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Highway toll pricing. (English) Zbl 1253.91015
Summary: For a tolled highway where consecutive segments allow vehicles to enter and exit unrestrictedly, we propose a simple toll pricing method. It is shown that the method is the unique method satisfying the classical axioms of Additivity and Dummy in the cost sharing literature, and the axioms of Toll Upper Bound for Local Traffic and Routing-proofness. We also show that the toll pricing method is the only method satisfying Routing-proofness Axiom and Cost Recovery Axiom. The main axiom in the characterizations is Routing-proofness which says that no vehicle can reduce its toll charges by exiting and re-entering intermediately. In the special case when there is only one unit of traffic (vehicle) for each (feasible) pair of entrance and exit, we show that our toll pricing method is the Shapley value of an associated game to the problem. In the case when there is one unit of traffic entering at each entrance but they all exit at the last exit, our toll pricing method coincides with the well-known airport landing fee solution-the Sequential Equal Contribution rule of S. C. Littlechild and G. Owen [Manage. Sci., Theory 20, 370–372 (1973; Zbl 0307.90095)].

MSC:
91A12 Cooperative games
90B10 Deterministic network models in operations research
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[1] Alberto, Castaño-Pardo; Alberto, Garcia-Diaz, Highway cost allocation: an application of the theory of nonatomic games, Transportation research, 29, 187-203, (1995)
[2] Chen, A.; Zhou, Z.; Xu, X., A self-adaptive gradient projection algorithm for the nonadditive traffic equilibrium problem, Computers and operations research, 39, 127-138, (2012) · Zbl 1251.90083
[3] De Palma, A.; Lindsey, R.; Proost, S., Research challenges in modelling urban road pricing: an overview, Transport policy, 13, 97-105, (2006)
[4] Henriet, D.; Moulin, H., Traffic-based cost allocation in a network, RAND journal of economics, 27, 332-345, (1996)
[5] Hoesel, S., An overview of Stackelberg pricing in networks, European journal of operational research, 189, 1393-1402, (2008) · Zbl 1146.91018
[6] Johansson, B.; Mattson, L., Principles of road pricing, ()
[7] Littlechild, S.; Owen, G., A simple expression for the Shapley value in a special case, Management science, 20, 370-372, (1973) · Zbl 0307.90095
[8] Morrison, S.A., A survey of road pricing, Transportation research, 20, 87-97, (1986)
[9] Moulin, H., Axiomatic cost and surplus sharing, () · Zbl 0536.90006
[10] Moulin, H., 2009. Pricing traffic in a spanning network. In: Proceedings of the ACM Conference on Electronic Commerce. Stanford. · Zbl 1294.91037
[11] Moulin, H.; Shenker, S., Serial cost sharing, Econometrica, 60, 1009-1037, (1992) · Zbl 0766.90013
[12] Newbery, D., Road damage externalities and road user charges, Econometrica, 56, 295-316, (1988)
[13] Newbery, D., Cost recovery from optimally designed roads, Economica, 56, 165-185, (1989)
[14] Parry, I.W.H.; Walls, M.; Harrington, W., Automobile externalities and policies, Journal of economic literature, 45, 373-399, (2007)
[15] Shapley, L.S., A value for n-person games, (), 307-317 · Zbl 0050.14404
[16] Small, K.A.; Winston, C.; Evans, C.A., Road work: A new highway pricing and investment policy, (1991), Brookings Institute Press
[17] Sun, Lian-Ju.; Gao, Zi-You., An equilibrium model for urban transit assignment based on game theory, European journal of operational research, 181, 305-314, (2007) · Zbl 1121.90029
[18] Thomson, W., 2007. Cost allocation and airport problems. Working Paper, University of Rochester-Center for Economic Research (RCER).
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