Exact Price of Anarchy for Polynomial Congestion Games
SIAM Journal on Computing
Capacitated network design games
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
Convergence of best-response dynamics in games with conflicting congestion effects
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
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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. 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 $\mathcal{D}$, the pure Price of Anarchy is at most $\rho(\mathcal{D})$, i.e. it is bounded by the Price of Anarchy for non-atomic congestion games. As a by-product of our analysis, we obtain that for symmetric network congestion games with latency functions in class $\mathcal{D}$, the Price of Stability is at most $\rho(\mathcal{D})$.