Pure Nash Equilibria in Player-Specific and Weighted Congestion Games

  • Heiner Ackermann
  • Heiko Röglin
  • Berthold Vöcking
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4286)


Unlike standard congestion games, weighted congestion games and congestion games with player-specific delay functions do not necessarily possess pure Nash equilibria. It is known, however, that there exist pure equilibria for both of these variants in the case of singleton congestion games, i. e., if the players’ strategy spaces contain only sets of cardinality one. In this paper, we investigate how far such a property on the players’ strategy spaces guaranteeing the existence of pure equilibria can be extended. We show that both weighted and player-specific congestion games admit pure equilibria in the case of matroid congestion games, i. e., if the strategy space of each player consists of the bases of a matroid on the set of resources. We also show that the matroid property is the maximal property that guarantees pure equilibria without taking into account how the strategy spaces of different players are interweaved. In the case of player-specific congestion games, our analysis of matroid games also yields a polynomial time algorithm for computing pure equilibria.


Nash Equilibrium Minimum Delay Strategy Space Delay Function Congestion Game 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Heiner Ackermann
    • 1
  • Heiko Röglin
    • 1
  • Berthold Vöcking
    • 1
  1. 1.Department of Computer ScienceRWTH AachenAachenGermany

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