发表机构
University of California, Santa Barbara（加利福尼亚大学圣塔芭芭拉分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究在联盟一般Lotto博弈中，针对玩家对对手或盟友预算存在乘法不确定性的情形，精确刻画了存在使双方受益的稳健预算转移的博弈集合，并证明此类转移在正测度博弈集中存在，表明信息不明时结盟仍可能有效。
AI 中文摘要
与共同对手竞争的智能体往往能通过结盟获得优势，但当它们缺乏关于对手或盟友的精确信息时，决定是否结盟便十分困难。我们研究不确定性如何影响联盟博弈（coalitional General Lotto game）中的结盟机会，在该博弈中，两个玩家通过将各自的资源预算分配至一组独立的、有价值的竞赛上来与共同的对手竞争。当所有智能体都知晓彼此预算时，已知从一方到另一方的预算转移可使双方受益。我们探究当玩家仅知道相关预算至多相差一个乘法因子时，此类联盟是否仍然成立。在两种模型下——一种模型中玩家对对手的预算不确定，另一种模型中玩家对彼此的预算不确定——我们精确刻画了在与其推测可能一致的所有博弈中，哪些博弈允许存在使双方受益的转移。在两种模型中，我们均证明：对于任意不确定性水平，此类稳健转移存在于一组具有正测度的博弈中。这些结果表明，即使盟友在很大程度上处于信息不明状态，结盟仍可能是有价值的。
英文摘要
Agents competing against a common opponent can often gain an edge by forming alliances, but deciding whether to do so is difficult when they lack precise knowledge about their opponent or ally. We study how uncertainty affects opportunities for alliance formation in the coalitional General Lotto game, in which two players compete aganist a shared adversary by allocating their resource budgets over separate sets of valued contests. When all agents know one another's budgets, it is known that a budget transfer from one player to the other can benefit both players. We ask whether such alliances survive when the players know the relevant budgets only up to a multiplicative factor. Under two models, one in which the players are uncertain about the adversary's budget and one in which they are uncertain about each other's budgets, we characterize exactly which games admit a transfer that benefits both players in every game consistent with what they conjecture to be possible. In both models, we show that such robust transfers exist in a set of games of positive measure for every level of uncertainty. These results suggest that alliances can remain worthwhile even when allies are largely in the dark.
