Congestion Games with Capacitated Resources

Abstract

Abstract. The players of a congestion game interact by allocating bundles of resources from a common pool. This type of games leads to well studied models for analyzing strategic situations, including networks operated by uncoordinated selfish users. Congestion games constitute a subclass of potential games, meaning that a pure Nash equilibrium emerges from a myopic process where the players iteratively react by switching to a strategy that diminishes their individual cost. With the aim of covering more applications, for instance in communication networks, we extend congestion games to the setting where every resource is endowed with a capacity which possibly limits its number of users. From the negative side, we show that a pure Nash equilibrium is not guaranteed to exist in any case and we prove that deciding whether a game possesses a pure Nash equilibrium is NP-complete. Our positive results state that congestion games with capacities are potential games in the well studied singleton case. Polynomial algorithms that compute these equilibria are also provided.

Scheduling games with machine-dependent priority lists

“…Recently, Biló and Vinci [5] studied a congestion game with a global priority classes that can contain multiple jobs and characterize the price of anarchy as a function of the number of classes. Gourvès et al [15] studied capacitated congestion games to characterize the existence of pure Nash equilibria and computation of an equilibrium when they exist. Piliouras et al [24] assumed that the priority lists are unknown to the players a priori and consider different risk attitudes towards having a uniform at random ordering.…”

Scheduling Games with Machine-Dependent Priority Lists

“…Farzad et al [16] studied priority based selfish routing for non-atomic and atomic users and analyzed the inefficiency of equilibrium. Gourvès et al [19] studied capacitated congestion games to characterize the existence of pure Nash equilibria and computation of an equilibrium when they exist. Piliouras et al [29] assumed that the priority lists are unknown to the players a priori and consider different risk attitudes towards having a uniform at random ordering.…”

“…We analyze a potential function that is introduced by Gourvès et al [19]. Define the rank of job i ∈ N on machine j ∈ M by r(i, j) = |{i ∈ N | π j (i ) ≤ π j (i)}|.…”

Statics and Dynamics of Selfish Interactions in Distributed Service Systems

“…Rosenthal showed that pure Nash equilibria always exist for such games [13]. Weighted congestion games, with player-specific utility functions, were introduced by Milchtaich [14], and recently studied in several contexts [15][16][17][18][19]. In particular, a class of congestion games with capacitated resources, where each resource is associated with a capacity level, representing the maximum number of users that such a resource may simultaneously accommodate, was recently investigated in [19].…”