Abstract: We analyze the strategic allocation of resources across two contests as in the canonical Colonel Blotto game. Such environments were among the first to be studied in game theory. In the games we study, two players simultaneously allocate their forces across two fields of battle. The larger force on each front wins that battle, and the payoff to a player is the sum of the values of fronts won. We completely characterize the set of Nash equilibria of all two battlefield Blotto games and provide the unique equilibrium payoffs. Our characterization extends to cover previously unstudied games with nonlinear resource constraints.
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Scott T. Macdonell, Ph.D. 