Multiagent Maximum Coverage Problems: The Trade-off Between Anarchy and Stability

TL;DR

This paper explores the fundamental trade-off between the price of anarchy and the price of stability in multiagent covering games, providing a Pareto frontier and methods to improve system performance by incorporating system-level information.

Contribution

It characterizes the explicit Pareto frontier between the price of anarchy and stability and shows how system-level info can enhance performance beyond this trade-off.

Findings

Explicit Pareto frontier between price of anarchy and stability

Trade-off: optimizing one metric worsens the other

Incorporating worst-agent performance info improves outcomes

Abstract

The price of anarchy and price of stability are three well-studied performance metrics that seek to characterize the inefficiency of equilibria in distributed systems. The distinction between these two performance metrics centers on the equilibria that they focus on: the price of anarchy characterizes the quality of the worst-performing equilibria, while the price of stability characterizes the quality of the best-performing equilibria. While much of the literature focuses on these metrics from an analysis perspective, in this work we consider these performance metrics from a design perspective. Specifically, we focus on the setting where a system operator is tasked with designing local utility functions to optimize these performance metrics in a class of games termed covering games. Our main result characterizes a fundamental trade-off between the price of anarchy and price of stability in the form of a fully explicit Pareto frontier. Within this setup, optimizing the price of anarchy comes directly at the expense of the price of stability (and vice versa). Our second results demonstrates how a system-operator could incorporate an additional piece of system-level information into the design of the agents' utility functions to breach these limitations and improve the system's performance. This valuable piece of system-level information pertains to the performance of worst performing agent in the system.