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How to find Nash equilibria with extreme total latency in network congestion games?

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  • Heike Sperber

Abstract

We study the complexity of finding extreme pure Nash equilibria in symmetric network congestion games and analyse how it is influenced by the graph topology and the number of users. In our context best and worst equilibria are those with minimum or maximum total latency, respectively. We establish that both problems can be solved by a Greedy type algorithm equipped with a suitable tie breaking rule on extension-parallel graphs. On series-parallel graphs finding a worst Nash equilibrium is NP-hard for two or more users while finding a best one is solvable in polynomial time for two users and NP-hard for three or more. additionally we establish NP-hardness in the strong sense for the problem of finding a worst Nash equilibrium on a general acyclic graph. Copyright Springer-Verlag 2010

Suggested Citation

  • Heike Sperber, 2010. "How to find Nash equilibria with extreme total latency in network congestion games?," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(2), pages 245-265, April.
    • Handle: RePEc:spr:mathme:v:71:y:2010:i:2:p:245-265
    DOI: 10.1007/s00186-009-0293-6
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