On approximate pure Nash equilibria in weighted congestion games with polynomial latencies

We consider weighted congestion games with polynomial latency functions of maximum degree d≥1. For these games, we investigate the existence and efficiency approximate pure Nash equilibria which are obtained through sequences unilateral improvement moves by players. By exploiting a simple technique, firstly show that admit an infinite set d-approximate potential functions. This implies there always exists equilibrium can be reached any sequence As corollary, also obtain that, under mild assumptions on structure players' strategies, constant function. Secondly, using function argument, able to (d+δ)-approximate cost at most (d+1)/(d+δ) times optimal state exists, for every δ∈[0,1].