Inefficiency of pure Nash equilibria in network congestion games: the impact of symmetry and network structure

Abstract

We study the inefficiency of pure Nash equili bria in symmetric unweighted network congestion games. We first explore the impact of symmetry on the worst-case PoA of network congestion games. For polynomial delay functions with highest degree p , we construct a family of symmetric congestion games over arbitrary networks which achieves the same worst-case PoA of asymmetric network congestion games. Next, we explore the impact of network structure within the class of symmetric network congestion games. For delay functions in class 𝒟, we introduce a quantity y (𝒟) and we show that the PoA is at most y (𝒟) in games defined over series-parallel networks. Thus, for polynomial delays with highest degree p , the PoA cannot exceed 2 p +1 - 1, which is significantly smaller than the worst-case PoA in games defined over arbitrary networks. Moreover, we prove that the worst-case PoA quickly degrades from sub-linear to exponential when relaxing the network topology form extension-parallel to series-parallel. Finally, we consider measuring the social cost as the maximum players’ cost. For polynomial delays of maximum degree p we show that the worst-case PoA is significantly smaller than that of general symmetric congestion games, but dramatically larger than that of games defined over extension-parallel networks.