As renewable energy penetration increases, managing demand-side flexibility becomes critical to ensure grid reliability and price stability. Demand response (DR) programs, especially those driven by dynamic pricing, are emerging as key tools in this transition. Retail electricity markets must integrate uncertain and volatile factors such as fluctuating consumer demand, wholesale prices, and generation costs. Designing pricing strategies that optimize consumer flexibility without inducing market inefficiencies requires a rigorous mathematical framework.

The authors propose a bilevel stochastic game-theoretical model where electricity retailers act as leaders setting dynamic tariffs, and consumers respond as rational followers optimizing their consumption. Two market structures are explored:

• Imperfect competition: Modeled as a Mathematical Program with Equilibrium Constraints (MPEC) where retailers exert market power.
• Perfect competition: Represented via Mixed-Integer Linear Programming (MILP) solving the KKT conditions jointly for all players.

The MPEC problem is solved using Artelys Knitro with numerical simulations based on real data from the European Energy Exchange (EEX). Artelys Knitro’s advanced optimization capabilities enable efficient handling of the non-linearity structure of the problem.

Authors: Arega Getaneh (Technical University of Denmark, Elektrovej, Denmark), Rossana Riccardi, Carlos Ruiz.