Routing Games with Progressive Filling

TL;DR

This paper extends max-min fairness in network bandwidth allocation to non-uniform, time-dependent rates within a game-theoretic framework, analyzing equilibria, computational complexity, and potential for optimal design.

Contribution

It introduces progressive filling games (PFGs), analyzes their equilibria, computational complexity, and shows how rate adjustments can lead to optimal solutions.

Findings

Pure Nash and strong equilibria exist in PFGs.

Polynomial algorithms are available for certain Max-Min-Fair Games.

Design adjustments can achieve optimal strong equilibria.

Abstract

Max-min fairness (MMF) is a widely known approach to a fair allocation of bandwidth to each of the users in a network. This allocation can be computed by uniformly raising the bandwidths of all users without violating capacity constraints. We consider an extension of these allocations by raising the bandwidth with arbitrary and not necessarily uniform time-depending velocities (allocation rates). These allocations are used in a game-theoretic context for routing choices, which we formalize in progressive filling games (PFGs). We present a variety of results for equilibria in PFGs. We show that these games possess pure Nash and strong equilibria. While computation in general is NP-hard, there are polynomial-time algorithms for prominent classes of Max-Min-Fair Games (MMFG), including the case when all users have the same source-destination pair. We characterize prices of anarchy and stability for pure Nash and strong equilibria in PFGs and MMFGs when players have different or the same source-destination pairs. In addition, we show that when a designer can adjust allocation rates, it is possible to design games with optimal strong equilibria. Some initial results on polynomial-time algorithms in this direction are also derived.