The structure and complexity of Nash equilibria for a selfish routing game

  • Authors:

  • Dimitris Fotakis;Spyros Kontogiannis;Elias Koutsoupias;Marios Mavronicolas;Paul Spirakis

  • Affiliations:

  • Department of Information and Communication Systems Engineering, University of the Aegean, 83200 Samos, Greece;Department of Computer Science, University of Ioannina, 45110 Ioannina, Greece and Research Academic Computer Technology Institute, N. Kazantzaki Str., University Campus, 26500 Patras, Greece;Department of Informatics, University of Athens, Greece;Department of Computer Science, University of Cyprus, P.O. Box 20537, Nicosia CY-1678, Cyprus;Department of Computer Engineering and Informatics, University of Patras, Rion, 26500 Patras, Greece and Research Academic Computer Technology Institute, N. Kazantzaki Str., University Campus, 265 ...

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2009

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Abstract

In this work, we study the combinatorial structure and the computational complexity of Nash equilibria for a certain game that models selfish routing over a network consisting of m parallel links. We assume a collection of n users, each employing a mixed strategy, which is a probability distribution over links, to control the routing of her own traffic. In a Nash equilibrium, each user selfishly routes her traffic on those links that minimize her expected latency cost, given the network congestion caused by the other users. The social cost of a Nash equilibrium is the expectation, over all random choices of the users, of the maximum, over all links, latency through a link. We embark on a systematic study of several algorithmic problems related to the computation of Nash equilibria for the selfish routing game we consider. In a nutshell, these problems relate to deciding the existence of a pure Nash equilibrium, constructing a Nash equilibrium, constructing the pure Nash equilibria of minimum and maximum social cost, and computing the social cost of a given mixed Nash equilibrium. Our work provides a comprehensive collection of efficient algorithms, hardness results, and structural results for these algorithmic problems. Our results span and contrast a wide range of assumptions on the syntax of the Nash equilibria and on the parameters of the system.