Abstract
We study a general class of non-cooperative games coming from combinatorial covering and facility location problems. A game for k players is based on an integer programming formulation. Each player wants to satisfy a subset of the constraints. Variables represent resources, which are available in costly integer units and must be bought. The cost can be shared arbitrarily between players. Once a unit is bought, it can be used by all players to satisfy their constraints. In general the cost of pure-strategy Nash equilibria in this game can be prohibitively high, as both prices of anarchy and stability are in Θ(k). In addition, deciding the existence of pure Nash equilibria is NP-hard. These results extend to recently studied single-source connection games. Under certain conditions, however, cheap Nash equilibria exist: if the integrality gap of the underlying integer program is 1 and in the case of single constraint players. In addition, we present algorithms that compute cheap approximate Nash equilibria in polynomial time.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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)
Anshelevich, E., Dasgupta, A., Tardos, É., Wexler, T.: Near-optimal network design with selfish agents. In: Proc. 35th STOC, pp. 511–520 (2003)
Cardinal, J., Hoefer, M.: Selfish serive installation in networks. In: Spirakis, P.G., Mavronicolas, M., Kontogiannis, S.C. (eds.) WINE 2006. LNCS, vol. 4286, Springer, Heidelberg (2006)
Deng, X., Ibaraki, T., Nagamochi, H.: Combinatorial optimization games. In: Proc. 8th SODA, pp. 720–729 (1997)
Devanur, N., Garg, N., Khandekar, R., Pandit, V., Saberi, A., Vazirani, V.: Price of anarchy, locality gap, and a network service provider game. In: Deng, X., Ye, Y. (eds.) WINE 2005. LNCS, vol. 3828, pp. 1046–1055. Springer, Heidelberg (2005)
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)
Eiselt, H., Laporte, G., Thisse, J.-F.: Competitive location models: A framework and bibliography. Transport. Sci. 27, 44–54 (1993)
Goemans, M., Skutella, M.: Cooperative facility location games. In: Proc. 11th SODA, pp. 76–85 (2000)
Guha, S., Khuller, S.: Greedy strikes back: Improved facility location algorithms. J. Algorithms 31, 228–248 (1999)
Hoefer, M.: Non-cooperative tree creation. In: Královič, R., Urzyczyn, P. (eds.) MFCS 2006. LNCS, vol. 4162, pp. 517–527. Springer, Heidelberg (2006)
Immorlica, N., Mahdian, M., Mirrokni, V.: Limitations of cross-monotonic cost sharing schemes. In: Proc. 16th SODA, pp. 602–611 (2005)
Jain, K., Mahdian, M., Markakis, E., Saberi, A., Vazirani, V.: Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP. J. ACM 50(6), 795–824 (2003)
Jain, K., Vazirani, V.: Applications of approximation algorithms to cooperative games. In: Proc. 33rd STOC, pp. 364–372 (2001)
Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999)
Li, X., Sun, Z., Wang, W.: Cost sharing and strategyproof mechanisms for set cover games. In: Diekert, V., Durand, B. (eds.) STACS 2005. LNCS, vol. 3404, pp. 218–230. Springer, Heidelberg (2005)
Mahdian, M., Ye, Y., Zhang, J.: Improved approximation algorithms for metric facility location problems. In: Jansen, K., Leonardi, S., Vazirani, V.V. (eds.) APPROX 2002. LNCS, vol. 2462, pp. 229–242. Springer, Heidelberg (2002)
Mettu, R., Plaxton, G.: The online median problem. SIAM J. Comp. 32(3), 816–832 (2003)
Miller, T., Friesz, T., Tobin, R.: Equilibrium Facility Location in Networks. Springer, Heidelberg (1996)
Pál, M., Tardos, É.: Group strategyproof mechanisms via primal-dual algorithms. In: Proc. 44th FOCS, pp. 584–593 (2003)
Sun, Z., Li, X., Wang, W., Chu, X.: Mechanism design for set cover games when elements are agents. In: Megiddo, N., Xu, Y., Zhu, B. (eds.) AAIM 2005. LNCS, vol. 3521, Springer, Heidelberg (2005)
Vetta, A.: Nash equilibria in competitive societies with application to facility location, traffic routing and auctions. In: Proc. 43rd FOCS, p. 416 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hoefer, M. (2006). Non-cooperative Facility Location and Covering Games. In: Asano, T. (eds) Algorithms and Computation. ISAAC 2006. Lecture Notes in Computer Science, vol 4288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11940128_38
Download citation
DOI: https://doi.org/10.1007/11940128_38
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-49694-6
Online ISBN: 978-3-540-49696-0
eBook Packages: Computer ScienceComputer Science (R0)