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Strong equilibrium in cost sharing connection games

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

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.

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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    Cited by:

    1. Kukushkin, Nikolai, 2019. "Quasiseparable aggregation in games with common local utilities," MPRA Paper 93588, University Library of Munich, Germany.
    2. György Dósa & Leah Epstein, 2019. "Quality of strong equilibria for selfish bin packing with uniform cost sharing," Journal of Scheduling, Springer, vol. 22(4), pages 473-485, August.
    3. 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.
    4. Clempner, Julio B. & Poznyak, Alexander S., 2015. "Computing the strong Nash equilibrium for Markov chains games," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 911-927.
    5. Tami Tamir, 2023. "Cost-sharing games in real-time scheduling systems," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(1), pages 273-301, March.
    6. Le Breton, Michel & Shapoval, Alexander & Weber, Shlomo, 2021. "A game-theoretical model of the landscape theory," Journal of Mathematical Economics, Elsevier, vol. 92(C), pages 41-46.
    7. Di Feng & Bettina Klaus, 2022. "Preference revelation games and strict cores of multiple‐type housing market problems," International Journal of Economic Theory, The International Society for Economic Theory, vol. 18(1), pages 61-76, March.
    8. Gaëtan Fournier & Marco Scarsini, 2014. "Hotelling Games on Networks: Efficiency of Equilibria," Post-Print halshs-00983085, HAL.
    9. Bilò, Vittorio & Flammini, Michele & Moscardelli, Luca, 2020. "The price of stability for undirected broadcast network design with fair cost allocation is constant," Games and Economic Behavior, Elsevier, vol. 123(C), pages 359-376.
    10. Alexandre Belloni & Changrong Deng & Saša Pekeč, 2017. "Mechanism and Network Design with Private Negative Externalities," Operations Research, INFORMS, vol. 65(3), pages 577-594, June.
    11. 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.
    12. 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.
    13. 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.
    14. György Dósa & Leah Epstein, 2019. "Pareto optimal equilibria for selfish bin packing with uniform cost sharing," Journal of Combinatorial Optimization, Springer, vol. 37(3), pages 827-847, April.
    15. 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.
    16. Moulin, Hervé, 2014. "Pricing traffic in a spanning network," Games and Economic Behavior, Elsevier, vol. 86(C), pages 475-490.
    17. 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.

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