Inverse Equilibrium Analysis of Oligopolistic Electricity Markets

Abstract

Inverse equilibrium modeling fits parameters of an equilibrium model to observations. This allows investigation of whether market structures fit observed outcomes and it has predictive power. We introduce a methodology that leverages relaxed stationarity conditions from Karush-Kuhn-Tucker conditions to set up inverse equilibrium problems. This facilitates reframing of existing equilibrium approaches on power systems into inverse equilibrium programs. We illustrate the methodology on network-constrained and unconstrained Nash-Cournot games between price-making power generators. The inverse equilibrium problems in this paper reformulate into linear programming problems that are flexible and interpretable. Still, inverse equilibrium modeling provides generally inconsistent estimation and econometric approaches are better for this purpose.

Inverse Optimization: Theory and Applications

“…Under mild assumptions, the equilibria of these multi-player games can be described using variational inequalities and KKT conditions. To infer the {θ i } N i=1 terms, Bertsimas et al [29] considers a data-driven inverse VI approach while Ratliff et al [122] and Risanger et al [124] apply a data-driven inverse KKT approach. Allen et al [13] extends the inverse KKT approach to generalized Nash equilibria, where player decisions not only affect each other's objectives but also each other's feasible regions, for example, by sharing a joint capacity constraint ( N i=1 x i ≤ µ).…”

A Data-Driven Bilevel Model for Estimating Operational Information of a Neighboring Rival’s Reservoir in a Competitive Context

“…However, for an optimization model, these three variables cannot be uniquely determined without additional constraints provided, which means that multiple solutions will occur. That is the weakness of the inverse optimization methodology in its nature [33].…”

“…The inverse model is also driven by data but does not need to be trained repeatedly with plenty of data as some other data-driven methods need [32]. Furthermore, it is more interpretable than ANN-based methods [33].…”

“…In the literature, [33] proposes a methodology that leverages relaxed Karush-Kuhn-Tucker (KKT) conditions to set up inverse equilibrium models to analyze the market Nash equilibrium. Ref.…”