# Optimal Price of Anarchy in Cost-Sharing Games

## TL;DR

This paper develops a framework for designing distributed algorithms in multiagent systems that optimize the price of anarchy, ensuring near-optimal equilibrium efficiency in cost-sharing games through linear programming.

## Contribution

It introduces a method to compute and optimize agents' local cost functions to improve equilibrium efficiency in cost-sharing games using linear programming.

## Key findings

- The price of anarchy can be formulated as a linear program.
- Optimized cost functions lead to improved worst-case equilibrium efficiency.
- Application to convex, nondecreasing costs demonstrates practical effectiveness.

## Abstract

The design of distributed algorithms is central to the study of multiagent systems control. In this paper, we consider a class of combinatorial cost-minimization problems and propose a framework for designing distributed algorithms with a priori performance guarantees that are near-optimal. We approach this problem from a game-theoretic perspective, assigning agents cost functions such that the equilibrium efficiency (price of anarchy) is optimized. Once agents' cost functions have been specified, any algorithm capable of computing a Nash equilibrium of the system inherits a performance guarantee matching the price of anarchy. Towards this goal, we formulate the problem of computing the price of anarchy as a tractable linear program. We then present a framework for designing agents' local cost functions in order to optimize for the worst-case equilibrium efficiency. Finally, we investigate the implications of our findings when this framework is applied to systems with convex, nondecreasing costs.