Abstract
In this paper we introduce an asymmetric model of continuous electricity auctions with limited production capacity and bounded supply functions. The strategic bidding is studied with this model by means of an electricity market game. We prove that for every electricity market game with continuous cost functions a mixed-strategy Nash equilibrium always exists. In particular, we focus on the behavior of producers in the Spanish electricity market. We consider a very simple form for the Spanish electricity market: an oligopoly consisting just of independent hydro-electric power production units in a single wet period. We show that a pure-strategy Nash equilibrium for the Spanish electricity market game always exists.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Anderson, E. J., & Philpott, A. B. (2001). Using supply functions for offering generation into an electricity market. Operations Research, 50(3), 477–489.
Anderson, E. J., & Xu, H. (2001). Undercutting and overcutting for generator offers in an electricity market. Working paper, Australian Graduate School of Management, University of New South Wales, Sydney, NSW 2052.
Anderson, E. J., & Xu, H. (2004). Nash equilibria in electricity markets with discrete prices. Mathematical Methods of Operations Research, 60(2), 215–238.
Ausubel, L., & Cramton, P. (1998). Demand reduction and inefficiency in multi-unit auctions. Working Paper, Economics Department, University of Maryland, 98wpdr.
Baldick, R., & Hogan, W. W. (2002). Capacity constrained supply function equilibrium models of electricity markets: stability, non-decreasing constraints, and function space iterations. Working paper, Energy Institute, University of California, PWP-089.
Baldick, R., & Hogan, W. W. (2004). Polynomial approximations and supply function equilibrium stability. Working paper, Center for Business and Government, Harvard University.
Baldick, R., Grant, R., & Kahn, E. (2004). Theory and application of linear supply function equilibrium in electricity markets. Journal of Regulatory Economics, 25(2), 143–167.
Berry, C. A., Hobbs, B. F., Meroney, W. A., O’Neill, R. P., & Stewart Jr, W. R. (1999). Understanding how market power can arise in network competition: a game theoretic approach. Utilities Policy, 8(3), 139–158.
Binmore, K. G., & Swierzbinski, J. E. (2000). Treasury auctions: uniform or discriminatory? Review of Economic Design, 5(4), 387–410.
Day, C. J., & Bunn, D. W. (2001). Divestiture of generation assets in the electricity pool of England and Wales: a computational approach to analyzing market power. Journal of Regulatory Economics, 19(2), 123–141.
Delgado, J., & Moreno, D. (2004). Coalition-proof supply function equilibria in oligopoly. Journal of Economic Theory, 114(2), 231–254.
Fabra, N. (2003). Tacit collusion in repeated auctions: uniform versus discriminatory. Journal of Industrial Economics, 51, 271–293.
Fabra, N., Von der Fehr, N. H., & Harbord, D. (2002). Modeling electricity auctions. Electricity Journal, 15(7), 72–81.
Fudenberg, D., & Tirole, J. (1991). Game theory. Cambridge: MIT Press.
Green, R. (1996). Increasing competition in the British electricity spot market. The Journal of Industrial Economics, 44(2), 205–216.
Green, R., & Newbery, D. M. (1992). Competition in the British electricity spot market. Journal of Political Economy, 100(5), 929–953.
Grossman, S. (1981). Nash equilibrium and the industrial organization of markets with large fixed costs. Econometrica, 49, 1149–1172.
Hart, O. (1985). Imperfect competition in general equilibrium: an overview of recent work. In K. Arrow & S. Honkaphoja (Eds.), Frontiers in econometrics. Oxford: Basil Blackwell.
Hobbs, B. F., Metzler, C. A., & Pang, J. S. (2000). Strategic gaming analysis for electric power networks: an MPEC approach. IEEE Transactions on Power Systems, 15(2), 638–645.
Kelley, J. L. (1955). General topology. Princeton: Van Nostrand.
Klemperer, P. D., & Meyer, M. A. (1989). Supply function equilibria in oligopoly under uncertainty. Econometrica, 57, 1243–1277.
Madden, P. (1986). Concavity and optimization in microeconomics. Oxfordshire: Blackwell.
Nash, J. (1950). Equilibrium points in n-person games. Proceedings of the National Academy of Sciences, 36, 48–49.
Rudkevich, A. (1999). Supply function equilibrium in Poolco type power markets: learning all the way. Working paper, Tabors Caramanis and Associates, 1702.
Sancho, J. (2003). Análisis del mercado eléctrico español. Master thesis, University Miguel Hernández of Elche (in Spanish).
Von der Fehr, N. H., & Harbord, D. (1998). Competition in electricity spot market: economic theory and international experience. Memorandum n.5/1998, Department of Economics, University of Oslo.
Weber, J. D., & Overbye, T. J. (1999). A two-level optimization problem for analysis of market bidding strategies. IEEE Power Engineering Society Summer Meeting, 18(3), 1054–1061.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Aparicio, J., Ferrando, J.C., Meca, A. et al. Strategic bidding in continuous electricity auctions: an application to the Spanish electricity market. Ann Oper Res 158, 229–241 (2008). https://doi.org/10.1007/s10479-007-0236-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-007-0236-7