On the stability of an adaptive learning dynamics in traffic games

TL;DR

This paper analyzes the stability of adaptive learning in traffic games, showing how the dynamics converge to equilibria depending on parameters, with a detailed case study for two routes and players.

Contribution

It provides a comprehensive stability analysis of adaptive learning dynamics in traffic games, including a full characterization for the two-route, two-player case.

Findings

Number of equilibria varies with parameters (one, two, or three)

Trajectories generally converge to a rest point

Global convergence occurs for almost all initial conditions

Abstract

This paper investigates the dynamic stability of an adaptive learning procedure in a traffic game. Using the Routh-Hurwitz criterion we study the stability of the rest points of the corresponding mean field dynamics. In the special case with two routes and two players we provide a full description of the number and nature of these rest points as well as the global asymptotic behavior of the dynamics. Depending on the parameters of the model, we find that there are either one, two or three equilibria and we show that in all cases the mean field trajectories converge towards a rest point for almost all initial conditions.