In competitive resource allocation environments, agents often choose to form alliances; however, for some agents, doing so may not always be beneficial. Is there a method of forming alliances that always reward each of their members? We study this question using the framework of the coalitional Blotto game, in which two players compete against a common adversary by allocating their budgeted resources across disjoint sets of valued battlefields. On any given battlefield, the agent that allocates a greater amount of resources wins the corresponding battlefield value. Existing work has shown the surprising result that in certain game instances, if one player donates a portion of their budget to the other player, then both players win larger amounts in their separate competitions against the adversary. However, this transfer-based method of alliance formation is not always mutually beneficial, which motivates the search for alternate strategies. In this vein, we study a new method of alliance formation referred to as a joint transfer, whereby players publicly transfer battlefields and budgets between one another before they engage in their separate competitions against the adversary. We show that in almost all game instances, there exists a mutually beneficial joint transfer that strictly increases the payoff of each player.

翻译：在竞争性资源分配环境中，智能体常选择结盟；然而，对某些智能体而言，结盟未必总是有利。是否存在一种结盟方法，能始终使所有成员获益？我们通过联盟式布洛托博弈框架研究该问题：两名玩家通过将预算资源分配到互不相交的估值战场集合上，共同对抗一个对手。在任何特定战场上，分配资源量更大的智能体将赢得对应战场价值。现有研究表明，在某些博弈实例中，若一名玩家将部分预算捐赠给另一名玩家，则双方在各自对抗对手的竞争中均能赢得更大收益。然而，这种基于资源转移的结盟方式并非总是互惠的，这促使我们寻找替代策略。为此，我们研究了一种称为联合转移的新结盟方法：玩家在各自对抗对手前，公开进行战场与预算的相互转移。我们证明，在几乎所有博弈实例中，都存在严格提升各方收益的互惠联合转移方案。