Effect of information in Bayesian congestion games

Abstract

This thesis studies routing in a general single o-d network and information structure induced by any two heterogeneous information systems. To model the asymmetric information environment, we formulate a Bayesian congestion game, where travelers subscribing to one information system is seen as one population. We study properties of Bayesian Wardrop Equilibrium, where each population assigns their demand to routes with the lowest expected cost based on their belief. We show that if population beliefs about the state and the signal received by the other population are based on a common prior, as the population sizes change, qualitative properties of equilibrium strategies change, resulting in three distinct regimes. In the intermediate regime, the equilibrium edge load does not vary with the relative population size, and both populations face identical cost in equilibrium. In the other two regimes, the "minor" population has lower cost in equilibrium. We also introduce a metric to evaluate the impact of information. The relative population size effects the equilibrium outcome (edge load, costs) if and only if the impact of information on either population is tightly bounded by its size. Finally, we compute the bounds on the equilibrium social cost, and provide a sufficient condition for the bounds to be tight. Although we consider a more general information environment, the worst case inefficiency of equilibrium is the same as that in complete information games..