Strong Price of Anarchy, Utility Games and Coalitional Dynamics
We introduce a framework for studying the effect of cooperation on the quality of outcomes in utility games. Our framework is a coalitional analog of the smoothness framework of non-cooperative games. Coalitional smoothness implies bounds on the strong price of anarchy, the loss of quality of coalitionally stable outcomes. Our coalitional smoothness framework captures existing results bounding the strong price of anarchy of network design games. Moreover, we give novel strong price of anarchy results for any monotone utility-maximization game, showing that if each player’s utility is at least his marginal contribution to the welfare, then the strong price of anarchy is at most 2. This captures a broad class of games, including games that have a price of anarchy as high as the number of players. Additionally, we show that in potential games the strong price of anarchy is close to the price of stability, the quality of the best Nash equilibrium.
We also initiate the study of the quality of coalitional out-of-equilibrium outcomes in games. To this end, we define a coalitional version of myopic best-response dynamics, and show that the bound on the strong price of anarchy implied by coalitional smoothness, also extends with small degradation to the average quality of outcomes of the given dynamic.
KeywordsNash Equilibrium Congestion Game Potential Game Strong Equilibrium Pure Nash Equilibrium
Unable to display preview. Download preview PDF.
- 1.Albers, S.: On the value of coordination in network design. In: SODA (2008)Google Scholar
- 3.Anshelevich, E., Dasgupta, A., Kleinberg, J., Tardos, E., Wexler, T., Roughgarden, T.: The price of stability for network design with fair cost allocation. In: FOCS, pp. 295–304 (2004)Google Scholar
- 4.Anshelevich, E., Hoefer, M.: Contribution Games in Networks. Algorithmica, 1–37 (2011)Google Scholar
- 5.Aumann, R.J.: Acceptable points in general cooperative N-person games. In: Luce, R.D., Tucker, A.W. (eds.) Contribution to the theory of game IV, Annals of Mathematical Study 40, pp. 287–324. University Press (1959)Google Scholar
- 6.Bachrach, Y., Syrgkanis, V., Tardos, É., Vojnovic, M.: Strong price of anarchy and coalitional dynamics. CoRR, abs/1307.2537 (2013)Google Scholar
- 7.Blum, A., Mansour, Y.: Learning, Regret Minimization and Equilibria. Camb. Univ. Press (2007)Google Scholar
- 9.Goemans, M., Mirrokni, V., Vetta, A.: Sink equilibria and convergence. In: FOCS, pp. 142–154 (2005)Google Scholar
- 13.Maschler, M.: The bargaining set, kernel, and nucleolus. In: Handbook of Game Theory with Economic Applications, vol. 1, ch.18, pp. 591–667. Elsevier (1992)Google Scholar
- 15.Nessah, R., Tian, G.: On the existence of strong nash equilibria. Working Papers 2009-ECO-06, IESEG School of Management (2009)Google Scholar
- 16.Roughgarden, T.: Intrinsic robustness of the price of anarchy. In: STOC (2009)Google Scholar
- 17.Roughgarden, T.: The price of anarchy in games of incomplete information. In: ACM EC (2012)Google Scholar
- 18.Roughgarden, T., Schoppmann, F.: Local smoothness and the price of anarchy in atomic splittable congestion games. In: SODA (2011)Google Scholar
- 20.Syrgkanis, V.: Bayesian Games and the Smoothness Framework. ArXiv e-prints (March 2012)Google Scholar
- 21.Syrgkanis, V., Tardos, E.: Composable and efficient mechanisms. In: STOC (2013)Google Scholar
- 22.Vetta, A.: Nash equilibria in competitive societies, with applications to facility location, traffic routing and auctions (2002)Google Scholar