Minimizing Rosenthal's Potential in Monotone Congestion Games

TL;DR

This paper investigates the computational complexity of finding minimum potential states in monotone congestion games, providing complexity classifications and approximation algorithms for various cases.

Contribution

It characterizes the complexity landscape of potential minimization in monotone congestion games and offers tight approximation algorithms for NP-hard instances.

Findings

Polynomial-time solvable cases identified

NP-hard cases established for certain instances

Tight approximation algorithms developed for complex cases

Abstract

Congestion games are attractive because they can model many concrete situations where some competing entities interact through the use of some shared resources, and also because they always admit pure Nash equilibria which correspond to the local minima of a potential function. We explore the problem of computing a state of minimum potential in this setting. Using the maximum number of resources that a player can use at a time, and the possible symmetry in the players' strategy spaces, we settle the complexity of the problem for instances having monotone (i.e., either non-decreasing or non-increasing) latency functions on their resources. The picture, delineating polynomial and NP-hard cases, is complemented with tight approximation algorithms.