Chapter 3 Adaptive Dynamics in Traffic Games

Abstract

The equilibrium concepts discussed in the previous chapters were eminently static, with traffic modeled as a steady state that results from the adaptive behavior of drivers. These models assume implicitly the existence of a hidden mechanism that leads to equilibrium, though they are stated directly in the form of equilibrium equations which are not tied to a specific adaptive dynamics. Furthermore, they consider a non-atomic framework that ignores individual drivers and uses continuous variables to represent aggregate flows. In this chapter we discuss a dynamical model for the adaptive behavior of finitely many drivers in a simple network and we study its convergence towards a steady state.