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

Abstract: 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.