Most familiar equilibrium concepts, such as Nash and correlated equilibrium, guarantee only that no single player can improve their utility by deviating unilaterally. They offer no guarantees against profitable coordinated deviations by coalitions. Although the literature proposes solution concepts that provide stability against multilateral deviations (\emph{e.g.}, strong Nash and coalition-proof equilibrium), these generally fail to exist. In this paper, we study an alternative solution concept that minimizes coalitional deviation incentives, rather than requiring them to vanish, and is therefore guaranteed to exist. Specifically, we focus on minimizing the average gain of a deviating coalition, and extend the framework to weighted-average and maximum-within-coalition gains. In contrast, the minimum-gain analogue is shown to be computationally intractable. For the average-gain and maximum-gain objectives, we prove a lower bound on the complexity of computing such an equilibrium and present an algorithm that matches this bound. Finally, we use our framework to solve the \emph{Exploitability Welfare Frontier} (EWF), the maximum attainable social welfare subject to a given exploitability (the maximum gain over all unilateral deviations).

翻译：大多数熟悉的均衡概念（如纳什均衡和相关均衡）仅保证没有单个参与者能通过单方偏离来提高自身效用，而不保证联盟通过协同偏离获利的情况。尽管文献提出了针对多方偏离提供稳定性的解概念（例如强纳什均衡和防联盟均衡），但这些概念通常不存在。本文研究了一种替代解概念，其目标是最小化联盟偏离激励而非要求其消失，因此保证存在性。具体而言，我们专注于最小化偏离联盟的平均收益，并将该框架推广至加权平均收益和联盟内最大收益。相反，最小收益类比被证明在计算上不可行。针对平均收益和最大收益目标，我们证明了计算此类均衡的复杂度下界，并提出了一种匹配该下界的算法。最后，我们利用该框架求解可被利用性福利前沿（EWF），即给定可被利用性（所有单方偏离的最大收益）下的最大可达社会福利。