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Using EPECs to model bilevel games in restructured electricity markets with locational prices

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Hu, X.
Ralph, R.
Abstract

CWPE0619 (EPRG0602) Xinmin Hu and Daniel Ralph (Feb 2006) Using EPECs to model bilevel games in restructured electricity markets with locational prices We study a bilevel noncooperative game-theoretic model of electricity markets with locational marginal prices. Each player faces a bilevel optimization problem that we remodel as a mathematical program with equilibrium constraints, MPEC. This gives an EPEC, equilibrium problem with equilibrium constraints. We establish sufficient conditions for existence of pure strategy Nash equilibria for this class of bilevel games and give some applications. We show by examples the effect of network transmission limits, i.e. congestion, on existence of equilibria. Then we study, for more general EPECs, the weaker pure strategy concepts of local Nash and Nash stationary equilibria. We model the latter via complementarity problems, CPs. Finally, we present numerical examples of methods that attempt to find local Nash or Nash stationary equilibria of randomly generated electricity market games. The CP solver PATH is found to be rather effective in this context.

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Paper provided by Faculty of Economics, University of Cambridge in its series Cambridge Working Papers in Economics with number 0619.

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Date of creation: Feb 2006
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Handle: RePEc:cam:camdae:0619

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Keywords: electricity market; bilevel game; MPEC; EPEC; Nash stationary point; equilibrium constraints; complementarity problem;

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Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
Q40 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - General

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  1. Hung-po Chao & Stephen Peck, 1997. "An Institutional Design for an Electricity Contract Market with Central Dispatch," The Energy Journal, International Association for Energy Economics, vol. 18(1), pages 85-110.
  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. [Downloadable!] (restricted)
  3. Klemperer, Paul D & Meyer, Margaret A, 1989. "Supply Function Equilibria in Oligopoly under Uncertainty," Econometrica, Econometric Society, vol. 57(6), pages 1243-77, November. [Downloadable!] (restricted)
  4. 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. 18(1), pages 63-84.
  5. Ehrenmann, A. & Neuhoff, K., 2003. "A Comparison of Electricity Market Designs in Networks," Cambridge Working Papers in Economics 0341, Faculty of Economics, University of Cambridge. [Downloadable!]
  6. 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. [Downloadable!]
  7. Hogan, William W, 1992. "Contract Networks for Electric Power Transmission," Journal of Regulatory Economics, Springer, vol. 4(3), pages 211-42, September.
  8. Steven Stoft, 1999. "Financial Transmission Rights Meet Cournot: How TCCs Curb Market Power," The Energy Journal, International Association for Energy Economics, vol. 20(1), pages 1-24.
  9. Balder, Erik J, 1995. "A Unifying Approach to Existence of Nash Equilibrium," International Journal of Game Theory, Springer, vol. 24(1), pages 79-94.
  10. Green, Richard J & Newbery, David M, 1992. "Competition in the British Electricity Spot Market," Journal of Political Economy, University of Chicago Press, vol. 100(5), pages 929-53, October. [Downloadable!] (restricted)
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