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Strong equilibrium in cost sharing connection games

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

    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Games and Economic Behavior.

    Volume (Year): 67 (2009)
    Issue (Month): 1 (September)
    Pages: 51-68

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    Handle: RePEc:eee:gamebe:v:67:y:2009:i:1:p:51-68

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    Web page: http://www.elsevier.com/locate/inca/622836

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    Keywords: Strong equilibrium Price of anarchy Strong price of anarchy Coalitions Cost sharing Network design;

    References

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    1. Holzman, Ron & Law-Yone, Nissan, 1997. "Strong Equilibrium in Congestion Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 85-101, October.
    2. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-37, September.
    3. Hervé Moulin & Scott Shenker, 2001. "Strategyproof sharing of submodular costs:budget balance versus efficiency," Economic Theory, Springer, vol. 18(3), pages 511-533.
    4. 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.
    5. Milchtaich, Igal, 2006. "Network topology and the efficiency of equilibrium," Games and Economic Behavior, Elsevier, vol. 57(2), pages 321-346, November.
    6. 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.
    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. Ruben Juarez & Rajnish Kumar, 2012. "Implementing Efficient Graphs in Connection Networks," Working Papers 201203, University of Hawaii at Manoa, Department of Economics.
    2. Martin Hoefer, 2013. "Strategic cooperation in cost sharing games," International Journal of Game Theory, Springer, vol. 42(1), pages 29-53, February.
    3. Gaëtan Fournier & Marco Scarsini, 2014. "Hotelling Games on Networks: Efficiency of Equilibria," Documents de travail du Centre d'Economie de la Sorbonne 14033, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.

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