Bottleneck model with heterogeneous information

This paper studies the effects of heterogeneous information on traffic equilibria and the resulting travel costs (both individual and social) when commuters make departure time choices to cross an unreliable bottleneck link. Increasing adoption and improved predictive abilities of Traveler Information Systems (TIS) enable commuters to plan their trips; however, there are inherent heterogeneities in information access and TIS accuracies. Our work addresses the open problem posed in Arnott et al. (1991) about the need to consider asymmetrically informed commuters in the bottleneck model of traffic congestion. We consider a Bayesian game with two heterogeneous commuter populations: one population is privately informed of the realized network state while the other only knows the public information about the distribution of states. We characterize the equilibrium of the game, in which each population chooses a departure rate function over time to minimize its expected cost based on its private belief about the state and the behavior of the other population. We provide a full equilibrium characterization for the complete range of values of link reliability, incident probability, and information penetration. The populations' equilibrium strategies can broadly be categorized into two distinct regimes. Specifically, when information penetration is above a certain threshold, the populations' equilibrium strategies are non-unique, and the relative Value of Information (VoI) is 0, i.e. the two populations face the same cost. On the other hand, when information penetration is below the threshold, equilibrium is unique, and VoI is positive and decreasing in information penetration. Importantly, we find that the lowest social cost is always achieved when a non-zero fraction of commuters are uninformed. The more unreliable the link, the higher the information penetration that achieves this minimum. We define the Value of Heterogeneity (VoH) as the difference between the minimum social cost and the cost under complete information penetration, and find that it can be significant under practically relevant conditions.