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Strong equilibrium in cost sharing connection games


  • Epstein, Amir
  • Feldman, Michal
  • Mansour, Yishay


We study network games in which each player wishes to connect his source and sink, and the cost of each edge is shared among its users either equally (in Fair Connection Games--FCG's) or arbitrarily (in General Connection Games--GCG's). We study the existence and quality of strong equilibria (SE)--strategy profiles from which no coalition can improve the cost of each of its members--in these settings. We show that SE always exist in the following games: (1) Single source and sink FCG's and GCG's. (2) Single source multiple sinks FCG's and GCG's on series parallel graphs. (3) Multi source and sink FCG's on extension parallel graphs. As for the quality of the SE, in any FCG with n players, the cost of any SE is bounded by H(n) (i.e., the harmonic sum), contrasted with the [Theta](n) price of anarchy. For any GCG, any SE is optimal.

Suggested Citation

  • Epstein, Amir & Feldman, Michal & Mansour, Yishay, 2009. "Strong equilibrium in cost sharing connection games," Games and Economic Behavior, Elsevier, vol. 67(1), pages 51-68, September.
  • Handle: RePEc:eee:gamebe:v:67:y:2009:i:1:p:51-68

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    References listed on IDEAS

    1. Hervé Moulin & Scott Shenker, 2001. "Strategyproof sharing of submodular costs:budget balance versus efficiency," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 18(3), pages 511-533.
    2. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-1037, September.
    3. Holzman, Ron & Law-Yone, Nissan, 1997. "Strong Equilibrium in Congestion Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 85-101, October.
    4. Holzman, Ron & Law-yone (Lev-tov), Nissan, 2003. "Network structure and strong equilibrium in route selection games," Mathematical Social Sciences, Elsevier, vol. 46(2), pages 193-205, October.
    5. Milchtaich, Igal, 2006. "Network topology and the efficiency of equilibrium," Games and Economic Behavior, Elsevier, vol. 57(2), pages 321-346, November.
    6. Bernheim, B. Douglas & Peleg, Bezalel & Whinston, Michael D., 1987. "Coalition-Proof Nash Equilibria I. Concepts," Journal of Economic Theory, Elsevier, vol. 42(1), pages 1-12, June.
    7. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
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    Cited by:

    1. Martin Hoefer, 2013. "Strategic cooperation in cost sharing games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(1), pages 29-53, February.
    2. Ruben Juarez & Rajnish Kumar, 2013. "Implementing efficient graphs in connection networks," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(2), pages 359-403, October.
    3. repec:eee:apmaco:v:265:y:2015:i:c:p:911-927 is not listed on IDEAS
    4. Kukushkin, Nikolai S., 2017. "Strong Nash equilibrium in games with common and complementary local utilities," Journal of Mathematical Economics, Elsevier, vol. 68(C), pages 1-12.
    5. Gaëtan Fournier & Marco Scarsini, 2014. "Hotelling Games on Networks: Efficiency of Equilibria," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00983085, HAL.
    6. Philipp von Falkenhausen & Tobias Harks, 2013. "Optimal Cost Sharing for Resource Selection Games," Mathematics of Operations Research, INFORMS, vol. 38(1), pages 184-208, February.
    7. Moulin, Hervé, 2014. "Pricing traffic in a spanning network," Games and Economic Behavior, Elsevier, vol. 86(C), pages 475-490.
    8. Ron Holzman & Dov Monderer, 2015. "Strong equilibrium in network congestion games: increasing versus decreasing costs," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(3), pages 647-666, August.
    9. Harks, Tobias & von Falkenhausen, Philipp, 2014. "Optimal cost sharing for capacitated facility location games," European Journal of Operational Research, Elsevier, vol. 239(1), pages 187-198.


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