On Approximate Pure Nash Equilibria in Weighted Congestion Games with Polynomial Latencies

Authors Ioannis Caragiannis, Angelo Fanelli

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Ioannis Caragiannis
  • University of Patras & CTI "Diophantus", Patras, Greece
Angelo Fanelli
  • CNRS (UMR-6211), Caen, France

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Ioannis Caragiannis and Angelo Fanelli. On Approximate Pure Nash Equilibria in Weighted Congestion Games with Polynomial Latencies. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 133:1-133:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


We consider the problem of the existence of natural improvement dynamics leading to approximate pure Nash equilibria, with a reasonable small approximation, and the problem of bounding the efficiency of such equilibria in the fundamental framework of weighted congestion game with polynomial latencies of degree at most d >= 1. In this work, by exploiting a simple technique, we firstly show that the game always admits a d-approximate potential function. This implies that every sequence of d-approximate improvement moves by the players always leads the game to a d-approximate pure Nash equilibrium. As a corollary, we also obtain that, under mild assumptions on the structure of the players' strategies, the game always admits a constant approximate potential function. Secondly, by using a simple potential function argument, we are able to show that in the game there always exists a (d+delta)-approximate pure Nash equilibrium, with delta in [0,1], whose cost is 2/(1+delta) times the cost of an optimal state.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory
  • Theory of computation → Convergence and learning in games
  • Congestion games
  • approximate pure Nash equilibrium
  • potential functions
  • approximate price of stability


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