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Selfish Network Creation with Non-uniform Edge Cost

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Algorithmic Game Theory (SAGT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 10504))

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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.

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References

  1. 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)

    MATH  Google Scholar 

  2. Alon, N., Demaine, E.D., Hajiaghayi, M.T., Leighton, T.: Basic network creation games. SIAM J. Discret. Math. 27(2), 656–668 (2013)

    Article  MathSciNet  Google Scholar 

  3. Àlvarez, C., Blesa, M.J., Duch, A., Messegué, A., Serna, M.: Celebrity games. Theor. Comput. Sci. 648, 56–71 (2016)

    Article  MathSciNet  Google Scholar 

  4. 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

    Chapter  Google Scholar 

  5. Bala, V., Goyal, S.: A noncooperative model of network formation. Econometrica 68(5), 1181–1229 (2000)

    Article  MathSciNet  Google Scholar 

  6. Barabási, A.-L.: Network Science. Cambridge University Press, Cambridge (2016)

    MATH  Google Scholar 

  7. 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 

  8. 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

    Chapter  Google Scholar 

  9. Chauhan, A., Lenzner, P., Melnichenko, A., Molitor, L.: Selfish network creation with non-uniform edge cost (2017). arXiv preprint arXiv:1706.10200

  10. Corbo, J., Parkes, D.: The price of selfish behavior in bilateral network formation. In: PODC 2005, pp. 99–107. ACM, New York (2005)

    Google Scholar 

  11. 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

    Chapter  Google Scholar 

  12. 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

    Chapter  Google Scholar 

  13. 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)

    Article  MathSciNet  Google Scholar 

  14. 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)

    Google Scholar 

  15. Graham, R., Hamilton, L., Levavi, A., Loh, P.-S.: Anarchy is free in network creation. ACM Trans. Algorithms (TALG) 12(2), 15 (2016)

    MathSciNet  MATH  Google Scholar 

  16. Jackson, M.O., Wolinsky, A.: A strategic model of social and economic networks. J. Econ. Theory 71(1), 44–74 (1996)

    Article  MathSciNet  Google Scholar 

  17. Kawald, B., Lenzner, P.: On dynamics in selfish network creation. In: SPAA 2013, pp. 83–92. ACM (2013)

    Google Scholar 

  18. 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

    Chapter  Google Scholar 

  19. 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

    Chapter  Google Scholar 

  20. Leskovec, J., Kleinberg, J., Faloutsos, C.: Graphs over time: densification laws, shrinking diameters and possible explanations. In: SIGKDD 2005, pp. 177–187. ACM (2005)

    Google Scholar 

  21. 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

    Chapter  MATH  Google Scholar 

  22. 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)

    Google Scholar 

  23. 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

    Chapter  Google Scholar 

  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

    Chapter  Google Scholar 

  25. Monderer, D., Shapley, L.S.: Potential games. Games Econ. Behav. 14(1), 124–143 (1996)

    Article  MathSciNet  Google Scholar 

  26. Papadimitriou, C.H.: Algorithms, games, and the internet. In: Proceedings on 33rd Annual ACM Symposium on Theory of Computing, pp. 749–753 (2001)

    Google Scholar 

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Authors and Affiliations

  1. Algorithm Engineering Group, Hasso Plattner Institute, Potsdam, Germany

    Ankit Chauhan, Pascal Lenzner, Anna Melnichenko & Louise Molitor

Authors
  1. Ankit Chauhan
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  2. Pascal Lenzner
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  3. Anna Melnichenko
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  4. Louise Molitor
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Corresponding author

Correspondence to Pascal Lenzner .

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Editors and Affiliations

  1. University of Salento, Lecce, Italy

    Vittorio Bilò

  2. University of L'Aquila, L'Aquila, Italy

    Michele Flammini

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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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  • DOI: https://doi.org/10.1007/978-3-319-66700-3_13

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