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In the Colonel Blotto game, two players with a fixed budget simultaneouslyallocate their resources across n battlefields to maximize the aggregate valuegained from the battlefields where they have the higher allocation. Despite itslong-standing history and important applications, the Colonel Blotto game stilllacks a complete Nash equilibrium characterization in its most general formwhere players are asymmetric and battlefields' values are heterogeneous acrossbattlefields and different between the two players---this is called theGeneralized Colonel Blotto game. In this work, we propose a simply-constructedclass of strategies---the independently uniform strategies---and we prove thatthey are approximate equilibria of the Generalized Colonel Blotto game;moreover, we characterize the approximation error according to the game'sparameters. We also consider an extension called the Generalized Lottery Blottogame, with stochastic winner-determination rules allowing more flexibility inmodeling practical contests. We prove that the proposed strategies are alsoapproximate equilibria of the Generalized Lottery Blotto game.

Approximate Equilibria in Generalized Colonel Blotto and Generalized Lottery Blotto Games