christian Ewerhart
This paper studies Colonel Blotto games with two battle...elds where one player has a head start in the form of additional troops on one of the battle...elds. Such games arise naturally in marketing, electoral competition, and military con ‡ict. Sion and Wolfe (1957) have shown that, if the strategy space is continuous, a mixed-strategy Nash equilibrium need not exist. Therefore, we consider a ...nite approximation. Using the iterated elimination of (weakly) dominated strategies, we identify an
more » ... equilibrium for all parameter constellations and discuss its uniqueness properties. In equilibrium, resource decisions are typically not uniform but tend to concern units that roughly correspond in size to multiples of the head start. Moreover, competition takes the form of a hideand-seek game, where the favorite tries to outguess the number of units that the underdog commits to the balanced battle...eld. Somewhat unexpectedly, equilibrium payo¤s of ...nite approximations of the Sion-Wolfe game accumulate around precisely three values. We also discuss the relation to the model with heterogeneous budgets but no head start.
doi:10.5167/uzh-220546 fatcat:bqsn7ebr5fhz5lwtcaw7ordtrm