This Website uses cookies. By using this website you are agreeing to our use of cookies and to the terms and conditions listed in our data protection policy. Read more

European Journal of Operational Research

Numerical Calculation of an Asymmetric Supply Function Equilibrium with Capacity Constraints

Scientific Article in English
Reference
Holmberg, Pär (2009). “Numerical Calculation of an Asymmetric Supply Function Equilibrium with Capacity Constraints”. European Journal of Operational Research 199(1), 285–295. doi.org/10.1016/j.ejor.2008.10.029

Author
Pär Holmberg

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.

Pär Holmberg

+46 (0)8 665 4559
+46 (0)72 511 6866
par.holmberg@ifn.se