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

Utility Design for Distributed Resource Allocation -- Part II: Applications to Submodular, Covering, and Supermodular Problems