A Continuous Colonel Blotto Game

Abstract

Abstract : Colonel Blotto and the enemy are confronted with the following situation: Colonel Blotto has at his disposal a total of B( 0) units of attack, capable of continuous partition; whereas the enemy has E( 0) units of like character. They are to attack simultaneously and in full force a set of n hills of different value, such that the payoff by the enemy to C. B. for the jth hill is +a(sub j)( 0) if Blotto's forces exceed his there, -a(sub j) if the enemy's exceed Blotto's, and 0 otherwise. How should they play?

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