Road pricing with limited information and heterogeneous users: A successful case (original) (raw)

Different Policy Objectives of the Road-Pricing Problem: A Game-theoretic Approach

Pricing in Road Transport

Using game theory we investigate a new approach to formulate and solve optimal tolls with a focus on different policy objectives of the road authority. The aim is to gain more insight into determining optimal tolls as well as into the behavior of users after tolls have been imposed on the network. The problem of determining optimal tolls is stated and defined using utility maximization theory, including elastic demand on the travelers' side and different objectives for the road authority. Game theory notions are adopted regarding different games and players, rules and outcomes of the games played between travelers on the one hand and the road authority on the other. Different game concepts (Cournot, Stackelberg and social planner game) are mathematically formulated and the relationship between players, their payoff functions, and rules of the games are defined. The games are solved for different scenarios and different objectives for the road authority, using the Nash equilibrium concept. Using the Stackelberg game concept as being most realistic for road pricing, a few experiments are presented illustrating the optimal toll design problem subject to different pricing policies considering different objectives of the road authority. Results show different outcomes both in terms of optimal tolls as well as in payoffs for travelers. There exist multiple optimal solutions and the objective functions may have a non-continuous shape. The main contribution is the two-level separation between the network users and the road authority in terms of their objectives and influences.

Preference heterogeneity and congestion pricing: The two route case revisited

Transportation Research Part B: Methodological, 2018

This paper studies first-best and second-best congestion pricing in the presence of unobserved and observed preference heterogeneity using a stylised stochastic user equilibrium choice model. Travellers choose between multiple alternatives, have heterogeneous values of travel times, and may differ in their valuation of variety. We derive first-best and second-best tolls taking into account how the overall network demand responds to expected generalized prices, including tolls. For second-best pricing, we show that with homogeneous values of times the welfare losses of second-best pricing are smaller when route choice is probabilistic than when route choice is deterministic. Furthermore, we find that with heterogeneous values of times and benefits of variety, uniform second-best tolls and group-differentiated tolls can be very close, implying potentially low welfare losses from the inability to differentiate tolls. Finally, we show that there are cases where all groups benefit from second-best congestion pricing, but that these cases are likely to be politically unacceptable because tolls are then higher for low income groups.

Toward a general framework for dynamic road pricing

2007

This paper develops a general framework for analysing and calculating dynamic road toll. The optimal network flow is first determined by solving an optimal control problem with statedependent responses such that the overall benefit of the network system is maximized. An optimal toll is then sought to decentralise this optimal flow. This control theoretic formulation can work with general travel time models and cost functions. Deterministic queue is predominantly used in dynamic network models.

Probabilistic Choice and Congestion Pricing with Heterogeneous Travellers and Price-Sensitive Demand

SSRN Electronic Journal, 2014

This paper deals with first-best and second-best congestion pricing of a stylised two-link network with probabilistic route choice of travellers. Travellers may have heterogeneous values of travel times and may differ in their idiosyncratic route preferences. We derive firstbest and second-best tolls taking into account how the overall network demand responds to generalized costs including the tolls that are levied. We show that with homogeneous values of times the welfare losses of second-best pricing, of one link only, may be smaller if route choice is probabilistic. Furthermore, we show that with heterogeneous values of times, common second-best tolls and group-differentiated tolls can be very close when route choice is governed by random utility maximisation, leading to low welfare losses from the inability to differentiate tolls.

CONGESTION PRICING WITH HETEROGENEOUS TRAVELLERS

2011

Heterogeneity in preferences of users affects both the aggregate efficiency effects as the distributional effects of congestion pricing. This thesis considers two dimensions of heterogeneity. Proportional heterogeneity scales the values of time and schedule delay proportionally. More proportional heterogeneity raises the welfare gain of road pricing, because the efficiency gain from the reordering of the arrival times increases. More heterogeneity in the ratio between the value of time and value of schedule delay lowers the gain from tolling, because congestion externalities decrease. This thesis finds that, in the bottleneck model of congestion, the distributional effects of congestion pricing are non-monotonic in the value of time and value of schedule delay. It is not users with the lowest values who lose most—or gain the least—from tolling, but an intermediate type of user. This differs from the traditional view that is based on the static flow model of congestion, and states that the higher the value of time is, the less harmful tolling is. Preference heterogeneity also affects empirical estimates. If two heterogeneous marginal utilities are correlated, it can even bias the willingness-to-pay estimates obtained by logit estimation. The empirical chapters find that travel-cost compensation lowers price elasticities and increases the value of time and the values of restricting the timings of the travel moments.

Optimal Road Pricing with Congestion and Fund Procurement Paper Identification number: SCS12-034

2012

This paper discussed the optimal road pricing, which maximizes social surplus under a user equilibrium condition with imperfect substitution assumption for route choice in a transportation network with many nodes and links. So far several attempts to integrate road pricing theory as economic measure and transportation network equilibrium analysis have been made but they are inconsistent with the economic theory. First, we took account of the marginal cost of funding from road pricing. In general, congestion pricing is based on the principle of marginal cost pricing which equal to the difference between marginal social and marginal private cost. In this study, we defined the social welfare function which consists of a sum of indirect utility function as consumers’ surplus and road pricing revenue as producer’s surplus. Following this definition, we formulated the user behaviour maximizing a quasi-linear utility with imperfect substitution between any route as defined the consumer’s u...

Welfare effects of road pricing and traffic information under alternative ownership regimes

Transportation Research Part A: Policy and Practice, 2012

Willingness to pay for information Private road operator Private information provider ICT a b s t r a c t This paper models strategic interactions between a road supplier, a provider of traffic information, and road users, with stochastic travel times. Using a game-theoretical analysis of suppliers' pricing strategies, we assess the social welfare effects of traffic information under various ownership regimes. The results show that the distortive welfare effect of monopolistic information pricing appears relatively small. Collusion of the road operator and information provider yields higher social welfare than independent pricing by two firms. The intuition behind this result resembles that behind the welfare effects of double marginalization, but is not exactly the same, as traffic information is not strictly complementary to road use.

Congestion Pricing of Road Networks with Users Having Different Time Values

Applied Optimization, 2006

We study congestion pricing of road networks with users differing only in their time values. In particular, we analyze the marginal social cost (MSC) pricing, a tolling scheme that charges each user a penalty corresponding to the value of the delays inflicted on other users, as well as its implementation through fixed tolls. We show that the variational inequalities characterizing the corresponding equilibria can be stated in symmetric or nonsymmetric forms. The symmetric forms correspond to optimization problems, convex in the fixed-toll case and nonconvex in the MSC case, which hence may have multiple equilibria. The objective of the latter problem is the total value of travel time, which thus is minimized at the global optima of that problem. Implementing close-to-optimal MSC tolls as fixed tolls leads to equilibria with possibly non-unique class specific flows, but with identical close-to-optimal values of the total value of travel time. Finally we give an adaptation, to the MSC setting, of the Frank-Wolfe algorithm, which is further applied to some test cases, including Stockholm.