We provide a unifying, black-box tool for establishing existence of approximate equilibria in weighted congestion games and, at the same time, bounding their Price of Stability. Our framework can handle resources with general costs—including, in particular, decreasing ones—and is formulated in terms of a set of parameters which are determined via elementary analytic properties of the cost functions. We demonstrate the power of our tool by applying it to recover the recent result of Caragiannis and Fanelli [ICALP’19] for polynomial congestion games; improve upon the bounds for fair cost sharing games by Chen and Roughgarden [Theory Comput. Syst., 2009]; and derive new bounds for nondecreasing concave costs. An interesting feature of our framework is that it can be readily applied to mixtures of different families of cost functions; for example, we provide bounds for games whose resources are conical combinations of polynomial and concave costs. In the core of our analysis lies the use of a unifying approximate potential function which is simple and general enough to be applicable to arbitrary congestion games, but at the same time powerful enough to produce state-of-the-art bounds across a range of different cost functions.

我们提供了一个统一的黑盒工具，用于在加权拥塞博弈中建立近似均衡的存在，同时限制其稳定性价格。我们的框架可以处理具有一般成本的资源（特别是包括递减成本），并且根据一组参数来制定，这些参数是通过成本函数的基本分析属性确定的。我们通过应用我们的工具来恢复 Caragiannis 和 Fanelli [ICALP'19] 多项式拥塞游戏的最新结果来展示我们的工具的强大功能；改进 Chen 和 Roughgarden 的公平成本分摊游戏的界限 [理论计算。系统，2009]；并得出不减凹成本的新界限。我们框架的一个有趣的特点是它可以很容易地应用于混合物不同族的成本函数；例如，我们为资源是多项式和凹成本的圆锥组合的游戏提供界限。我们分析的核心在于使用统一的近似势函数，该函数简单且通用，足以适用于任意拥塞博弈，但同时又足够强大，可以在一系列不同的成本函数。