Producers submit offer curves to a procurement auction, e.g. an electricity auction, before uncertain demand has been realised. In the supply function equilibrium (SFE), every ﬁrm commits to the offer curve that maximises its expected proﬁt, given the offer curves of competitors. The equilibrium is given by a system of differential equations. In practice, it has been very difﬁcult to ﬁnd valid SFE, i.e. non-decreasing solutions, from this system, especially for asymmetric producers. This paper shows that valid SFE can be calculated by means of a shooting algorithm that combines numerical integration with an optimisation procedure that searches for an end-condition. Multiple/parallel shooting is used for ill-conditioned cases. Ó 2008 Elsevier B.V. All rights reserved.
European Journal of Operational Research
Numerical Calculation of an Asymmetric Supply Function Equilibrium with Capacity Constraints
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