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Approximate Pure Nash Equilibria in Weighted Congestion Games

Authors Christoph Hansknecht, Max Klimm, Alexander Skopalik

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Christoph Hansknecht
Max Klimm
Alexander Skopalik

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Christoph Hansknecht, Max Klimm, and Alexander Skopalik. Approximate Pure Nash Equilibria in Weighted Congestion Games. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 28, pp. 242-257, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2014)


We study the existence of approximate pure Nash equilibria in weighted congestion games and develop techniques to obtain approximate potential functions that prove the existence of alpha-approximate pure Nash equilibria and the convergence of alpha-improvement steps. Specifically, we show how to obtain upper bounds for approximation factor alpha for a given class of cost functions. For example for concave cost functions the factor is at most 3/2, for quadratic cost functions it is at most 4/3, and for polynomial cost functions of maximal degree d it is at at most d + 1. For games with two players we obtain tight bounds which are as small as for example 1.054 in the case of quadratic cost functions.
  • Congestion game
  • Pure Nash equilibrium
  • Approximate equilibrium
  • Existence
  • Potential function


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