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

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., 2020), which we measure by the price of anarchy. The purpose of this article 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 with 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.

Automated summary

This article focuses on the design of local utility functions in distributed control using game-theoretic approach. It specializes the results for submodular, covering, and supermodular problems, providing tight expressions for the price of anarchy that often surpass the guarantees of state-of-the-art approximation algorithms. Two applications, specifically the vehicle-target assignment problem and a coverage problem in wireless data caching, are presented with corresponding numerical results.