Bayesian Equilibria of Heterogeneous Non-Atomic Routing Games with Private Information

We study non-atomic Bayesian routing games whereby a transportation network is shared by two types of traffic: a coordinated fleet and a mass of selfish users. The links in the network are characterized by travel time functions that depend both on the aggregate flow on the link and on a random state of the world $W$ that, in general, is not directly observable. Rather, we assume that both the fleet coordinator and the selfish users know the prior distribution of $W$, observe (different) private messages that are correlated with $W$ and possibly among themselves, and make routing decisions based on such heterogeneous partial information. Under the assumption that both the state of the world and the private message sets are finite, we prove the existence and uniqueness of a Bayesian equilibrium for the ensuing Bayesian routing game.