Abstract
We study a basic network design game where n self-interested agents, each having individual connectivity requirements, wish to build a network by purchasing links from a given set of edges. A fundamental cost sharing mechanism is Shapley cost sharing that splits the cost of an edge in a fair manner among the agents using the edge. In this paper we investigate if an optimal minimum-cost network represents an attractive, relatively stable state that agents might want to purchase. We resort to the concept of α-approximate Nash equilibria. We prove that for single source games in undirected graphs, any optimal network represents an H(n)-approximate Nash equilibrium, where H(n) is the n-th Harmonic number. We show that this bound is tight. We extend the results to cooperative games, where agents may form coalitions, and to weighted games. In both cases we give tight or nearly tight lower and upper bounds on the stability of optimal solutions. Finally we show that in general source-sink games and in directed graphs, minimum-cost networks do not represent good states.
Work supported by a Gottfried Wilhelm Leibniz Award of the German Research Foundation.
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References
Albers, S.: On the value of coordination in network design. SIAM Journal on Computing 38, 2273–2302 (2009)
Alon, N., Demaine, E.D., Hajiaghayi, M., Leighton, T.: Basic network creation games. In: Proc. 22nd Annual ACM Symposium on Parallel Algorithms and Architectures, pp. 106–113 (2010)
Aumann, R.J.: Acceptable points in general cooperative n-person games. In: Tucker, A.W., Luce, R.D. (eds.) Contributions to the Theory of Games, vol. IV. Annals of Mathematics Studies, vol. 40, pp. 287–324 (1959)
Anshelevich, E., Dasgupta, A., Kleinberg, J.M., Tardos, E., Wexler, T., Roughgarden, T.: The price of stability for network design with fair cost allocation. SIAM Journal on Computing 38, 1602–1623 (2008)
Anshelevich, E., Dasgupta, A., Tardos, E., Wexler, T.: Near optimal network design with selfish agents. Theory of Computing 4, 77–109 (2008)
Chekuri, C., Chuzhoy, J., Lewin-Eytan, L., Naor, J., Orda, A.: Non-cooperative multicast and facility location games. In: Proc. 7th ACM Conference on Electronic Commerce (EC), pp. 72–81 (2006)
Chen, H.-L., Roughgarden, T.: Network design with weighted players. Theory of Computing Systems 45, 302–324 (2009)
Chen, H.-L., Roughgarden, T., Valiant, G.: Designing network protocols for good equilibria. SIAM Journal on Computing 39, 1799–1832 (2010)
Corbo, J., Parkes, D.: The price of selfish behavior in bilateral network formation. In: Proc. 24th Annual ACM Symposium on Principles of Distributed Computing (PODC), pp. 99–107 (2005)
Demaine, E.D., Hajiaghayi, M., Mahini, H., Zadimoghaddam, M.: The price of anarchy in cooperative network creation games. In: Proc. 26th International Symposium on Theoretical Aspects of Computer Science (STACS), pp. 301–312 (2009)
Devanur, N.R., Mihail, M., Vazirani, V.V.: Strategyproof cost-sharing mechanisms for set cover and facility location games. Decision Support Systems 39, 11–22 (2005)
Epstein, A., Feldman, M., Mansour, Y.: Strong equilibrium in cost sharing connection games. In: Proc. 8th ACM Conference on Electronic Commerce, pp. 84–92 (2007)
Fabrikant, A., Luthra, A., Maneva, E., Papadimitriou, C.H., Shenker, S.: On a network creation game. In: Proc. 22nd Annual ACM Symposium on Principles of Distributed Computing (PODC), pp. 347–351 (2003)
Fiat, A., Kaplan, H., Levy, M., Olonetsky, S., Shabo, R.: On the price of stability for designing undirected networks with fair cost allocations. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4051, pp. 608–618. Springer, Heidelberg (2006)
Gupta, A., Srinivasan, A., Tardos, E.: Cost-sharing mechanisms for network design. Algorithmica 50, 98–119 (2008)
Halevi, Y., Mansour, Y.: A network creation game with nonuniform interests. In: Deng, X., Graham, F.C. (eds.) WINE 2007. LNCS, vol. 4858, pp. 287–292. Springer, Heidelberg (2007)
Hoefer, M.: Non-cooperative tree creation. Algorithmica 53, 104–131 (2009)
Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999)
Laoutaris, N., Poplawski, L.J., Rajaraman, R., Sundaram, R., Teng, S.-H.: Bounded budget connection (BBC) games or how to make friends and influence people, on a budget. In: Proc. 27th Annual ACM Symposium on Principles of Distributed Computing (PODC), pp. 165–174 (2008)
Nguyen, T., Tardos, E.: Approximate pure Nash equilibria via Lovász local lemma. In: Leonardi, S. (ed.) WINE 2009. LNCS, vol. 5929, pp. 160–171. Springer, Heidelberg (2009)
Pal, M., Tardos, E.: Group strategyproof mechanisms via primal-dual algorithms. In: Proc. 44th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 584–593 (2003)
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Albers, S., Lenzner, P. (2010). On Approximate Nash Equilibria in Network Design. In: Saberi, A. (eds) Internet and Network Economics. WINE 2010. Lecture Notes in Computer Science, vol 6484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17572-5_2
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DOI: https://doi.org/10.1007/978-3-642-17572-5_2
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