Abstract
We study a geometric version of a simple non-cooperative network creation game introduced in [2], assuming Euclidean edge costs on the plane. The price of anarchy in such geometric games with k players is Θ(k). Hence, we consider the task of minimizing players incentives to deviate from a payment scheme, purchasing the minimum cost network. In contrast to general games, in small geometric games (2 players and 2 terminals per player), a Nash equilibrium purchasing the optimum network exists. This can be translated into a (1+ε)-approximate Nash equilibrium purchasing the optimum network under more practical assumptions, for any ε > 0. For more players there are games with 2 terminals per player, such that any Nash equilibrium purchasing the optimum solution is at least \(\left(\frac{4}{3}-\epsilon\right)\)-approximate. On the algorithmic side, we show that playing small games with best-response strategies yields low-cost Nash equilibria. The distinguishing feature of our paper are new techniques to deal with the geometric setting, fundamentally different from the techniques used in [2].
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., Tardos, É., Wexler, T., Roughgarden, T.: The price of stability for network design with fair cost allocation. In: Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 295–304 (2004)
Anshelevich, E., Dasgupta, A., Tardos, É., Wexler, T.: Near-optimal network design with selfish agents. In: Proceedings of the 35th Annual Symposium on Theory of Computing (STOC), pp. 511–520 (2003)
Arora, S.: Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems. Journal of the ACM 45(5), 753–782 (1998)
Bala, V., Goyal, S.: A non-cooperative model of network formation. Econometrica 68, 1181–1229 (2000)
Chlebík, M., Chlebíková, J.: Approximation hardness of the Steiner tree problem in graphs. In: Penttonen, M., Schmidt, E.M. (eds.) SWAT 2002. LNCS, vol. 2368, pp. 170–179. Springer, Heidelberg (2002)
Czumaj, A., Krysta, P., Vöcking, B.: Selfish traffic allocation for server farms. In: Proceedings of the 34th Annual ACM Symposium on the Theory of Computing (STOC), pp. 287–296 (2002)
de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry - Algorithms and Applications. Springer, Heidelberg (1997)
Dutta, D., Goel, A., Heidemann, J.: Oblivious AQMand Nash equilibrium. In: Proceedings of the 22nd Annual Joint Conference of the IEEE Computer and Communications Societies, INFOCOM (2003)
Fabrikant, A., Luthera, A., Maneva, E., Papadimitriou, C., Shenker, S.: On a network creation game. In: Proceedings of the 22nd Annual ACMSymposium on Principles of Distributed Computing (PODC), pp. 347–351 (2003)
Gilbert, E., Pollak, H.: Steiner Minimal Trees. SIAM Journal on Applied Mathematics 16, 1–29 (1968)
Goemams, M., Williamson, D.: A general approximation technique for constrained forest problems. SIAM Journal on Computing 24(2), 296–317 (1995)
Heller, H., Sarangi, S.: Nash networks with heterogeneous agents. Technical ReportWorking Paper Series, E-2001-1, Virginia Tech (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)
Melzak, Z.: On the problem of Steiner. Canadian Mathematical Bulletin 4, 143–148 (1961)
Robins, G., Zelikovsky, A.: Improved Steiner tree approximation in graphs. In: Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 770–779 (2000)
Roughgarden, T., Tardos, É.: How bad is selfish routing? Journal of the ACM 49(2), 236–259 (2002)
Schulz, A., Stier Moses, N.: Selfish routing in capacitated networks. Mathematics of Operations Research 29(4), 961–976 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hoefer, M., Krysta, P. (2005). Geometric Network Design with Selfish Agents. In: Wang, L. (eds) Computing and Combinatorics. COCOON 2005. Lecture Notes in Computer Science, vol 3595. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11533719_19
Download citation
DOI: https://doi.org/10.1007/11533719_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28061-3
Online ISBN: 978-3-540-31806-4
eBook Packages: Computer ScienceComputer Science (R0)