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Timing Matters: Online Dynamics in Broadcast Games

  • Shuchi Chawla
  • Joseph (Seffi) Naor
  • Debmalya Panigrahi
  • Mohit Singh
  • Seeun William Umboh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11316)

Abstract

This paper studies the equilibrium states that can be reached in a network design game via natural game dynamics. First, we show that an arbitrarily interleaved sequence of arrivals and departures of players can lead to a polynomially inefficient solution at equilibrium. This implies that the central controller must have some control over the timing of agent arrivals and departures in order to ensure efficiency of the system at equilibrium. Indeed, we give a complementary result showing that if the central controller is allowed to restore equilibrium after every set of arrivals/departures via improving moves, the eventual equilibrium states reached have exponentially better efficiency.

References

  1. 1.
    Aland, S., Dumrauf, D., Gairing, M., Monien, B., Schoppmann, F.: Exact price of anarchy for polynomial congestion games. SIAM J. Comput. 40(5), 1211–1233 (2011)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Albers, S.: On the value of coordination in network design. SIAM J. Comput. 38(6), 2273–2302 (2009)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Alon, N., Awerbuch, B., Azar, Y., Buchbinder, N., Naor, J.: A general approach to online network optimization problems. ACM Trans. Algorithms 2(4), 640–660 (2006)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Anshelevich, E., Dasgupta, A., Kleinberg, J.M., Tardos, É., Wexler, T., Roughgarden, T.: The price of stability for network design with fair cost allocation. SIAM J. Comput. 38(4), 1602–1623 (2008)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Awerbuch, B., Azar, Y., Bartal, Y.: On-line generalized steiner problem. Theor. Comput. Sci. 324(2–3), 313–324 (2004)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Balcan, M.-F., Blum, A., Mansour, Y.: Circumventing the price of anarchy: leading dynamics to good behavior. SIAM J. Comput. 42(1), 230–264 (2013)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Beier, R., Czumaj, A., Krysta, P., Vöcking, B.: Computing equilibria for a service provider game with (im)perfect information. ACM Trans. Algorithms 2(4), 679–706 (2006)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Berman, P., Coulston, C.: On-line algorithms for steiner tree problems. In: Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing, pp. 344–353. ACM (1997)Google Scholar
  9. 9.
    Bilò, V., Bove, R.: Bounds on the price of stability of undirected network design games with three players. J. Interconnect. Netw. 12(1–2), 1–17 (2011)CrossRefGoogle Scholar
  10. 10.
    Bilò, V., Flammini, M., Moscardelli, L.: The price of stability for undirected broadcast network design with fair cost allocation is constant. In: FOCS, pp. 638–647 (2013)Google Scholar
  11. 11.
    Charikar, M., Karloff, H.J., Mathieu, C., Naor, J., Saks, M.E.: Online multicast with egalitarian cost sharing. In: SPAA, pp. 70–76 (2008)Google Scholar
  12. 12.
    Chawla, S., Naor, J., Panigrahi, D., Singh, M., Umboh, S.W.: Timing matters: online dynamics in broadcast games. CoRR, abs/1611.07745 (2016). http://arxiv.org/abs/1611.07745
  13. 13.
    Chekuri, C., Chuzhoy, J., Lewin-Eytan, L., Naor, J.(Seffi), Orda, A.: Non-cooperative multicast and facility location games. IEEE J. Sel. Areas Commun. 25(6), 1193–1206 (2007)CrossRefGoogle Scholar
  14. 14.
    Chen, H.-L., Roughgarden, T.: Network design with weighted players. Theory Comput. Syst. 45(2), 302–324 (2009)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Christodoulou, G., Chung, C., Ligett, K., Pyrga, E., van Stee, R.: On the price of stability for undirected network design. In: Bampis, E., Jansen, K. (eds.) WAOA 2009. LNCS, vol. 5893, pp. 86–97. Springer, Heidelberg (2010).  https://doi.org/10.1007/978-3-642-12450-1_8CrossRefGoogle Scholar
  16. 16.
    Ene, A., Chakrabarty, D., Krishnaswamy, R., Panigrahi, D.: Online buy-at-bulk network design. In: IEEE 56th Annual Symposium on Foundations of Computer Science, FOCS 2015, Berkeley, CA, USA, 17–20 October, 2015, pp. 545–562 (2015)Google Scholar
  17. 17.
    Fabrikant, A., Papadimitriou, C.H., Talwar, K.: The complexity of pure Nash equilibria. In: Proceedings of the 36th Annual ACM Symposium on Theory of Computing, Chicago, IL, USA, 13–16 June 2004, pp. 604–612 (2004)Google Scholar
  18. 18.
    Fanelli, A., Leniowski, D., Monaco, G., Sankowski, P.: The ring design game with fair cost allocation. Theor. Comput. Sci. 562, 90–100 (2015)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Fiat, A., Kaplan, H., Levy, M., Olonetsky, S., Shabo, R.: On the price of stability for designing undirected networks with fair cost allocations. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4051, pp. 608–618. Springer, Heidelberg (2006).  https://doi.org/10.1007/11786986_53CrossRefGoogle Scholar
  20. 20.
    Freeman, R., Haney, S., Panigrahi, D.: On the Price of stability of undirected multicast games. In: Cai, Y., Vetta, A. (eds.) WINE 2016. LNCS, vol. 10123, pp. 354–368. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-54110-4_25CrossRefGoogle Scholar
  21. 21.
    Gupta, A., Ravi, R., Talwar, K., Umboh, S.W.: LAST but not least: online spanners for buy-at-bulk. In: Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017, 16–19 January, Hotel Porta Fira, Barcelona, Spain, pp. 589–599 (2017)Google Scholar
  22. 22.
    Hajiaghayi, M.T., Liaghat, V., Panigrahi, D.: Online node-weighted steiner forest and extensions via disk paintings. In: FOCS, pp. 558–567 (2013)Google Scholar
  23. 23.
    Hajiaghayi, M.T., Liaghat, V., Panigrahi, D.: Near-optimal online algorithms for prize-collecting steiner problems. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds.) ICALP 2014. LNCS, vol. 8572, pp. 576–587. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-662-43948-7_48CrossRefGoogle Scholar
  24. 24.
    Harks, T., Klimm, M.: On the existence of pure nash equilibria in weighted congestion games. Math. Oper. Res. 37(3), 419–436 (2012)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Imase, M., Waxman, B.M.: Dynamic steiner tree problem. SIAM J. Discrete Math. 4(3), 369–384 (1991)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Kawase, Y., Makino, K.: Nash equilibria with minimum potential in undirected broadcast games. Theor. Comput. Sci. 482, 33–47 (2013)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Lee, E., Ligett, K.: Improved bounds on the price of stability in network cost sharing games. In: EC, pp. 607–620 (2013)Google Scholar
  28. 28.
    Li, J.: An O(log(n)/log(log(n))) upper bound on the price of stability for undirected shapley network design games. Inf. Process. Lett. 109(15), 876–878 (2009)CrossRefGoogle Scholar
  29. 29.
    Milchtaich, I.: Congestion games with player-specific payoff function. Games Econ. Behav. 13, 111–124 (1996)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Monderer, D., Shapley, L.S.: Potential games. Games Econ. Behav. 14, 124–143 (1996)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Naor, J., Panigrahi, D., Singh, M.: Online node-weighted steiner tree and related problems. In: FOCS, pp. 210–219 (2011)Google Scholar
  32. 32.
    Qian, J., Umboh, S.W., Williamson, D.P.: Online constrained forest and prize-collecting network design. Algorithmica 80(11), 3335–3364 (2018)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Law-Yone, N., Holzman, R.: Strong equilibrium in congestion games. Games Econ. Behav. 21, 85–101 (1997)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Rosenthal, R.W.: A class of games possessing pure-strategy Nash equilibria. Int. J. Game Theory 2(1), 65–67 (1973)MathSciNetCrossRefGoogle Scholar
  35. 35.
    Ui, T.: A shapley value representation of potential games. Games Econ. Behav. 31(1), 121–135 (2000)MathSciNetCrossRefGoogle Scholar
  36. 36.
    Umboh, S.: Online network design algorithms via hierarchical decompositions. In: Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1373–1387. SIAM (2015)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Shuchi Chawla
    • 1
  • Joseph (Seffi) Naor
    • 2
  • Debmalya Panigrahi
    • 3
  • Mohit Singh
    • 4
  • Seeun William Umboh
    • 5
  1. 1.Computer Sciences DepartmentUniversity of Wisconsin - MadisonMadisonUSA
  2. 2.Department of Computer ScienceTechnionHaifaIsrael
  3. 3.Department of Computer ScienceDuke UniversityDurhamUSA
  4. 4.H. Milton Stewart School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA
  5. 5.School of Information TechnologiesThe University of SydneySydneyAustralia

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