On Existence and Properties of Approximate Pure Nash Equilibria in Bandwidth Allocation Games

  • Maximilian DreesEmail author
  • Matthias Feldotto
  • Sören Riechers
  • Alexander Skopalik
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9347)


In bandwidth allocation games (BAGs), the strategy of a player consists of various demands on different resources. The player’s utility is at most the sum of these demands, provided they are fully satisfied. Every resource has a limited capacity and if it is exceeded by the total demand, it has to be split between the players. Since these games generally do not have pure Nash equilibria, we consider approximate pure Nash equilibria, in which no player can prove her utility by more than some fixed factor \({\alpha }\) through unilateral strategy changes. There is a threshold \({\alpha }_{\delta }\) (where \(\delta \) is a parameter that limits the demand of each player on a specific resource) such that \({\alpha }\)-approximate pure Nash equilibria always exist for \(\alpha \ge \alpha _\delta \), but not for \(\alpha < \alpha _\delta \). We give both upper and lower bounds on this threshold \(\alpha _\delta \) and show that the corresponding decision problem is \(\mathsf{NP}\)-hard. We also show that the \(\alpha \)-approximate price of anarchy for BAGs is \(\alpha +1\). For a restricted version of the game, where demands of players only differ slightly from each other (e.g. symmetric games), we show that approximate Nash equilibria can be reached (and thus also be computed) in polynomial time using the best-response dynamic. Finally, we show that a broader class of utility-maximization games (which includes BAGs) converges quickly towards states whose social welfare is close to the optimum.


Nash Equilibrium Strategy Profile Strategy Space Congestion Game Potential Game 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Maximilian Drees
    • 1
    Email author
  • Matthias Feldotto
    • 1
  • Sören Riechers
    • 1
  • Alexander Skopalik
    • 1
  1. 1.Heinz Nixdorf Institute & Department of Computer ScienceUniversity of PaderbornPaderbornGermany

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