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Strong price of anarchy

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

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    Bibliographic Info

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

    Volume (Year): 65 (2009)
    Issue (Month): 2 (March)
    Pages: 289-317

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    Handle: RePEc:eee:gamebe:v:65:y:2009:i:2:p:289-317

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

    Related research

    Keywords: Strong equilibrium Price of anarchy Strong price of anarchy Coalitions Congestion games Network formation Job scheduling;

    References

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    1. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
    2. 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.
    3. 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.
    4. Hervé Moulin & Scott Shenker, 2001. "Strategyproof sharing of submodular costs:budget balance versus efficiency," Economic Theory, Springer, vol. 18(3), pages 511-533.
    5. Dutta, Bhaskar & Mutuswami, Suresh, 1997. "Stable Networks," Journal of Economic Theory, Elsevier, vol. 76(2), pages 322-344, October.
      • Dutta, Bhaskar & Mutuswami, Suresh, 1996. "Stable Networks," Working Papers 971, California Institute of Technology, Division of the Humanities and Social Sciences.
    6. Igal Milchtaich, 1998. "Crowding games are sequentially solvable," International Journal of Game Theory, Springer, vol. 27(4), pages 501-509.
    7. Holzman, Ron & Law-Yone, Nissan, 1997. "Strong Equilibrium in Congestion Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 85-101, October.
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    Cited by:
    1. Martin Hoefer, 2013. "Strategic cooperation in cost sharing games," International Journal of Game Theory, Springer, vol. 42(1), pages 29-53, February.
    2. Ruben Juarez & Rajnish Kumar, 2012. "Implementing Efficient Graphs in Connection Networks," Working Papers 201203, University of Hawaii at Manoa, Department of Economics.
    3. Tobias Harks & Max Klimm & Rolf Möhring, 2013. "Strong equilibria in games with the lexicographical improvement property," International Journal of Game Theory, Springer, vol. 42(2), pages 461-482, May.

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