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Tolling, collusion and equilibrium problems with equilibrium constraints

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  • Koh, Andrew
  • Shepherd, Simon

Abstract

An Equilibrium Problem with an Equilibrium Constraint (EPEC) is a mathematical construct that can be applied to private competition in highway networks. In this paper we consider the problem of finding a Nash Equilibrium in a situation of competition in toll pricing on a network utilising two alternative algorithms. In the first algorithm, we utilise a Gauss Seidel fixed point approach based on the cutting constraint algorithm for toll pricing. The second algorithm that we propose, a novel contribution of this paper, is the extension of an existing sequential linear complementarity programming approach for finding the competitive Nash equilibrium when there is a lower level equilibrium constraint. Finally we develop an intuitive approach to represent collusion between players and demonstrate that as the level of collusion goes from none to full collusion so the solution maps from the Nash to monopolistic solution. However we also show that there may be local solutions for the collusive monopoly which lie closer to the second best welfare toll solution than does the competitive Nash equilibrium.

Suggested Citation

  • Koh, Andrew & Shepherd, Simon, 2010. "Tolling, collusion and equilibrium problems with equilibrium constraints," European Transport \ Trasporti Europei, ISTIEE, Institute for the Study of Transport within the European Economic Integration, issue 44, pages 3-22.
    • Handle: RePEc:sot:journl:y:2010:i:44:p:3-22
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    File URL: http://hdl.handle.net/10077/6150
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    References listed on IDEAS

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    1. Economides, Nicholas & Salop, Steven C, 1992. "Competition and Integration among Complements, and Network Market Structure," Journal of Industrial Economics, Wiley Blackwell, vol. 40(1), pages 105-123, March.
    2. Cardell, Judith B. & Hitt, Carrie Cullen & Hogan, William W., 1997. "Market power and strategic interaction in electricity networks," Resource and Energy Economics, Elsevier, vol. 19(1-2), pages 109-137, March.
    3. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
    4. Andrew Koh & Simon Shepherd & Agachai Sumalee, 2009. "Second best toll and capacity optimisation in networks: solution algorithm and policy implications," Transportation, Springer, vol. 36(2), pages 147-165, March.
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    Cited by:

    1. Herty, Michael & Steffensen, Sonja & Thünen, Anna, 2022. "Multiscale control of Stackelberg games," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 468-488.
    2. Michael Herty & Sonja Steffensen & Anna Thunen, 2018. "Solving Quadratic Multi-Leader-Follower Games by Smoothing the Follower's Best Response," Papers 1808.07941, arXiv.org, revised Apr 2020.
    3. Michael Herty & Sonja Steffensen & Anna Thunen, 2020. "Multiscale Control of Stackelberg Games," Papers 2011.03405, arXiv.org.
    4. Francesco Caruso & Maria Carmela Ceparano & Jacqueline Morgan, 2021. "A Local Variation Method for Bilevel Nash Equilibrium Problems," CSEF Working Papers 620, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.

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