A Unifying Approximate Potential for Weighted Congestion Games

TL;DR

This paper introduces a versatile approximate potential framework for weighted congestion games, enabling the analysis of equilibria existence, bounds on the Price of Stability, and applicability to various cost functions including polynomial, concave, and mixed costs.

Contribution

It presents a unifying, black-box analytical tool that generalizes previous results and derives new bounds for diverse congestion game cost structures.

Findings

Recovered recent polynomial congestion game bounds

Improved bounds for fair cost sharing games

Derived new bounds for nondecreasing concave costs

Abstract

We provide a unifying, black-box tool for establishing existence of approximate equilibria in weighted congestion games and, at the same time, bounding their Price of Stability. Our framework can handle resources with general costs--including, in particular, decreasing ones--and is formulated in terms of a set of parameters which are determined via elementary analytic properties of the cost functions. We demonstrate the power of our tool by applying it to recover the recent result of Caragiannis and Fanelli [ICALP'19] for polynomial congestion games; improve upon the bounds for fair cost sharing games by Chen and Roughgarden [Theory Comput. Syst., 2009]; and derive new bounds for nondecreasing concave costs. An interesting feature of our framework is that it can be readily applied to mixtures of different families of cost functions; for example, we provide bounds for games whose resources are conical combinations of polynomial and concave costs. In the core of our analysis lies the use of a unifying approximate potential function which is simple and general enough to be applicable to arbitrary congestion games, but at the same time powerful enough to produce state-of-the-art bounds across a range of different cost functions.