Optimal Utility Design with Arbitrary Information Networks

TL;DR

This paper develops a linear programming framework to optimize local utility functions in multi-agent systems with arbitrary information networks, maximizing the system's efficiency despite communication constraints.

Contribution

It introduces a general LP-based method to design utilities that maximize the Price of Anarchy in complex information networks, extending prior approaches.

Findings

LP characterizes the PoA for any utility and network.

Optimized utility design improves system efficiency.

Framework is robust to communication failures.

Abstract

We consider multi-agent systems with general information networks where an agent may only observe a subset of other agents. A system designer assigns local utility functions to the agents guiding their actions towards an outcome which determines the value of a given system objective. The aim is to design these local utility functions such that the Price of Anarchy (PoA), which equals the ratio of system objective at worst possible outcome to that at the optimal, is maximized. Towards this, we first develop a linear program (LP) that characterizes the PoA for any utility design and any information network. This leads to another LP that optimizes the PoA and derives the optimal utility design. Our work substantially generalizes existing approaches to the utility design problem. We also numerically show the robustness of proposed framework against unanticipated communication failures.