Mathematical Methods of Operations Research

, Volume 60, Issue 2, pp 215–238

Nash equilibria in electricity markets with discrete prices


DOI: 10.1007/s001860400364

Cite this article as:
Anderson, E. & Xu, H. Math Meth Oper Res (2004) 60: 215. doi:10.1007/s001860400364


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.


Electricity markets Nash equilibria Stability of equilibria Stochastic demand 

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Australian Graduate School of ManagementUniversity of New South WalesSYDNEYAustralia
  2. 2.School of MathematicsUniversity of SouthamptonUK