Abstract
We study network connection games where the nodes of a network perform edge swaps in order to improve their communication costs. For the model proposed by [2], in which the selfish cost of a node is the sum of all shortest path distances to the other nodes, we use the probabilistic method to provide a new, structural characterization of equilibrium graphs. We show how to use this characterization in order to prove upper bounds on the diameter of equilibrium graphs in terms of the size of the largest k-vicinity (defined as the the set of vertices within distance k from a vertex), for any k ≥ 1 and in terms of the number of edges, thus settling positively a conjecture of [2] in the cases of graphs of large k-vicinity size (including graphs of large maximum degree) and of graphs which are dense enough.
Next, we present a new swap-based network creation game, in which selfish costs depend on the immediate neighborhood of each node; in particular, the profit of a node is defined as the sum of the degrees of its neighbors. We prove that, in contrast to the previous model, this network creation game admits an exact potential, and also that any equilibrium graph contains an induced star. The existence of the potential function is exploited in order to show that an equilibrium can be reached in expected polynomial time even in the case where nodes can only acquire limited knowledge concerning non-neighboring nodes.
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References
Albers, S., Eilts, S., Even-Dar, E., Mansour, Y., Roditty, L.: On Nash equilibria for a network creation game. In: Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithm, SODA 2006, pp. 89–98. ACM, New York (2006)
Alon, N., Demaine, E.D., Hajiaghayi, M., Leighton, T.: Basic network creation games. In: Proceedings of the 22nd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 106–113. ACM, New York (2010)
Anshelevich, E., Dasgupta, A., Kleinberg, J., Tardos, E., Wexler, T., Roughgarden, T.: The Price of Stability for Network Design with Fair Cost Allocation. In: The 45th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 59–73 (2004)
Demaine, E.D., Hajiaghayi, M., Mahini, H., Zadimoghaddam, M.: The price of anarchy in network creation games. In: Proceedings of the Twenty-Sixth Annual ACM Symposium on Principles of Distributed Computing, PODC 2007, pp. 292–298. ACM, New York (2007)
Ehsani, S., Fazli, M., Mehrabian, A., Sadeghian Sadeghabad, S., Safari, M., Saghafian, M., ShokatFadaee, S.: On a bounded budget network creation game. In: Proceedings of the 23rd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pp. 207–214 (2011)
Fabrikant, A., Luthra, A., Maneva, E., Papadimitriou, C.H., Shenker, S.: On a network creation game. In: Proceedings of the 22nd Annual Symposium on Principles of Distributed Computing, Boston, Massachusetts, pp. 347–351 (2003)
Fischer, E.: The art of uninformed decisions: A primer to property testing. The Computational Complexity Column of The Bulletin of the European Association for Theoretical Computer Science 75, 97–126 (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)
Lenzner, P.: On Dynamics in Basic Network Creation Games. In: Persiano, G. (ed.) SAGT 2011. LNCS, vol. 6982, pp. 254–265. Springer, Heidelberg (2011)
Mihalák, M., Schlegel, J.C.: Asymmetric Swap-Equilibrium: A Unifying Equilibrium Concept for Network Creation Games. In: Rovan, B., Sassone, V., Widmayer, P. (eds.) MFCS 2012. LNCS, vol. 7464, pp. 693–704. Springer, Heidelberg (2012)
Mihalák, M., Schlegel, J.C.: The price of anarchy in network creation games is (Mostly) constant. In: Kontogiannis, S., Koutsoupias, E., Spirakis, P.G. (eds.) SAGT 2010. LNCS, vol. 6386, pp. 276–287. Springer, Heidelberg (2010)
Monderer, D., Shapley, L.S.: Potential games. Games and Economic Behavior 14(1), 124–143 (1996)
Nikoletseas, S., Panagopoulou, P., Raptopoulos, C., Spirakis, P.G.: On the Structure of Equilibria in Basic Network Formation, http://students.ceid.upatras.gr/~panagopp/FCT2013_full.pdf
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Nikoletseas, S., Panagopoulou, P., Raptopoulos, C., Spirakis, P.G. (2013). On the Structure of Equilibria in Basic Network Formation. In: Gąsieniec, L., Wolter, F. (eds) Fundamentals of Computation Theory. FCT 2013. Lecture Notes in Computer Science, vol 8070. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40164-0_25
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DOI: https://doi.org/10.1007/978-3-642-40164-0_25
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