Mixed Equilibria with Common Constraints on Transportation Networks

Xia Yang (), Xuegang Jeff Ban () and Rui Ma ()
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Xia Yang: Rensselaer Polytechnic Institute
Xuegang Jeff Ban: University of Washington
Rui Ma: University of California, Davis

Networks and Spatial Economics, 2017, vol. 17, issue 2, No 8, 547-579

Abstract: Abstract This study concerns about modeling the mixed equilibrium (ME) problem, including user equilibrium, system optimum, and Cournot-Nash players, with general common constraints (CCs) on transportation networks. The CCs capture the interactions of the decision variables of different players in ME, which could be internal interactions such as road link capacity constraints or external such as emission or congestion control policies. It is shown that ME with CCs can be modeled as a generalized Nash equilibrium problem (GNEP). The study proves that, under certain conditions, the GNEP-based ME is jointly convex, which can be reformulated as a variational inequality (VI). We then study the solution existence, uniqueness and solving method for the VI-based model, followed by a discussion on its potential applications. Numerical tests are conducted with common nonlinear link emission constraints as the CCs on a simple two-node, three-link network first, and then on the Nguyen Dupus network. The results show that modeling users’ route choice behavior with CCs is more general in evaluating system performance, planning link capacities, and making congestion or emission control related policies.

Keywords: Mixed equilibrium; Cournot-Nash players; Generalized Nash equilibrium; Jointly convex; Variational inequality; Nonlinear complementarity problem (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s11067-016-9335-9

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