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Nash equilibria in electricity markets with discrete prices

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  • E. J. Anderson
  • H. Xu

Abstract

In this paper we analyse the equilibrium structure for a particular type of electricity market. We consider a market with two generators offering electricity into a pool. Generators are centrally dispatched, with cheapest offers used first. The pool price is determined as the highest-priced offer dispatched, and both generators are paid this price for all the electricity they provide. First generators set their price points (at which bids will later be made) and these are announced. Then each generator chooses the quantities to offer at each price. This reflects the behaviour of the Australian electricity market in which prices are set for 24-hours at a time, but different quantities can be offered within each half-hour period. The demand for electricity is uncertain when offers are made (and is drawn from a probability distribution known to both players). We begin by analysing an example of this two stage game for a simple case where only one price can be chosen. The main results of the paper concern the structure of a Nash equilibrium for the quantity-setting sub-game in which each player aims to maximise their expected profit when prices have already been announced. The distribution of demand plays an important role in the existence of a Nash equilibrium. In the quantity setting game there may be Nash equilibria which are not stable. We show that, under certain circumstances, if the equilibrium offers are sufficiently close to the generators’ marginal costs, then the equilibrium will be stable. Copyright Springer-Verlag 2004

Suggested Citation

  • E. J. Anderson & H. Xu, 2004. "Nash equilibria in electricity markets with discrete prices," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(2), pages 215-238, October.
    • Handle: RePEc:spr:mathme:v:60:y:2004:i:2:p:215-238
    DOI: 10.1007/s001860400364
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    Citations

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    Cited by:

    1. Fellipe Fernandes Goulart dos Santos & Marcus Vinícius de Castro Lobato & Douglas Alexandre Gomes Vieira & Adriano Chaves Lisboa & Rodney Rezende Saldanha, 2022. "A Nash Equilibrium Approach to the Brazilian Seasonalization of Energy Certificates," Energies, MDPI, vol. 15(6), pages 1-13, March.
    2. Holmberg, Pär & Newbery, David & Ralph, Daniel, 2013. "Supply function equilibria: Step functions and continuous representations," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1509-1551.
    3. Anderson, Edward & Holmberg, Pär, 2018. "Price instability in multi-unit auctions," Journal of Economic Theory, Elsevier, vol. 175(C), pages 318-341.
    4. Holmberg, Pär & Newbery, David, 2010. "The supply function equilibrium and its policy implications for wholesale electricity auctions," Utilities Policy, Elsevier, vol. 18(4), pages 209-226, December.
    5. Sankaranarayanan, Sriram & Feijoo, Felipe & Siddiqui, Sauleh, 2018. "Sensitivity and covariance in stochastic complementarity problems with an application to North American natural gas markets," European Journal of Operational Research, Elsevier, vol. 268(1), pages 25-36.
    6. Juan Aparicio & Juan Ferrando & Ana Meca & Julia Sancho, 2008. "Strategic bidding in continuous electricity auctions: an application to the Spanish electricity market," Annals of Operations Research, Springer, vol. 158(1), pages 229-241, February.
    7. Marek Kočan, 2008. "Cyclic behavior in dynamic investment decisions for deregulated energy markets," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(1), pages 67-78, March.
    8. Edward Anderson & Huifu Xu, 2006. "Optimal Supply Functions in Electricity Markets with Option Contracts and Non-smooth Costs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(3), pages 387-411, July.
    9. Tashpulatov, Sherzod N., 2015. "Analysis of electricity industry liberalization in Great Britain: How did the bidding behavior of electricity producers change?," Utilities Policy, Elsevier, vol. 36(C), pages 24-34.

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