Uniqueness of equilibria in atomic splittable polymatroid congestion games

Harks, Tobias; Timmermans, Veerle

doi:10.1007/s10878-017-0166-5

Cited by 2 publications

(1 citation statement)

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“…In all of the above models, the fact that (E, S i ) is a matroid for each player i plays a key role to guaranteeing the existence of a pure Nash equilibrium. A further generalized model in which the strategy space is represented by a polymatroid is studied in [18,20]. A different kind of relation between matroids and congestion games is investigated in [13].…”

Section: Theorem 25 ([3]mentioning

confidence: 99%

Generalizations of Weighted Matroid Congestion Games: Pure Nash Equilibrium, Sensitivity Analysis, and Discrete Convex Function

Takazawa

2019

Lecture Notes in Computer Science

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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.

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Section: Theorem 25 ([3]mentioning

confidence: 99%