Informational aspects in a class of Bayesian congestion games

We study a Bayesian congestion game which models routing in environments where the route costs are affected by a random network state. Each player is subscribed to one of two Traveler Information Systems (TIS), which estimate the state with different levels of accuracy. The TISs induce two traveler populations with heterogeneous access to information about the state. Each traveler population then routes its demand on a network of two parallel routes based on its private beliefs of the state and of the other population. For simplicity, we assume that one TIS provides a more accurate estimate than the other in all states. We characterize the equilibria of the game under two information structures. The first information structure is specified by objective beliefs, i.e., those consistent with a common prior distribution on the network state and type profiles, whereas the second is specified by subjective beliefs that do not admit a common prior. Our equilibrium results permit an analysis of social costs with respect to changes in the relative size of two populations. We show that the equilibrium social cost is minimized either for a unique ratio of population sizes, or for a continuous range of population sizes, and that information access heterogeneity is always socially beneficial. However, this ratio (or range) of population sizes differ between the subjective and objective cases. Finally, we study examples of information structures in which travelers in the population with access to more accurate information about the state are worse off than the other travelers.