Consensus at Competitive Equilibrium: Dynamic Flow of Autonomous Cars in Traffic Networks

The objective of this paper is to initiate a qualitative analysis of dynamic flow in traffic networks by using the competitive equilibrium model of multiple market systems. A network is modeled as a dynamic graph where routes (edges) are viewed by drivers (agents) as gross substitute commodities which they choose by considering the traffic densities as prices of the individual routes. By borrowing from economic equilibrium models the notions of gross substitution and homogeneity of excess demand functions, we will be able to show that the chosen decision rule of the drivers will lead to a consensus resulting in an even distribution of traffic density over all routes of the network.