Theory of Computing Systems

, Volume 57, Issue 3, pp 598–616 | Cite as

Congestion Games with Capacitated Resources

  • Laurent GourvèsEmail author
  • Jérôme Monnot
  • Stefano Moretti
  • Nguyen Kim Thang


The players of a congestion game interact by allocating bundles of resources from a common pool. This type of games leads to well studied models for analyzing strategic situations, including networks operated by uncoordinated selfish users. Congestion games constitute a subclass of potential games, meaning that a pure Nash equilibrium emerges from a myopic process where the players iteratively react by switching to a strategy that diminishes their individual cost. With the aim of covering more applications, for instance in communication networks, we extend congestion games to the setting where every resource is endowed with a capacity which possibly limits its number of users. From the negative side, we show that a pure Nash equilibrium is not guaranteed to exist in any case and we prove that deciding whether a game possesses a pure Nash equilibrium is NP-complete. Our positive results state that congestion games with capacities are potential games in the well studied singleton case. Polynomial algorithms that compute these equilibria are also provided.


Congestion games Pure nash equilibrium Potential function Algorithms 



We thank the anonymous referees for their comments which lead to significant improvements of the manuscript.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Laurent Gourvès
    • 1
    Email author
  • Jérôme Monnot
    • 1
  • Stefano Moretti
    • 1
  • Nguyen Kim Thang
    • 2
  1. 1.LAMSADE, CNRS UMR 7243Université Paris DauphineParisFrance
  2. 2.IBISCUniversité d’Evry Val d’EssonneÉvryFrance

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