Congestion games offer a primary model in the study of pure Nash equilibria in non-cooperative games, and a number of generalized models have been proposed in the literature. One line of generalization includes weighted congestion games, in which the cost of a resource is a function of the total weight of the players choosing that resource. Another line includes congestion games with mixed costs, in which the cost imposed on a player is a convex combination of the total cost and the maximum cost of the resources in her strategy. This model is further generalized to that of congestion games with complementarities. For the above models, the existence of a pure Nash equilibrium is proved under some assumptions, including that the strategy space of each player is the base family of a matroid and that the cost functions have a certain kind of monotonicity. In this paper, we deal with common generalizations of these two lines, namely weighted matroid congestion games with complementarities, and its further generalization. Our main technical contribution is a proof of the existence of pure Nash equilibria in these generalized models under a simplified assumption on the monotonicity, which provide a common extension of the previous results. We also present some extensions on the existence of pure Nash equilibria in player-specific and weighted matroid congestion games with mixed costs.

翻译：拥塞博弈是非合作博弈中研究纯纳什均衡的主要模型，文献中已提出多种推广形式。一类推广包括加权拥塞博弈，其中资源的成本是关于选择该资源的玩家总权重的函数。另一类推广包括混合成本拥塞博弈，玩家承担的成本是其策略中资源总成本与最大成本的凸组合。该模型进一步推广为带互补性的拥塞博弈。对于上述模型，纯纳什均衡的存在性已在某些假设下得到证明，包括每个玩家的策略空间是拟阵的基族，以及成本函数具有某种单调性。本文研究这两类推广的共同推广形式，即带互补性的加权拟阵拥塞博弈及其进一步推广。我们的主要技术贡献在于，在简化的单调性假设下证明了这些推广模型中纯纳什均衡的存在性，这为先前结果提供了统一的扩展。同时，我们还给出了玩家特定加权拟阵拥塞博弈与混合成本博弈中纯纳什均衡存在性的若干扩展结果。