Pure Nash equilibria in weighted matroid congestion games with non-additive aggregation and beyond

Abstract

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 non-additive aggregation. For the above models, the existence of a pure Nash equilibrium is proved under some assumptions, including the case in which the strategy space of each player is the base family of a matroid and the case in which 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 non-additive aggregation, 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 provides a common extension of the previous results. We also present an extension on the existence of pure Nash equilibria in weighted matroid congestion games with mixed costs.