How hard is it to find extreme Nash equilibria in network congestion games?

Authors:
Elisabeth Gassner;Johannes Hatzl;Sven O. Krumke;Heike Sperber;Gerhard J. Woeginger
Affiliations:
Graz University of Technology, Institute of Optimization and Discrete Mathematics, Steyrergasse 30, Graz, Austria;Graz University of Technology, Institute of Optimization and Discrete Mathematics, Steyrergasse 30, Graz, Austria;University of Kaiserslautern, Department of Mathematics, P.O. Box 3049, 67653 Kaiserslautern, Germany;University of Kaiserslautern, Department of Mathematics, P.O. Box 3049, 67653 Kaiserslautern, Germany;Eindhoven University of Technology, Department of Mathematics and Computer Science, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
Venue:
Theoretical Computer Science
Year:
2009

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Abstract

We study the complexity of finding extreme pure Nash equilibria in symmetric (unweighted) network congestion games. In our context best and worst equilibria are those with minimum respectively maximum makespan. On series-parallel graphs a worst Nash equilibrium can be found by a Greedy approach while finding a best equilibrium is NP-hard. For a fixed number of users we give a pseudo-polynomial algorithm to find the best equilibrium in series-parallel networks. For general network topologies also finding a worst equilibrium is NP-hard.