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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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    References listed on IDEAS

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    Cited by:

    1. repec:spr:jogath:v:46:y:2017:i:3:d:10.1007_s00182-016-0560-8 is not listed on IDEAS
    2. 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.
    3. Harks, Tobias & Klimm, Max, 2015. "Equilibria in a class of aggregative location games," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 211-220.
    4. 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.
    5. 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.

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