2006–2010

Numerical Calculation of an Asymmetric Supply Function Equilibrium with Capacity Constraints

Reprint No. 2009:26

Author(s): Pär HolmbergYear: 2009 Title: European Journal of Operational Research Volume (No.): 199 (1) Pages: 285–295
Online article (restrictions may apply)


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.


Reference:
Holmberg, Pär (2009), "Numerical Calculation of an Asymmetric Supply Function Equilibrium with Capacity Constraints". European Journal of Operational Research 199(1), 285–295.

Pär Holmberg

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