This paper studies a generalized variant of the Colonel Blotto game, referred to as the Colonel Blotto game with costs. Unlike the classic Colonel Blotto game, which imposes the use-it-or-lose-it budget assumption, the Colonel Blotto game with costs captures the strategic importance of costs related both to obtaining resources and assigning them across battlefields. We show that every instance of the Colonel Blotto game with costs is strategically equivalent to an instance of the zero-sum Colonel Blotto game with one additional battlefield. This enables the computation of Nash equilibria of the Colonel Blotto game with costs in polynomial time with respect to the game parameters: the number of battlefields and the number of resources available to the players.

翻译：本文研究布洛托上校博弈的一种广义变体，称为带成本的布洛托上校博弈。与经典布洛托上校博弈采用"用尽或失效"的预算假设不同，带成本的布洛托上校博弈刻画了资源获取与战场分配相关成本的战略重要性。我们证明，任何带成本的布洛托上校博弈实例在战略上都等价于增加一个战场的零和布洛托上校博弈实例。这使得带成本的布洛托上校博弈的纳什均衡计算可在多项式时间内完成，计算复杂度取决于博弈参数：战场数量和玩家可用资源数量。