Value of Information in Bayesian Routing Games

We study a routing game in an environment with multiple heterogeneous information systems and an uncertain state that affects edge costs of a congested network. Each information system sends a noisy signal about the state to its subscribed traveler population. Travelers make route choices based on their private beliefs about the state and other populations' signals. The question then arises, "How does the presence of asymmetric and incomplete information affect the travelers' equilibrium route choices and costs?'' We develop a systematic approach to characterize the equilibrium structure, and determine the effect of population sizes on the relative value of information (i.e. difference in expected traveler costs) between any two populations. This effect can be evaluated using a population-specific size threshold. One population enjoys a strictly positive value of information in comparison to the other if and only if its size is below the corresponding threshold. We also consider the situation when travelers may choose an information system based on its value, and characterize the set of equilibrium adoption rates delineating the sizes of subscribed traveler populations. The resulting routing strategies are such that all travelers face an identical expected cost and no traveler has the incentive to change her subscription.