Utility Design for Distributed Resource Allocation – Part II: Applications to Submodular, Covering, and Supermodular Problems [article]

Dario Paccagnan, Jason R. Marden
2021 arXiv   pre-print
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
more » ... . 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.
arXiv:1807.01343v4 fatcat:osymwg7rlre7hbnaawe3bdtsde