The Strong Price of Anarchy of Linear Bottleneck Congestion Games

Abstract

We study the inefficiency of equilibrium outcomes in Bottleneck Congestion games. These games model situations in which strategic players compete for a limited number of facilities. Each player allocates his weight to a (feasible) subset of the facilities with the goal to minimize the maximum (weight-dependent) latency that he experiences on any of these facilities. We analyze the (strong) Price of Anarchy of these games for a natural load balancing social cost objective, i.e., minimize the maximum latency of a facility. In our studies, we focus on Bottleneck Congestion games with linear latency functions. These games still constitute a rich class of games and generalize, for example, Load Balancing games with identical or uniformly related machines (with or without restricted assignments). We derive upper and (asymptotically) matching lower bounds on the (strong) Price of Anarchy of these games. We also derive more refined bounds for several special cases of these games, including the cases of identical player weights, identical latency functions and symmetric strategy sets. Further, we provide lower bounds on the Price of Anarchy for k-strong equilibria.