Reinforcement Learning for Constrained Energy Trading Games With Incomplete Information

Area of Science:

• Computational Economics
• Game Theory
• Machine Learning

Background:

• Energy trading involves strategic players with incomplete information.
• Designing algorithms to find Nash equilibrium (NE) in such games is complex.
• Existing methods may not handle discontinuous pricing or ensure convergence.

Purpose of the Study:

• To design adaptive learning algorithms for finding the Nash equilibrium (NE) in constrained energy trading games.
• To ensure individual players maximize their average utility using learning automaton schemes.
• To guarantee the existence and uniqueness of a mixed-strategy Nash equilibrium.

Main Methods:

• Utilized learning automaton schemes for players to generate action probability distributions.
• Analyzed the convergence properties of admissible mixed-strategies to the NE.
• Proved utility function properties (upper semicontinuity, payoff security) for NE existence.
• Demonstrated NE uniqueness through the strict diagonal concavity of a regularized Lagrange function.

Main Results:

• Showcased that convergence of mixed-strategies to NE leads to almost sure convergence of average utility and trading quantity.
• Established the existence of a mixed-strategy NE due to the utility function's properties.
• Guaranteed the uniqueness of the mixed-strategy NE.

Conclusions:

• An adaptive learning algorithm is proposed to effectively seek the mixed-strategy Nash equilibrium.
• The developed algorithm ensures stable and optimal outcomes in constrained energy trading games.
• The theoretical guarantees support the practical application of these algorithms in real-world energy markets.