System optimum and pricing in multi-behaviors

The notions of user equilibrium (UE) and system optimum (SO) often allude to the literature together with the principle of marginal cost-pricing in the traffic network analyses. In reality, users do not always behave in a UE manner, typically when there exists oligopoly Cournot-Nash (CN) firms. In the presence of such UE-CN mixed equilibrium behaviors, we naturally ask whether a SO flow pattern remains attainable by meaningful link tolls. This paper provides a former answer to this question. We show that in a network with both UE and CN users, applying the traditional marginal-cost pricing for a system optimum requires that link tolls be differentiated across user classes. We then seek alternative meaningful tolls by establishing the existence of nonnegative uniform link tolls to support SO as a UE-CN mixed equilibrium with resort to a rigorous mathematical programming approach.