  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.
