Equilibrium Analysis of Day-Ahead Electricity Markets With Strategic Demand Aggregators Based on the Theory of Learning in Games

Demand Aggregators (DAs) are expected to have a continuously increasing impact in the operation of modern electricity markets. Such players tend to concentrate large portfolios of demand-side resources, leading to market power concentration and imperfect competition. Such imperfectly competitive markets are analyzed in the literature by studying their equilibria. However, little attention has been given to the learning dynamics through which players adapt their bidding strategies over time and, crucially, to which equilibria are actually learnable. In this paper, we propose the coarse-correlated equilibrium as a solution concept that is more relevant than the Nash equilibrium for such markets. In contrast to the typical approach of the literature on Equilibrium Problems with Equilibrium Constraints, we model the learning dynamics that strategic DAs use to gradually optimize their bidding strategies. At the same time, in contrast to generic model-free approaches, we account for the fact that market players would make better use of the markets’ available information by explicitly modeling their competitors. To that end, we propose a game-theoretic learning algorithm, in which each strategic DA observes the bids of its competitors and gradually builds beliefs about their bidding strategies. The resulting equilibria are compared to the pure Nash equilibria of the related literature. Our numerical results demonstrate that, in practice, strategic DAs can manipulate prices and market conditions to a greater extent than previously anticipated for the benefit of the energy system as a whole.