Congestion Games with Linearly Independent Paths: Convergence Time and Price of Anarchy

Abstract. We investigate the effect of linear independence in the strategies of congestion games on the convergence time of best improvement sequences and on the pure Price of Anarchy. In particular, we consider symmetric congestion games on extension-parallel networks, an interesting class of networks with linearly independent paths, and establish two remarkable properties previously known only for parallel-link games. More precisely, we show that for arbitrary (non-negative and non-decreasing) latency functions, any best improvement sequence reaches a pure Nash equilibrium in at most as many steps as the number of players, and that for latency functions in class D, the pure Price of Anarchy is at most ρ(D). As a by-product of our analysis, we obtain that for symmetric congestion games on general networks with latency functions in class D, the Price of Stability is at most ρ(D).

• Type: Journal
• Year: 2010
• Where: MST
• Authors: Dimitris Fotakis
• Keywords: Congestion Games, Latency Functions, MST 2010, Symmetric Congestion Games