Resource Competition on Integral Polymatroids

TL;DR

This paper investigates a broad class of resource allocation games with submodular constraints and convex costs, proving the existence of pure Nash equilibria and providing an algorithm to find them.

Contribution

It introduces a general model encompassing various congestion games and offers a pseudo-polynomial algorithm to compute pure Nash equilibria.

Findings

Pure Nash equilibrium existence is guaranteed in the model.

A pseudo-polynomial algorithm can compute equilibria.

The model generalizes multiple known congestion game frameworks.

Abstract

We study competitive resource allocation problems in which players distribute their demands integrally on a set of resources subject to player-specific submodular capacity constraints. Each player has to pay for each unit of demand a cost that is a nondecreasing and convex function of the total allocation of that resource. This general model of resource allocation generalizes both singleton congestion games with integer-splittable demands and matroid congestion games with player-specific costs. As our main result, we show that in such general resource allocation problems a pure Nash equilibrium is guaranteed to exist by giving a pseudo-polynomial algorithm computing a pure Nash equilibrium.