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Tolling, collusion and equilibrium problems with equilibrium constraints


  • Koh, Andrew
  • Shepherd, Simon


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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    References listed on IDEAS

    1. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, January.
    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.
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