Battlefield Transfers in Coalitional Blotto Games

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.