Computing approximate pure Nash equilibria in weighted congestion games with polynomial latency functions

We present an efficient algorithm for computing O(1)-approximate pure Nash equilibria in weighted congestion games with polynomial latency functions of constant maximum degree. For games with linear latency functions, the approximation guarantee is 3+ √ 5 2 + O(γ) for arbitrarily small γ > 0; for latency functions of maximum degree d, it is d. The running time is polynomial in the number of bits in the representation of the game and 1/γ. The algorithm extends our recent algorithm for unweighted congestion games [7] and is actually applied to a new class of games that we call Ψ-games. These are potential games that “approximate” weighted congestion games with polynomial latency functions, e.g., the existence of pure Nash equilibria in Ψ-games implies the existence of d!-approximate equilibria in weighted congestion games with polynomial latency functions of degree d. The analysis exploits the nice properties of the potential functions of Ψ-games. This work was partially supported by the grant NRF-RF2009-08 “Algorithmic aspects of coalitional games” and the EC-funded STREP Project FP7-ICT-258307 EULER. Research Academic Computer Technology Institute & Department of Computer Engineering and Informatics, University of Patras, 26500 Rio, Greece. Email: [email protected] Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore. Email: [email protected], [email protected], [email protected] 1