Risk Averse Second Best Toll Pricing

Xuegang (Jeff)Ban, Shu Lu, Michael Ferris and Henry X. Liu
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Xuegang (Jeff)Ban: Rensselaer Polytechnic Institute
Shu Lu: University of North Carolina at Chapel Hill
Michael Ferris: University of Wisconsin-Madison
Henry X. Liu: University of Minnesota

Chapter Chapter 10 in Transportation and Traffic Theory 2009: Golden Jubilee, 2009, pp 197-218 from Springer

Abstract: Abstract Existing second best toll pricing (SBTP) models determine optimal tolls of a subset of links in a transportation network by minimizing certain system objective, while the traffic flow pattern is assumed to follow user equilibrium (UE). We show in this paper that such toll design approach is risk prone, which tries to optimize for the best-case scenario, if the UE problem has multiple solutions. Accordingly, we propose a risk averse SBTP approach aiming to optimize for the worst-case scenario, which can be formulated as a min-max problem. We establish a general solution existence condition for the risk averse model and discuss in detail that such a condition may not be always satisfied in reality. In case a solution does not exist, it is possible to replace the exact UE solution set by a set of approximate solutions. This replacement guarantees the solution existence of the risk averse model. We then develop a scheme such that the solution set of an affine UE can be explicitly expressed. Using this explicit representation, an improved simplex method can be adopted to solve the risk averse SBTP model.

Keywords: Risk Averse; Nonlinear Complementarity Problem; User Equilibrium; Lower Level Problem; Optimal Toll (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (10)

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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4419-0820-9_10

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DOI: 10.1007/978-1-4419-0820-9_10

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