NDLI: Approximate pure nash equilibria in weighted congestion games: existence, efficient computation, and structure

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Approximate pure nash equilibria in weighted congestion games: existence, efficient computation, and structure

Content Provider	ACM Digital Library
Author	Caragiannis, Ioannis Gravin, Nick Skopalik, Alexander Fanelli, Angelo
Abstract	We consider structural and algorithmic questions related to the Nash dynamics of weighted congestion games. In weighted congestion games with linear latency functions, the existence of pure Nash equilibria is guaranteed by potential function arguments. Unfortunately, this proof of existence is inefficient and computing pure Nash equilibria in such games is a PLS-hard problem even when all players have unit weights. The situation gets worse when superlinear (e.g., quadratic) latency functions come into play; in this case, the Nash dynamics of the game may contain cycles and pure Nash equilibria may not even exist. Given these obstacles, we consider approximate pure Nash equilibria as alternative solution concepts. Do such equilibria exist? And if so, can we compute them efficiently? We provide positive answers to both questions for weighted congestion games with polynomial latency functions by exploiting an "approximation" of such games by a new class of potential games that we call Ψ-games. This allows us to show that these games have $^{d!}-approximate$ pure Nash equilibria, where $^{d}$ is the maximum degree of the latency functions. Our main technical contribution is an efficient algorithm for computing O(1)-approximate pure Nash equilibria when d is a constant. For games with linear latency functions, the approximation guarantee is 3+√5/2+O(γ) for arbitrarily small γ>0; for latency functions with maximum degree d e 2, it is $d^{2d+o(d)}.$ The running time is polynomial in the number of bits in the representation of the game and 1/γ. As a byproduct of our techniques, we also show the following interesting structural statement for weighted congestion games with polynomial latency functions of maximum degree d e 2: polynomially-long sequences of best-response moves from any initial state to a $d^{\{O(d^{2/})}-approximate$ pure Nash equilibrium exist and can be efficiently identified in such games as long as d is constant. To the best of our knowledge, these are the first positive algorithmic results for approximate pure Nash equilibria in weighted congestion games. Our techniques significantly extend our recent work on unweighted congestion games through the use of Ψ-games. The concept of approximating non-potential games by potential ones is interesting in itself and might have further applications.
Starting Page	284
Ending Page	301
Page Count	18
File Format	PDF
ISBN	9781450314152
DOI	10.1145/2229012.2229036
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2012-06-04
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Potential games Pure nash equilibria
Content Type	Text
Resource Type	Article

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