Abstract
Network creation games investigate complex networks from a game-theoretic point of view. Based on the original model by Fabrikant et al. [PODC’03] many variants have been introduced. However, almost all versions have the drawback that edges are treated uniformly, i.e. every edge has the same cost and that this common parameter heavily influences the outcomes and the analysis of these games.
We propose and analyze simple and natural parameter-free network creation games with non-uniform edge cost. Our models are inspired by social networks where the cost of forming a link is proportional to the popularity of the targeted node. Besides results on the complexity of computing a best response and on various properties of the sequential versions, we show that the most general version of our model has constant Price of Anarchy. To the best of our knowledge, this is the first proof of a constant Price of Anarchy for any network creation game.
References
Albers, S., Eilts, S., Even-Dar, E., Mansour, Y., Roditty, L.: On Nash equilibria for a network creation game. ACM TEAC 2(1), 2 (2014)
Alon, N., Demaine, E.D., Hajiaghayi, M.T., Leighton, T.: Basic network creation games. SIAM J. Discret. Math. 27(2), 656–668 (2013)
Àlvarez, C., Blesa, M.J., Duch, A., Messegué, A., Serna, M.: Celebrity games. Theor. Comput. Sci. 648, 56–71 (2016)
Àlvarez, C., Messeguè, A.: Max celebrity games. In: Bonato, A., Graham, F.C., Prałat, P. (eds.) WAW 2016. LNCS, vol. 10088, pp. 88–99. Springer, Cham (2016). doi:10.1007/978-3-319-49787-7_8
Bala, V., Goyal, S.: A noncooperative model of network formation. Econometrica 68(5), 1181–1229 (2000)
Barabási, A.-L.: Network Science. Cambridge University Press, Cambridge (2016)
Bilò, D., Gualà, L., Leucci, S., Proietti, G.: Locality-based network creation games. In: SPAA 2014, pp. 277–286. ACM, New York (2014)
Bilò, D., Gualà, L., Leucci, S., Proietti, G.: Network creation games with traceroute-based strategies. In: Halldórsson, M.M. (ed.) SIROCCO 2014. LNCS, vol. 8576, pp. 210–223. Springer, Cham (2014). doi:10.1007/978-3-319-09620-9_17
Chauhan, A., Lenzner, P., Melnichenko, A., Molitor, L.: Selfish network creation with non-uniform edge cost (2017). arXiv preprint arXiv:1706.10200
Corbo, J., Parkes, D.: The price of selfish behavior in bilateral network formation. In: PODC 2005, pp. 99–107. ACM, New York (2005)
Cord-Landwehr, A., Lenzner, P.: Network creation games: think global – act local. In: Italiano, G.F., Pighizzini, G., Sannella, D.T. (eds.) MFCS 2015. LNCS, vol. 9235, pp. 248–260. Springer, Heidelberg (2015). doi:10.1007/978-3-662-48054-0_21
Cord-Landwehr, A., Mäcker, A., auf der Heide, F.M.: Quality of service in network creation games. In: Liu, T.-Y., Qi, Q., Ye, Y. (eds.) WINE 2014. LNCS, vol. 8877, pp. 423–428. Springer, Cham (2014). doi:10.1007/978-3-319-13129-0_34
Demaine, E.D., Hajiaghayi, M.T., Mahini, H., Zadimoghaddam, M.: The price of anarchy in network creation games. ACM Trans. Algorithms 8(2), 13 (2012)
Fabrikant, A., Luthra, A., Maneva, E., Papadimitriou, C.H., Shenker, S.: On a network creation game. In: PODC 2003, pp. 347–351. ACM, New York (2003)
Graham, R., Hamilton, L., Levavi, A., Loh, P.-S.: Anarchy is free in network creation. ACM Trans. Algorithms (TALG) 12(2), 15 (2016)
Jackson, M.O., Wolinsky, A.: A strategic model of social and economic networks. J. Econ. Theory 71(1), 44–74 (1996)
Kawald, B., Lenzner, P.: On dynamics in selfish network creation. In: SPAA 2013, pp. 83–92. ACM (2013)
Lenzner, P.: On dynamics in basic network creation games. In: Persiano, G. (ed.) SAGT 2011. LNCS, vol. 6982, pp. 254–265. Springer, Heidelberg (2011). doi:10.1007/978-3-642-24829-0_23
Lenzner, P.: Greedy selfish network creation. In: Goldberg, P.W. (ed.) WINE 2012. LNCS, vol. 7695, pp. 142–155. Springer, Heidelberg (2012). doi:10.1007/978-3-642-35311-6_11
Leskovec, J., Kleinberg, J., Faloutsos, C.: Graphs over time: densification laws, shrinking diameters and possible explanations. In: SIGKDD 2005, pp. 177–187. ACM (2005)
Mamageishvili, A., Mihalák, M., Müller, D.: Tree Nash equilibria in the network creation game. In: Bonato, A., Mitzenmacher, M., Prałat, P. (eds.) WAW 2013. LNCS, vol. 8305, pp. 118–129. Springer, Cham (2013). doi:10.1007/978-3-319-03536-9_10
Meirom, E.A., Mannor, S., Orda, A.: Network formation games with heterogeneous players and the internet structure. In: EC 2014, pp. 735–752. ACM (2014)
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). doi:10.1007/978-3-642-16170-4_24
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). doi:10.1007/978-3-642-32589-2_60
Monderer, D., Shapley, L.S.: Potential games. Games Econ. Behav. 14(1), 124–143 (1996)
Papadimitriou, C.H.: Algorithms, games, and the internet. In: Proceedings on 33rd Annual ACM Symposium on Theory of Computing, pp. 749–753 (2001)
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Chauhan, A., Lenzner, P., Melnichenko, A., Molitor, L. (2017). Selfish Network Creation with Non-uniform Edge Cost. In: Bilò, V., Flammini, M. (eds) Algorithmic Game Theory. SAGT 2017. Lecture Notes in Computer Science(), vol 10504. Springer, Cham. https://doi.org/10.1007/978-3-319-66700-3_13
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