A fundamental component of the game theoretic approach to distributed control is the design of local utility functions.Relative to resource allocation problems that are additive over the resources, Part I showed how to design local utilities so as to maximize the associated performance guarantees [Paccagnan et al., TAC 2019] which we measure by the price of anarchy. The purpose of the present manuscript is to specialize these results to the case of submodular, covering, and supermodular problems. In all these cases we obtain tight expressions for the price of anarchy that often match or improve the guarantees associated to state-of-the-art approximation algorithms. Two applications and corresponding numerics are presented: the vehicle-target assignment problem and a coverage problem arising in wireless data caching.

翻译：分散控制游戏理论方法的一个基本组成部分是设计当地公用事业功能。与资源添加的资源分配问题相对应,第一部分展示了如何设计当地公用事业,以最大限度地实现相关的绩效保障[Pacagnan等人,TAC 2019],我们用无政府状态的代价来衡量,本手稿的目的是将这些结果专门用于亚模块、覆盖和超模块问题。在所有这些情况下,我们都获得了与最新近似算法相关的保障相对应或改进的无政府状态价格的严格表达方式。提出了两种应用程序和相应的数字:车辆目标分配问题和无线数据堆积产生的覆盖问题。