We study the subclass of singleton congestion games with identical and increasing cost functions, i.e., each agent tries to utilize from the least crowded resource in her accessible subset of resources. Our main contribution is a novel approach for proving the existence of equilibrium outcomes that are resilient to weakly improving deviations: $(i)$ by singletons (Nash equilibria), $(ii)$ by the grand coalition (Pareto efficiency), and $(iii)$ by coalitions with respect to an a priori given partition coalition structure (partition equilibria). To the best of our knowledge, this is the strongest existence guarantee in the literature of congestion games that is resilient to weakly improving deviations by coalitions.

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具有抗共谋弹性的单例拥塞博弈

我们研究了具有相同且递增的成本函数的单例拥塞游戏的子类，即，每个代理都试图利用其可访问的资源子集中最不拥挤的资源。我们的主要贡献是一种新方法，用于证明对弱改进偏差具有弹性的均衡结果的存在：$(i)$ 由单身人士（纳什均衡），$(ii)$ 由大联盟（帕累托效率）和(iii)$由关于先验给定的分区联盟结构（分区均衡）的联盟。据我们所知，这是拥塞博弈文献中最强大的存在保证，它能够抵御联盟弱改进偏差。