Triggering a variety of Nash-equilibria in oligopolistic electricity markets

Abstract

Liberalized electricity markets promise a cost-efficient operation and expansion of power systems but may as well introduce opportunities for strategic gaming for price-making agents. Given the rapid transition of today’s energy systems, unconventional generation and consumption patterns are emerging, presenting new challenges for regulators and policymakers to prevent strategic behavior. The strategic offering of various price-making agents in oligopolistic electricity markets resembles a multi-leader-common-follower game. The decision problem of each agent can be modeled as a bi-level optimization problem, consisting of the strategic agent’s decision problem at the upper-level, and the market clearing at the lower-level. When modeling a multi-leader game, i.e., a set of bi-level optimization problems, the resulting equilibrium problem with equilibrium constraints poses several challenges. Real-life applicability or policy-oriented studies are challenged by the potential multiplicity of equilibria and the difficulty of exhaustively exploring this range of equilibria. In this paper, the range of equilibria is explored by using a novel simultaneous solution method. The proposed solution technique relies on applying Scholtes’ regularization before concatenating the strategic actor’s decision problems’ optimality conditions. Hence, the attained solutions are stationary points with high confidence. In a stylized example, different strategic agents, including an energy storage system, are modeled to capture the asymmetric opportunities they may face when exercising market power. Our analysis reveals that these models’ outcomes may span a broad range, impacting the derived economic metrics significantly.