How do different alliance mechanisms compare? In this work, we analyze various methods of forming an alliance in the Coalitional General Lotto game, a simple model of competitive resource allocation. In the game, Players 1 and 2 independently compete against a common Adversary by allocating their limited resource budgets towards separate sets of contests; an agent wins a contest by allocating more resources towards it than their opponent. In this setting, we study three alliance mechanisms: budget transfers (resource donation), contest transfers (contest redistribution), and joint transfers (both simultaneously). For all three mechanisms, we study when they present opportunities for collective improvement (the sum of the Players' payoffs increases) or mutual improvement (both Players' individual payoffs increase). In our first result, we show that all three are fundamentally different with regards to mutual improvement; in particular, mutually beneficial budget and contest transfers exist in distinct, limited subsets of games, whereas mutually beneficial joint transfers exist in almost all games. However, in our second result, we demonstrate that all three mechanisms are equivalent when it comes to collective improvement; that is, collectively beneficial budget, contest, and joint transfers exist in almost all game instances, and all three mechanisms achieve the same maximum collective payoff. Together, these results demonstrate that differences between mechanisms depend fundamentally on the objective of the alliance.

翻译：不同联盟机制如何相互比较？在本研究中，我们分析了联盟化广义洛托博弈中形成联盟的多种方法，该博弈是竞争性资源分配的简化模型。在此博弈中，玩家1和玩家2通过将有限的资源预算分配到独立的竞赛集合中，分别与共同的对手展开竞争；智能体在某个竞赛中投入的资源多于对手时即赢得该竞赛。在此设定下，我们研究了三种联盟机制：预算转移（资源捐赠）、竞赛转移（竞赛重新分配）以及联合转移（两者同时进行）。针对所有三种机制，我们研究了它们在何时能带来集体改进（玩家总收益增加）或互惠改进（每位玩家的个体收益均增加）。在我们的第一个结果中，我们证明这三种机制在互惠改进方面存在根本性差异；具体而言，互惠的预算转移和竞赛转移仅存在于有限且互异的博弈子集中，而互惠的联合转移则存在于几乎所有博弈中。然而，在我们的第二个结果中，我们证明这三种机制在集体改进方面是等效的；也就是说，几乎所有博弈实例中都存在具有集体效益的预算转移、竞赛转移和联合转移，且三种机制均能达到相同的最大集体收益。这些结果共同表明，机制间的差异从根本上取决于联盟的目标。