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Strong price of anarchy

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  • Andelman, Nir
  • Feldman, Michal
  • Mansour, Yishay

Abstract

A strong equilibrium is a pure Nash equilibrium which is resilient to deviations by coalitions. We define the strong price of anarchy (SPoA) to be the ratio of the worst strong equilibrium to the social optimum. Differently from the Price of Anarchy (defined as the ratio of the worst Nash Equilibrium to the social optimum), it quantifies the loss incurred from the lack of a central designer in settings that allow for coordination. We study the SPoA in two settings, namely job scheduling and network creation. In the job scheduling game we show that for unrelated machines the SPoA can be bounded as a function of the number of machines and the size of the coalition. For the network creation game we show that the SPoA is at most 2. In both cases we show that a strong equilibrium always exists, except for a well defined subset of network creation games.

Suggested Citation

  • Andelman, Nir & Feldman, Michal & Mansour, Yishay, 2009. "Strong price of anarchy," Games and Economic Behavior, Elsevier, vol. 65(2), pages 289-317, March.
    • Handle: RePEc:eee:gamebe:v:65:y:2009:i:2:p:289-317
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    Cited by:

    1. Krzysztof R. Apt & Bart Keijzer & Mona Rahn & Guido Schäfer & Sunil Simon, 2017. "Coordination games on graphs," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(3), pages 851-877, August.
    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. Tobias Harks & Martin Hoefer & Anja Schedel & Manuel Surek, 2021. "Efficient Black-Box Reductions for Separable Cost Sharing," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 134-158, February.
    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. Michal Feldman & Tami Tamir, 2012. "Conflicting Congestion Effects in Resource Allocation Games," Operations Research, INFORMS, vol. 60(3), pages 529-540, June.
    8. Harks, Tobias & Klimm, Max, 2015. "Equilibria in a class of aggregative location games," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 211-220.
    9. Tobias Harks & Max Klimm & Rolf Möhring, 2013. "Strong equilibria in games with the lexicographical improvement property," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 461-482, May.
    10. Cong Chen & Paul Giessler & Akaki Mamageishvili & Matúš Mihalák & Paolo Penna, 2024. "Sequential solutions in machine scheduling games," Journal of Scheduling, Springer, vol. 27(4), pages 363-373, August.
    11. Rosner, Shaul & Tamir, Tami, 2023. "Scheduling games with rank-based utilities," Games and Economic Behavior, Elsevier, vol. 140(C), pages 229-252.
    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. Eleonora Braggion & Nicola Gatti & Roberto Lucchetti & Tuomas Sandholm & Bernhard von Stengel, 2020. "Strong Nash equilibria and mixed strategies," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(3), pages 699-710, September.
    14. Tobias Harks & Max Klimm, 2012. "On the Existence of Pure Nash Equilibria in Weighted Congestion Games," Mathematics of Operations Research, INFORMS, vol. 37(3), pages 419-436, August.
    15. Cong Chen & Yinfeng Xu, 0. "Coordination mechanisms for scheduling selfish jobs with favorite machines," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-33.
    16. Jasper Jong & Marc Uetz, 2020. "The quality of equilibria for set packing and throughput scheduling games," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 321-344, March.
    17. Cong Chen & Yinfeng Xu, 2020. "Coordination mechanisms for scheduling selfish jobs with favorite machines," Journal of Combinatorial Optimization, Springer, vol. 40(2), pages 333-365, August.
    18. 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.
    19. Leah Epstein & Sven O. Krumke & Asaf Levin & Heike Sperber, 2011. "Selfish bin coloring," Journal of Combinatorial Optimization, Springer, vol. 22(4), pages 531-548, November.

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