Congestion with heterogeneous commuters

We study a congestion model where a continuum of heterogeneous commuters make a binary choice between riding a bus and driving private vehicles for their commutes. Formulating the model as a large game, we establish the existence and uniqueness of a nontrivial Nash equilibrium and analyze how a gasoline tax affects the allocation of commuters between public transportation and private vehicles at the equilibrium. Based on the analysis, we provide a sufficient condition under which a gasoline tax is Pareto improving. We also prove the existence of a socially optimal policy that minimizes the aggregate loss to all commuters.