Cordon toll competition in a network of two cities: formulation and sensitivity to traveller route and demand responses

Article English OPEN
Watling, DP ; Shepherd, S ; Koh, A (2015)
  • Publisher: Elsevier
  • Journal: Transportation Research Part B: Methodological (issn: 0191-2615, vol: 76, pp: 93-116)
  • Related identifiers: doi: 10.1016/j.trb.2015.02.007
  • Subject: Management Science and Operations Research | Transportation

While there exists extensive literature on the first- and second-best tolling of congested transportation networks, much of it presumes the existence of a single agent responsible for toll-setting. The present paper extends the small but growing body of work studying the impact of several agents independently regulating tolls on different parts of a network. Specifically we consider the problem of a network consisting of two ‘cities’, each city independently regulated by a city ‘authority’ able to set a single cordon toll for entry to the city. It is supposed that each authority aims to maximise the social welfare of its own residents, anticipating the impact of its toll on travellers’ route and demand decisions, while reacting to the toll level levied by the other authority. In addition, we model the possibility of the cities entering into a ‘tax-exporting agreement’, in which city A agrees to share with city B the toll revenues it collects from city B residents using city A’s network. It is assumed that the sensitivity of travellers, in terms of their route and demand responses, is captured by an elastic demand, stochastic user equilibrium (SUE) model. Conditions for a Nash Equilibrium (NE) between cities are set out as an Equilibrium Problem with Equilibrium Constraints (EPEC). It is shown that weaker, ‘local’ solutions to the EPEC (which we term LNE for local NE) satisfy a single variational inequality, using the smooth implicit function of the SUE map. Standard variational algorithms may then be used to identify such LNE solutions, allowing NE solutions to be identified from this candidate set; we test the use of a Sequential Linear Complementarity Problem algorithm. Numerical results are reported in which we see that the sensitivity of travellers may affect many factors, including: the number of LNE solutions, the initial conditions for which algorithms might determine such solutions, the gap between LNE and a global regulator solution, and the incentive for cities to cooperate in terms of tax-exporting.
  • References (13)
    13 references, page 1 of 2

    Acemoglu, D., Ozdaglar, A., 2007. Competition and efficiency in congested markets. Mathematics of Operations Research 32 (1), 1-31.

    Bell, M.G.H., Iida, Y., 1997. Transportation Network Analysis. Wiley, New York.

    Cantarella, G.E., 1997. A general fixed-point approach to multimode multi-user equilibrium assignment with elastic demand. Transportation Science 31 (2), 107-128.

    Connors, R.D., Sumalee, A., Watling, D.P., 2007. Sensitivity analysis of the variable demand probit stochastic user equilibrium with multiple user classes. Transportation Research Part B 41 (6), 593-615.

    Cottle, R.W., Pang, J.-S., Stone, R.E., 2009. The Linear Complementarity Problem. Society for Industrial and Applied Mathematics, Philadelphia.

    De Borger, B., Proost, S., 2012. Transport policy competition between governments: a selective survey of the literature. Economics of Transportation 1 (1-2), 35-48.

    De Borger, B., Proost, S., van Dender, K., 2005. Congestion and tax competition on a parallel network. European Economic Review 49 (8), 2013-2040.

    De Borger, B., Dunkerley, F., Proost, S., 2007. Strategic investment and pricing decisions in a congested transport corridor. Journal of Urban Economics 62 (2), 294-316.

    de Palma, A., Lindsey, R., 2000. Private roads: competition under various ownership regimes. Annals of Regional Science 34 (1), 13-35.

    de Palma, A., Lindsey, R., 2011. Traffic congestion pricing methodologies and technologies. Transportation Research Part C 19 (6), 1377-1399.

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