EXISTENCE OF OPTIMAL LINK TOLLS FOR SYSTEM OPTIMUM ON NETWORKS WITH MIXED EQUILIBRIUM 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 traffic network analyses. This pricing principle states that the UE flow pattern on a network can be driven to a SO in the sense of total travel cost minimization by charging a toll on each link equal to the difference between marginal social cost and marginal private cost: In reality, users do not always behave in a UE manner, typically when there exist oligopoly Cournot-Nash (CN) firms. Users in a CN firm cooperate among themselves to minimize total cost of the firm and compete against others. 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 the SO as a UE-CN mixed equilibrium with resort to a rigorous mathematical programming approach