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Second best toll pricing within the framework of bounded rationality

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  • Di, Xuan
  • Liu, Henry X.
  • Ban, Xuegang (Jeff)

Abstract

The network design problem is usually formulated as a bi-level program, assuming the user equilibrium is attained in the lower level program. Given boundedly rational route choice behavior, the lower-level program is replaced with the boundedly rational user equilibria (BRUE). The network design problem with boundedly rational route choice behavior is understudied due to non-uniqueness of the BRUE. In this study, thus, we mainly focus on boundedly rational toll pricing (BR-TP) with affine link cost functions. The topological properties of the lower level BRUE set are first explored. As the BRUE solution is generally non-unique, urban planners cannot predict exactly which equilibrium flow pattern the transportation network will operate after a planning strategy is implemented. Due to the risk caused by uncertainty of people’s reaction, two extreme scenarios are considered: the traffic flow patterns with either the minimum system travel cost or the maximum, which is the “risk-prone” (BR-TP-RP) or the “risk-averse” (BR-TP-RA) scenario respectively. The upper level BR-TP is to find an optimal toll minimizing the total system travel cost, while the lower level is to find the best or the worst scenario. Accordingly BR-TP can be formulated as either a min –min or a min –max program. Solution existence is discussed based on the topological properties of the BRUE and algorithms are proposed. Two examples are accompanied to illustrate the proposed methodology.

Suggested Citation

  • Di, Xuan & Liu, Henry X. & Ban, Xuegang (Jeff), 2016. "Second best toll pricing within the framework of bounded rationality," Transportation Research Part B: Methodological, Elsevier, vol. 83(C), pages 74-90.
    • Handle: RePEc:eee:transb:v:83:y:2016:i:c:p:74-90
    DOI: 10.1016/j.trb.2015.11.002
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    References listed on IDEAS

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    13. Di, Xuan & Ban, Xuegang Jeff, 2019. "A unified equilibrium framework of new shared mobility systems," Transportation Research Part B: Methodological, Elsevier, vol. 129(C), pages 50-78.
    14. Xuan Di & Henry X. Liu & Shanjiang Zhu & David M. Levinson, 2017. "Indifference bands for boundedly rational route switching," Transportation, Springer, vol. 44(5), pages 1169-1194, September.
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