Pareto Efficiency Analysis of Private Toll Road Networks

We consider the problem of setting tolls and capacities in transportation networks serving single origin-destination markets. The motivation is to understand the effects of network structure and of decentralized decision-making on the performance of such systems, as well as to identify opportunities for government intervention. Performance, in this case, refers to social welfare and profits, with the latter determining private firms' incentives to participate in road operation. We first extend the Pareto efficiency analysis appearing in the literature for the single road case. Specifically, we consider a network operated by a single firm and show that aggregate Pareto-efficient capacity levels provide the same service quality as in the single road case and that any convex combination of social welfare-maximizing and profit-maximizing route tolls can be Pareto efficient, suggesting that such outcomes can arise naturally from negotiations between a government and a private operator. In the second part of the paper, we consider a market where, following bilateral negotiations with a government, self-interested, private operators set tolls and capacities independently. Again, we show that the optimal capacity for each link is set to achieve the same service level as that in the single road case. Further, we adapt the concept and show that decentralized Pareto-efficient tolling strategies are bounded. Characterization of Pareto-efficient tolling and capacity strategies for the two benchmark cases reveals when (government) interventions can lead to increased social welfare, operator profit, or both. As an example, we analyze simple stage networks and, among other results, show that, even under bilateral negotiations and decentralized decision-making, sufficient competition can lead to aggregate Pareto efficiency.