Nash equilibrium in a pay-as-bid electricity market Part 2 - best response of a producer

Abstract

We consider a multi-leader-common-follower model of a pay-as-bid electricity market in which the producers provide the regulator with either linear or quadratic bids. We prove that for a given producer only linear bids can maximize his profit. Such linear bids are referred as the ‘best response’ of the given producer. They are obtained assuming the demand is known and some estimate of the bids of the other producers is available. Nevertheless we also show that whenever no best response exists, the optimal profit can be asymptotically attained by a sequence of quadratic bids converging to the so-called ‘limiting best response’. An explicit formula for such a sequence is provided.

Keywords:

• Electricity market
• multi-leader-follower game
• Nash equilibrium
• best response

Notes

The views and opinions expressed in this article are those of the authors and do not necessarily reflect the official policy or position of the EDF group. Assumptions made within the analysis of this article are not reflective of the position of the EDF group.

Dedicated to Professor Franco Giannessi on the occasion of his 80th birthday and to Professor Diethard Pallaschke on the occasion of his 75th birthday.

Additional information

Funding

This research benefited from the support of the ‘FMJH Program Gaspard Monge in optimization and operation research’, and from the support to this program from EDF. This research has been also supported by the European Regional Development Fund and the Ministry of Education, Youth and Sports of the Czech Republic under the Regional Innovation Center for Electrical Engineering (RICE) [project number CZ.1.05/2.1.00/03.0094].