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:
Institute of Optimization and Discrete Mathematics, Graz University of Technology, Graz, Austria;Institute of Optimization and Discrete Mathematics, Graz University of Technology, Graz, Austria;Department of Mathematics, University of Kaiserslautern, Kaiserslautern, Germany 67653;Department of Mathematics, University of Kaiserslautern, Kaiserslautern, Germany 67653;Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands 5600 MB
Venue:
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Year:
2008

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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.