Network Creation Games: Think Global – Act Local

  • Andreas Cord-LandwehrEmail author
  • Pascal LenznerEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9235)


We investigate a non-cooperative game-theoretic model for the formation of communication networks by selfish agents. Each agent aims for a central position at minimum cost for creating edges. In particular, the general model (Fabrikant et al., PODC’03) became popular for studying the structure of the Internet or social networks. Despite its significance, locality in this game was first studied only recently (Bilò et al., SPAA’14), where a worst case locality model was presented, which came with a high efficiency loss in terms of quality of equilibria. Our main contribution is a new and more optimistic view on locality: agents are limited in their knowledge and actions to their local view ranges, but can probe different strategies and finally choose the best. We study the influence of our locality notion on the hardness of computing best responses, convergence to equilibria, and quality of equilibria. Moreover, we compare the strength of local versus non-local strategy changes. Our results address the gap between the original model and the worst case locality variant. On the bright side, our efficiency results are in line with observations from the original model, yet we have a non-constant lower bound on the Price of Anarchy.


Nash Equilibrium Solution Concept Locality Constraint Tree Network Pure Nash Equilibrium 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Albers, S., Eilts, S., Even-Dar, E., Mansour, Y., Roditty, L.: On nash equilibria for a network creation game. ACM Trans. Econ. Comput. 2(1), 2 (2014)CrossRefzbMATHGoogle Scholar
  2. 2.
    Anshelevich, E., Dasgupta, A., Kleinberg, J., Tardos, E., Wexler, T., Roughgarden, T.: The price of stability for network design with fair cost allocation. SIAM J. Comput. 38(4), 1602–1623 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Bala, V., Goyal, S.: A noncooperative model of network formation. Econometrica 68(5), 1181–1229 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    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, Heidelberg (2014) Google Scholar
  5. 5.
    Bilò, D., Gualà, L., Leucci, S., Proietti, G.: Locality-based network creation games. In: SPAA 2014, pp. 277–286. ACM, New York (2014)Google Scholar
  6. 6.
    Corbo, J., Parkes, D.: The price of selfish behavior in bilateral network formation. In: PODC 2005 Proceedings, pp. 99–107. ACM, New York (2005)Google Scholar
  7. 7.
    Cord-Landwehr, A., Lenzner, P.: Network creation games: Think global - act local. CoRR, abs/1506.02616 (2015)Google Scholar
  8. 8.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Ehsani, S., Fazli, M., Mehrabian, A., Sadeghabad, S.S., Safari, M., Saghafian, M., ShokatFadaee, S.: On a bounded budget network creation game. In: SPAA 2011, pp. 207–214. ACM (2011)Google Scholar
  10. 10.
    Fabrikant, A., Luthra, A., Maneva, E., Papadimitriou, C.H., Shenker, S.: On a network creation game. In: PODC 2003 Proceedings, pp. 347–351. ACM (2003)Google Scholar
  11. 11.
    Hoefer, M.: Local matching dynamics in social networks. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 113–124. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  12. 12.
    Jackson, M.O., Wolinsky, A.: A strategic model of social and economic networks. J. Econ. Theory 71(1), 44–74 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Kawald, B., Lenzner, P.: On dynamics in selfish network creation. In: Proceedings of the 25th ACM Symposium on Parallelism in Algorithms and Architectures, pp. 83–92. ACM (2013)Google Scholar
  14. 14.
    Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, p. 404. Springer, Heidelberg (1999) CrossRefGoogle Scholar
  15. 15.
    Lenzner, P.: On dynamics in basic network creation games. In: Persiano, G. (ed.) SAGT 2011. LNCS, vol. 6982, pp. 254–265. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  16. 16.
    Lenzner, P.: Greedy selfish network creation. In: Goldberg, P.W. (ed.) WINE 2012. LNCS, vol. 7695, pp. 142–155. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  17. 17.
    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, Heidelberg (2013) CrossRefGoogle Scholar
  18. 18.
    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) CrossRefGoogle Scholar
  19. 19.
    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) CrossRefGoogle Scholar
  20. 20.
    Monderer, D., Shapley, L.S.: Potential games. Games Econ. Behav. 14(1), 124–143 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V.V.: Algorithmic Game Theory. Cambridge University Press, New York (2007) CrossRefzbMATHGoogle Scholar
  22. 22.
    Williamson, D.P., Shmoys, D.B.: The Design of Approximation Algorithms. Cambridge University Press, New York (2011) CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Heinz Nixdorf Institute and Department of Computer ScienceUniversity of PaderbornPaderbornGermany
  2. 2.Department of Computer ScienceFriedrich-Schiller-University JenaJenaGermany

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