Nash equilibria in routing games with edge priorities

TL;DR

This paper introduces a new routing game model with edge priorities, analyzing Nash equilibria, structural properties, and efficiency bounds, with applications to traffic and network flow scenarios.

Contribution

It presents a novel competitive routing model with edge priorities, proves equilibrium existence, and provides algorithms and bounds for efficiency measures.

Findings

Existence of Nash equilibria in the model

Algorithm for computing equilibria

Bounds on Price of Stability and Price of Anarchy

Abstract

In this paper we present a new competitive packet routing model with edge priorities. We consider players that route selfishly through a network over time and try to reach their destinations as fast as possible. If the number of players who want to enter an edge at the same time exceeds the inflow capacity of this edge, edge priorities with respect to the preceding edge solve these conflicts. Our edge priorities are well-motivated by applications in traffic. For this class of games, we show the existence of equilibrium solutions for single-source-single-sink games and we analyze structural properties of these solutions. We present an algorithm that computes Nash equilibria and we prove bounds both on the Price of Stability and on the Price of Anarchy. Moreover, we introduce the new concept of a Price of Mistrust. Finally, we also study the relations to earliest arrival flows.