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Nash-Cournot Equilibria in Electric Power Markets with Piecewise Linear Demand Functions and Joint Constraints

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  • Benjamin F. Hobbs

    (Department of Geography and Environmental Engineering, The Johns Hopkins University, Baltimore, Maryland 21218-2682)

  • J. S. Pang

    (Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York 12180-3590)

Abstract

Most previous Nash-Cournot models of competition among electricity generators have assumed smooth demand (price) functions, facilitating computation and proofs of existence and uniqueness. However, nonsmooth demand functions are an important feature of real power markets due, for example, to price caps and generator recognition of transmission constraints that limit exports. A more general model of Nash-Cournot competition on networks is proposed that accounts for these features by including (1) concave piecewise-linear demand curves and (2) joint constraints that include variables from other generating companies within the profit maximization problems for individual generators. The piecewise demand curves imply, in general, a nonmonotone multivalued variational inequality problem. Thus, for instance, imposition of a price cap can destroy the uniqueness properties found in previous models, so that distinct solutions can yield different sets of profits for market participants. The joint constraints turn the equilibrium problem into a quasi-variational inequality, which also can yield multiple solutions. The formulation poses computational challenges that can cause Lemke’s algorithm to fail; a restricted formulation is proposed that can be solved by that algorithm.

Suggested Citation

  • Benjamin F. Hobbs & J. S. Pang, 2007. "Nash-Cournot Equilibria in Electric Power Markets with Piecewise Linear Demand Functions and Joint Constraints," Operations Research, INFORMS, vol. 55(1), pages 113-127, February.
    • Handle: RePEc:inm:oropre:v:55:y:2007:i:1:p:113-127
    DOI: 10.1287/opre.1060.0342
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    References listed on IDEAS

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    1. Steffan Berridge & Jacek Krawczyk, "undated". "Relaxation Algorithms in Finding Nash Equilibrium," Computing in Economics and Finance 1997 159, Society for Computational Economics.
    2. William W. Hogan, 1997. "A Market Power Model with Strategic Interaction in Electricity Networks," The Energy Journal, International Association for Energy Economics, vol. 0(Number 4), pages 107-141.
    3. 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.
    4. C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, vol. 11(7), pages 681-689, May.
    5. WEI, Jing-Yuan & SMEERS, Yves, 1999. "Spatial oligopolistic electricity models with Cournot generators and regulated transmission prices," LIDAM Reprints CORE 1454, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Shmuel S. Oren, 1997. "Economic Inefficiency of Passive Transmission Rights in Congested Electricity Systems with Competitive Generation," The Energy Journal, International Association for Energy Economics, vol. 0(Number 1), pages 63-83.
    7. Jacqueline Boucher & Yves Smeers, 2001. "Alternative Models of Restructured Electricity Systems, Part 1: No Market Power," Operations Research, INFORMS, vol. 49(6), pages 821-838, December.
    8. Hogan, William W, 1992. "Contract Networks for Electric Power Transmission," Journal of Regulatory Economics, Springer, vol. 4(3), pages 211-242, September.
    9. Hu, X. & Ralph, D. & Ralph, E.K. & Bardsley, P. & Ferris, M.C., 2004. "Electricity Generation with Looped Transmission Networks: Bidding to an ISO," Cambridge Working Papers in Economics 0470, Faculty of Economics, University of Cambridge.
    10. BOUCHER , Jacqueline & SMEERS, Yves, 2001. "Alternative models of restructured electricity systems, part 1: no market power," LIDAM Reprints CORE 1538, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. Harker, Patrick T., 1991. "Generalized Nash games and quasi-variational inequalities," European Journal of Operational Research, Elsevier, vol. 54(1), pages 81-94, September.
    12. James Bushnell, 2003. "A Mixed Complementarity Model of Hydrothermal Electricity Competition in the Western United States," Operations Research, INFORMS, vol. 51(1), pages 80-93, February.
    13. Jong-Shi Pang & Masao Fukushima, 2005. "Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games," Computational Management Science, Springer, vol. 2(1), pages 21-56, January.
    14. Wei Jing-Yuan & Yves Smeers, 1999. "Spatial Oligopolistic Electricity Models with Cournot Generators and Regulated Transmission Prices," Operations Research, INFORMS, vol. 47(1), pages 102-112, February.
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