The Efficiency of Best-Response Dynamics
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Best response (BR) dynamics is a natural method by which players proceed toward a pure Nash equilibrium via a local search method. The quality of the equilibrium reached may depend heavily on the order by which players are chosen to perform their best response moves. A deviator rule S is a method for selecting the next deviating player. We provide a measure for quantifying the performance of different deviator rules. The inefficiency of a deviator rule S with respect to an initial strategy profile p is the ratio between the social cost of the worst equilibrium reachable by S from p and the social cost of the best equilibrium reachable from p. The inefficiency of S is the maximum such ratio over all possible initial profiles. This inefficiency always lies between 1 and the price of anarchy.
We study the inefficiency of various deviator rules in network formation games and job scheduling games (both are congestion games, where BR dynamics always converges to a pure NE). For some classes of games, we compute optimal deviator rules. Furthermore, we define and study a new class of deviator rules, called local deviator rules. Such rules choose the next deviator as a function of a restricted set of parameters, and satisfy a natural independence condition called independence of irrelevant players. We present upper bounds on the inefficiency of some local deviator rules, and also show that for some classes of games, no local deviator rule can guarantee inefficiency lower than the price of anarchy.
KeywordsCongestion games Best-response dynamics Deviator rules Price of anarchy
- 2.Alon, N., Demaine, E.D., Hajiaghayi, M., Leighton, T.: Basic network creation games. In: Proceedings of the 22nd ACM Symposium on Parallelism in Algorithms and Architectures, pp. 106–113 (2010)Google Scholar
- 11.Even-Dar, E., Mansour, Y.: Fast convergence of selfish rerouting. In: Proceedings of SODA, pp. 772–781 (2005)Google Scholar
- 12.Fabrikant, A., Luthra, A., Maneva, E., Papadimitriou, C., Shenker, S.: On a network creation game. In: Proceedings of PODC, pp. 347–351 (2003)Google Scholar
- 13.Fabrikant, A., Papadimitriou, C., Talwar, K.: The complexity of pure Nash equilibria. In: Proceedings of STOC, pp. 604–612 (2004)Google Scholar
- 18.Ieong, S., Mcgrew, R., Nudelman, E., Shoham, Y., Sun, Q., Fast, C.: A simple class of congestion games. In: Proceedinhgs of AAAI, pp. 489–494 (2005)Google Scholar
- 19.Kawald, B., Lenzner, P.: On dynamics in selfish network creation. In: Proceedings of SPAA, pp. 83–92 (2013)Google Scholar
- 23.Papadimitriou, C.H.: Algorithms, games, and the internet. In: Proceedings of 33rd STOC, pp. 749–753 (2001)Google Scholar
- 26.Vöcking, B.: Selfish load balancing (Chap. 20). In: Algorithmic Game Theory. Cambridge University Press, Cambridge (2007)Google Scholar