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 plus the number of resources available to the players.

翻译：本文研究布洛托上校博弈的一个广义变体，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"不用即废"的预算假设不同，带成本的布洛托上校博弈刻画了获取资源及在战场间分配资源所产生成本的战略重要性。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一个增加了一个战场的零和布洛托上校博弈实例。这使得我们能够以关于博弈参数（战场数量与玩家可用资源数量之和）的多项式时间计算带成本的布洛托上校博弈的纳什均衡。