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

我们考虑具有最大次数多项式潜伏期函数的加权拥塞游戏 $d\ge \mathrm{1个}$。对于这些游戏，我们研究了玩家通过单方面改进动作序列获得的近似纯纳什均衡的存在和效率。通过利用一种简单的技术，我们首先证明这些游戏允许d-近似势函数的无限集合。这意味着始终存在一个d-近似纯纳什均衡，玩家可以通过任何d-近似改善动作序列来达到该平衡。作为推论，我们还获得了这样的结论：在对玩家策略结构进行温和假设的情况下，这些游戏也接受了恒定的近似势函数。其次，使用简单的势函数参数，我们可以证明$（d+\delta ）$-近似成本的纯纳什均衡 $（d+\mathrm{1个}）/（d+\delta ）$ 最优状态的成本始终存在， $\delta \in [0，\mathrm{1个}]$。