We study equilibrium in a multi-battle attack-and-defense game in which victory in each single battle is deterministically awarded to the player who expends more conflict resources in the respective battle. One player has a pre-determined budget which can be allocated across two battlefields. The cost of the budget is sunk. The other player can mobilize an arbitrary amount of resources at given marginal costs. Our analysis reveals a strategic advantage of the player with the fixed and given budget: this player wins all battlefields with probability one if the budget is at least half the total value of winning.

中文翻译：

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如何在资源有限的多线冲突中抢占先机

我们研究了多战攻防游戏中的平衡，其中每场战斗的胜利确定性地授予在各自战斗中消耗更多冲突资源的玩家。一名玩家有一个预先确定的预算，可以分配给两个战场。预算的成本是沉没的。另一方可以以给定的边际成本调动任意数量的资源。我们的分析揭示了具有固定且给定预算的玩家的战略优势：如果预算至少是获胜总价值的一半，则该玩家以概率 1 赢得所有战场。