The Colonel Blotto game with applications to the economic, military and political sciences

Brian A Roberson, Purdue University


In the Colonel Blotto game, two players simultaneously distribute forces across n battlefields. Within each battlefield, the player that allocates more force wins. The payoff of the game is the proportion of the wins on the individual battlefields. An equilibrium of the Colonel Blotto game consists of a pair of n-variate distributions. Chapter 1 demonstrates how to separate the players' best response correspondences into a set of univariate marginal distributions and a mapping of this set into an n-variate distribution; fully characterizes the equilibrium univariate marginal distributions for this class of games; and constructs corresponding equilibrium n-variate distributions. Chapter 2 compares centralized to decentralized electoral competition in a model of redistributive politics with local public goods. In this setting, the level of inequality arising from each party's equilibrium redistribution schedule is higher in a centralized system. In addition, if the utilities provided by the local public goods are above a minimal threshold, then centralization is also found to create greater inefficiencies in the provision of the local public goods. However, the inefficiency of centralization is due to the targetability of local public goods and the ability to share resources across jurisdictions not to interjurisdictional externalities or heterogeneities in the production of or preferences for local public goods. Chapter 3 examines electoral competition in a model of redistributive politics with heterogeneous voter loyalties to political parties. We construct a natural measure of "party strength" based on the sizes and intensities of a party's loyal voter segments and demonstrate how party behavior varies with the two parties' strengths. In equilibrium, parties target or "poach" a strict subset of the opposition party's loyal voters: offering those voters a high expected transfer, while "freezing out" the remainder with a zero transfer. The size of the subset of opposition voters frozen out and, consequently, the level of inequality in a party's equilibrium redistribution schedule is increasing in the opposition party's strength. We also construct a measure of "political polarization" that is increasing in the sum and symmetry of the parties' strengths, and find that the inequality of the implemented policy is increasing in political polarization.




Moore, Purdue University.

Subject Area

Economic theory|Political science

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