2019/02/19 by Caragiannis, Ioannis, Fanelli, Angelo · 1 citation
#Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences
paper · doi:10.48550/arxiv.1902.07173
We study natural improvement dynamics in weighted congestion games with polynomial latencies of maximum degree d≥ 1. We focus on two problems regarding the existence and efficiency of approximate pure Nash equilibria, with a reasonable small approximation factor, in these games. By exploiting a simple technique, we firstly show that such a game always admits a d-approximate potential function. This implies that every sequence of d-approximate improvement moves by the players leads 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, using a simple potential function argument, we are able to show that a (d+δ)-approximate pure Nash equilibrium of cost at most (d+1)/(d+δ) times the cost of an optimal state always exists, for δ∈ [0,1].