A sequential Colonel Blotto game with a sensor network

In this paper, we pose a new sequential variant of the famous Colonel Blotto game in which two players, Player A and Player B, must allocate finite resources among N regions of a battlefield. A key new feature of our problem formulation is the introduction of a deterministic sensor network employed by Player B to gain an informational advantage over Player A. The existence of the sensor network and its properties are common knowledge in the game. We pose the resulting resource allocation game and obtain necessary conditions for Nash equilibrium optimal mixed strategies for the two players in terms of each player´s available resources and the sensor network characteristics. These conditions apply to the marginal probability distribution functions of each player´s strategy. The optimality conditions are developed using a novel case of the associated first-price all pay auctions with upper or lower bounds on the players´ allocations. A numerical example is included to show the tractability of our solution.