Selfish Service Installation in Networks
We consider a scenario of distributed service installation in privately owned networks. Our model is a non-cooperative vertex cover game for k players. Each player owns a set of edges in a graph G and strives to cover each edge by an incident vertex. Vertices have costs and must be purchased to be available for the cover. Vertex costs can be shared arbitrarily by players. Once a vertex is bought, it can be used by any player to fulfill the covering requirement of her incident edges. Despite its simplicity, the model exhibits a surprisingly rich set of properties. We present a cumulative set of results including tight characterizations for prices of anarchy and stability, NP-hardness of equilibrium existence, and polynomial time solvability for important subclasses of the game. In addition, we consider the task of finding approximate Nash equilibria purchasing an approximation to the optimum social cost, in which each player can improve her contribution by selfish defection only by at most a certain factor. A variation of the primal-dual algorithm for minimum weighted vertex cover yields a guarantee of 2, which is shown to be tight.
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- 1.Anshelevich, E., Dasgupta, A., Kleinberg, J., Roughgarden, T., Tardos, É., Wexler, T.: The price of stability for network design with fair cost allocation. In: Proc. 45th FOCS, pp. 295–304 (2004)Google Scholar
- 2.Anshelevich, E., Dasgupta, A., Tardos, É., Wexler, T.: Near-optimal network design with selfish agents. In: Proc. 35th STOC, pp. 511–520 (2003)Google Scholar
- 3.Awerbuch, B., Azar, Y., Epstein, A.: The price of routing unsplittable flow. In: Proc. 37th STOC, pp. 331–337 (2005)Google Scholar
- 6.Devanur, N., Mihail, M., Vazirani, V.: Strategyproof cost-sharing mechanisms for set cover and facility location problems. In: Proc. 4th EC, pp. 108–114 (2003)Google Scholar
- 7.Eidenbenz, S., Kumar, A., Zust, S.: Equilibria in topology control games for ad hoc networks. In: Proc. DIALM-POMC 2003, pp. 2–11 (2003)Google Scholar
- 8.Fabrikant, A., Luthera, A., Maneva, E., Papadimitriou, C., Shenker, S.: On a network creation game. In: Proc. 22nd PODC, pp. 347–351 (2003)Google Scholar
- 9.Halldórsson, M., Halpern, J., Li, L., Mirrokni, V.: On spectrum sharing games. In: Proc. 23rd PODC, pp. 107–114 (2004)Google Scholar
- 11.Immorlica, N., Mahdian, M., Mirrokni, V.: Limitations of cross-monotonic cost sharing schemes. In: Proc. 16th SODA, pp. 602–611 (2005)Google Scholar
- 12.Jain, K., Vazirani, V.: Applications of approximation algorithms to cooperative games. In: Proc. 33rd STOC, pp. 364–372 (2001)Google Scholar
- 13.Khot, S., Regev, O.: Vertex cover might be hard to approximate within 2-ε. In: Proc. 18th CCC, p. 379 (2003)Google Scholar
- 17.Papadimitriou, C.: Algorithms, games and the internet. In: Proc. 33rd STOC, pp. 749–753 (2001)Google Scholar