On Approximate Pure Nash Equilibria in Weighted Congestion Games with Polynomial Latencies
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.
Congestion games
approximate pure Nash equilibrium
potential functions
approximate price of stability
Theory of computation~Algorithmic game theory
Theory of computation~Convergence and learning in games
133:1-133:12
Track C: Foundations of Networks and Multi-Agent Systems: Models, Algorithms and Information Management
Ioannis
Caragiannis
Ioannis Caragiannis
University of Patras & CTI "Diophantus", Patras, Greece
Angelo
Fanelli
Angelo Fanelli
CNRS (UMR-6211), Caen, France
ANR-14-CE24-0007-01 "CoCoRICo-CoDec"
10.4230/LIPIcs.ICALP.2019.133
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Ioannis Caragiannis and Angelo Fanelli
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