A Blotto Game with Multi-Dimensional Incomplete Information

In the Colonel Blotto game, each of two players simultaneously allocates his fixed budget of a resource across a finite number n of battleelds. Within each battlefield, the player that allocates the higher level of the resource wins the battlefield. Each player's payoff is equal to the sum of the values of the battlefields he wins. In this paper we examine a multi-dimensional incomplete information version of the Colonel Blotto game in which each player's n-tuple of battlefield valuations is drawn from a common n-variate joint distribution function.