Nash Equilibria in Traffic Networks with Multiple Populations and Origins-Destinations

TL;DR

This paper proves the existence and uniqueness of Nash equilibria in traffic networks with multiple vehicle populations, each with distinct origins, destinations, and travel costs, under minimal cost continuity assumptions.

Contribution

It establishes the existence of Nash equilibria in complex traffic networks with multiple populations and provides conditions for their uniqueness, extending prior models.

Findings

Nash equilibrium exists under minimal cost continuity conditions.

Uniqueness of equilibrium is characterized under specific conditions.

Detailed analysis of particular cases of interest.

Abstract

Different populations of vehicles travel along a network. Each population has its origin, destination and travel costs - which may well be unbounded. Under the only requirement of the continuity of the travel costs, we prove the existence of a Nash equilibrium for all populations. Conditions for its uniqueness are also provided. A few cases are treated in detail to show specific situations of interest.