In this work, we consider the framework of coalitional Blotto games in which two players compete against a common adversary by allocating their budgeted resources across disjoint sets of valued battlefields; the agent that allocates a higher amount wins the corresponding battlefield value. At the beginning of the game, the budgets of the agents and the values of the battlefields are specified. In the first stage, the players are allowed to perform a battlefield transfer in which one player offloads a number of its battlefields onto the other player. In the second stage, the adversary observes this transfer and determines how to allocate their budget accordingly. Finally, in the third stage, the players and the adversary allocate their budgets to their battlefields, the game is played, and their payoffs are realized. We provide necessary and sufficient conditions for the existence of a battlefield transfer that strictly increases the payoff of each player. We then augment the model, allowing players to not only transfer subsets of battlefields, but also portions of their budget, in the first stage. We also provide sufficient conditions for the existence of a joint transfer of battlefields and budgets. The results demonstrate that in almost all game instances, both players would benefit from such a joint transfer.

翻译：在本文中，我们研究了联盟性布洛托博弈框架，其中两个玩家通过与共同对手竞争，将预算资源分配到不相交的价值战场集合上；分配资源较高的玩家赢得相应战场的价值。游戏开始时，玩家预算和战场价值已确定。在第一阶段，允许玩家进行战场转移，即一名玩家将其部分战场转移给另一名玩家。在第二阶段，对手观察到这一转移，并决定如何相应分配其预算。最后，在第三阶段，玩家与对手将其预算分配到各自战场，游戏进行，最终获得收益。我们提出了严格增加每位玩家收益的战场转移存在性的充要条件。随后，我们扩展模型，允许玩家在第一阶段不仅转移战场子集，还可转移部分预算。我们还提供了战场与预算联合转移存在性的充分条件。结果表明，在几乎所有的博弈实例中，两位玩家都将从这种联合转移中获益。