Solving conjectured multi-leader-follower equilibriums for electricity markets with quadratic optimization problems

Modeling competition in the future European Electricity Market (EEM) suggests considering new perspectives of leadership between the participant generators. EEM models should then be able to represent the possible existence of leaders and followers, and Conjectural Stackelberg equilibriums could be a powerful approach to do so. These asymmetric equilibriums can represent several types of competitive advantages among the market participants, though existing literature approaches generally assume single-leader-follower games. In addition, the complexity of the resolution methodologies sometimes compromises their applicability, especially if large-scale problems have to be solved. In this paper, a multi-leader-follower conjectural Stackelberg equilibrium model is presented. A simple convex quadratic optimization problem is proposed for its resolution, and the conditions for the equilibrium existence are discussed. A case study is presented to validate the model, and to analyze how market competition changes with the number of leaders or followers. The main conclusion is that if leadership spreads and Stackelberg models are used for its representation, regulatory policies should be oriented to increase the number of followers. However, there exists a maximum number of followers for which Stackelberg equilibriums does not exist, suggesting a deeper analysis for these cases to understand that matter and to decide the possible use of other market models.