Skip to main content
Log in

Network Formation for Asymmetric Players and Bilateral Contracting

  • Published:
Theory of Computing Systems Aims and scope Submit manuscript

Abstract

We study a network formation game where players wish to send traffic to other players. Players can be seen as nodes of an undirected graph whose edges are defined by contracts between the corresponding players. Each player can contract bilaterally with others to form bidirectional links or break unilaterally contracts to eliminate the corresponding links. Our model is an extension of the traffic routing model considered in Arcaute, E., Johari, R., Mannor, S., (IEEE Trans. Automat. Contr. 54(8), 1765–1778 2009) in which we do not require the traffic to be uniform and all-to-all. Player i specifies the amount of traffic t i j ≥ 0 that wants to send to player j. Our notion of stability is the network pairwise Nash stability, when no node wishes to deviate unilaterally and no pair of nodes can obtain benefit from deviating bilaterally. We show a characterization of the topologies that are pairwise Nash stable for a given traffic matrix. We prove that the best response problem is NP-hard and devise a myopic dynamics so that the deviation of the active node can be computed in polynomial time. We show the convergence of the dynamics to pairwise Nash configurations, when the contracting functions are anti-symmetric and affine, and that the expected convergence time is polynomial in the number of nodes when the node activation process is uniform.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

Notes

  1. The proof of convergence holds whenever the node activation process guarantees that almost surely all pair of nodes u and v are activated successively infinitely often (however the expected time will not necessarily be the same)

References

  1. 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 Algorithms, SODA 2006, Miami, Florida, USA, 22-26, 2006, pp 89–98. ACM Press (2006)

  2. 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)

    Article  MATH  Google Scholar 

  3. Alon, N., Demaine, E.D., Hajiaghayi, M., Kanellopoulos, P., Leighton, T.: Correction: Basic network creation games. SIAM J. Discret. Math. 28(3), 1638–1640 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  4. 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  MATH  Google Scholar 

  5. Arcaute, E., Johari, R., Mannor, S.: Network formation: Bilateral contracting and myopic dynamics. In: Deng, X., Graham, F.C. (eds.) Internet and Network Economics, Third International Workshop, WINE 2007, San Diego, CA, USA, December 12-14, 2007, Proceedings, volume 4858 of Lecture Notes in Computer Science, pp 191–207. Springer (2007)

  6. Arcaute, E., Johari, R., Mannor, S.: Local two-stage myopic dynamics for network formation games. In: Papadimitriou, C.H., Zhang, S. (eds.) Internet and Network Economics, 4th International Workshop, WINE 2008, Shanghai, China, December 17-20, 2008. Proceedings, volume 5385 of Lecture Notes in Computer Science, pp 263–277. Springer (2008)

  7. Arcaute, E., Johari, R., Mannor, S.: Network formation: Bilateral contracting and myopic dynamics. IEEE Trans. Automat. Contr. 54(8), 1765–1778 (2009)

    Article  MathSciNet  Google Scholar 

  8. Bilò, D., Gualà, L., Proietti, G.: Bounded-distance network creation games. In: Goldberg, P.W. (ed.) Internet and Network Economics - 8th International Workshop, WINE 2012, Liverpool, UK, December 10-12, 2012. Proceedings, volume 7695 of Lecture Notes in Computer Science, pp 72–85. Springer (2012)

  9. Brandes, U., Hoefer, M., Nick, B.: Network creation games with disconnected equilibria. In: Papadimitriou, C.H., Zhang, S. (eds.) Internet and Network Economics, 4th International Workshop, WINE 2008, Shanghai, China, December 17-20, 2008. Proceedings, volume 5385 of Lecture Notes in Computer Science, pp 394–401. Springer (2008)

  10. Corbo, J., Parkes, D.C.: The price of selfish behavior in bilateral network formation. In: Aguilera, M. K., Aspnes, J. (eds.) Proceedings of the Twenty-Fourth Annual ACM Symposium on Principles of Distributed Computing, PODC 2005, Las Vegas, NV, USA, 17-20, 2005, p 2005. ACM

  11. Demaine, E.D., Hajiaghayi, M., Mahini, H., Zadimoghaddam, M.: The price of anarchy in network creation games. In: Gupta, I., Wattenhofer, R. (eds.) Proceedings of the Twenty-Sixth Annual ACM Symposium on Principles of Distributed Computing, PODC 2007, Portland, Oregon, USA, August 12-15, 2007, pp 292–298. ACM (2007)

  12. Demaine, E.D., Hajiaghayi, M., Mahini, H., Zadimoghaddam, M.: The price of anarchy in cooperative network creation games. In: Albers, S., Marion, J. (eds.) 26th International Symposium on Theoretical Aspects of Computer Science, STACS 2009, February 26-28, 2009, Freiburg, Germany, Proceedings, volume 3 of LIPIcs, pp 301–312. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany (2009)

  13. Demaine, E.D., Hajiaghayi, M.T., Mahini, H., Zadimoghaddam, M.: The price of anarchy in cooperative network creation games. SIGecom Exchanges 8(2), 2 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  14. Demaine, E.D., Hajiaghayi, M.T., Mahini, H., Zadimoghaddam, M.: The price of anarchy in network creation games. ACM Trans. Algoritm. 8(2), 13 (2012)

    MathSciNet  MATH  Google Scholar 

  15. Fabrikant, A., Luthra, A., Maneva, E., Papadimitriou, C.H., Shenker, S.: On a network creation game. In: Proceedings of the Twenty-second Annual Symposium on Principles of Distributed Computing, PODC ’03, pp 347–351. ACM, NY, USA (2003)

  16. Jackson, M. O.: A survey of models of network formation: Stability and efficiency. Working Papers 1161, California Institute of Technology, Division of the Humanities and Social Sciences (2003)

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

    Article  MathSciNet  MATH  Google Scholar 

  18. Lenzner, P.: On dynamics in basic network creation games. In: Persiano, G. (ed.) Algorithmic Game Theory, 4th International Symposium, SAGT 2011, Amalfi, Italy, October 17-19, 2011. Proceedings, volume 6982 of Lecture Notes in Computer Science, pp 254–265. Springer (2011)

  19. Leonardi, S., Sankowski, P.: Network formation games with local coalitions. In: Gupta, I., Wattenhofer, R. (eds.) Proceedings of the Twenty-Sixth Annual ACM Symposium on Principles of Distributed Computing, PODC 2007, Portland, Oregon, USA, 12-15, 2007, pp 299–305. ACM (2007)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Maria Serna.

Additional information

Work partially supported by funds from the Spanish Ministry for Economy and Competitiveness (MINECO) and the European Union (FEDER funds) under grant TIN2013-46181-C02-1-R (COMMAS) and from AGAUR, Generalitat de Catalunya, under grant SGR 2014:1034 (ALBCOM).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Àlvarez, C., Serna, M. & Fernàndez, A. Network Formation for Asymmetric Players and Bilateral Contracting. Theory Comput Syst 59, 397–415 (2016). https://doi.org/10.1007/s00224-015-9640-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00224-015-9640-6

Keywords

Navigation