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On the Complexity of Pareto-Optimal Nash and Strong Equilibria

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Abstract

We consider the computational complexity of coalitional solution concepts in scenarios related to load balancing such as anonymous and congestion games. In congestion games, Pareto-optimal Nash and strong equilibria, which are resilient to coalitional deviations, have recently been shown to yield significantly smaller inefficiency. Unfortunately, we show that several problems regarding existence, recognition, and computation of these concepts are hard, even in seemingly special classes of games. In anonymous games with constant number of strategies, we can efficiently recognize a state as Pareto-optimal Nash or strong equilibrium, but deciding existence for a game remains hard. In the case of player-specific singleton congestion games, we show that recognition and computation of both concepts can be done efficiently. In addition, in these games there are always short sequences of coalitional improvement moves to Pareto-optimal Nash and strong equilibria that can be computed efficiently.

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Authors and Affiliations

  1. Department of Computer Science, RWTH Aachen University, Aachen, Germany

    Martin Hoefer & Alexander Skopalik

Authors
  1. Martin Hoefer
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  2. Alexander Skopalik
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Correspondence to Martin Hoefer.

Additional information

A preliminary version of this paper appeared in the proceedings of the 3rd International Symposium on Algorithmic Game Theory (SAGT 2010) [16].

M. Hoefer was supported by DFG through UMIC Research Center at RWTH Aachen University and grant Ho 3831/3-1.

A. Skopalik was supported in part by the German Israeli Foundation (GIF) under contract 877/05.

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Hoefer, M., Skopalik, A. On the Complexity of Pareto-Optimal Nash and Strong Equilibria. Theory Comput Syst 53, 441–453 (2013). https://doi.org/10.1007/s00224-012-9433-0

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