Mean Field Models to Regulate Carbon Emissions in Electricity Production

Area of Science:

• Environmental Economics
• Mathematical Modeling
• Energy Systems Analysis

Background:

• Climate change, driven by carbon emissions, poses a significant threat to ecosystems.
• Electricity producers face a trade-off between revenue and environmental externalities from carbon emissions.
• Balancing reliable fossil fuel power with uncertain renewable energy sources is a key challenge.

Purpose of the Study:

• To analyze electricity producer decisions regarding renewable energy adoption under a carbon tax.
• To compare outcomes of competitive (Nash equilibrium) versus cooperative (social optimum) strategies.
• To investigate the impact of a regulator on carbon tax policy and market dynamics.

Main Methods:

• Application of mean field control and mean field game models.
• Development and analysis of nonstandard forward-backward stochastic differential equation systems.
• Numerical experiments to illustrate producer behavior and policy impacts.

Main Results:

• Characterization and proof of unique solutions for Nash equilibrium and social optimum.
• Quantification of the trade-off between production revenue and carbon emission costs.
• Analysis of producer behavior under different market scenarios (competitive vs. cooperative).

Conclusions:

• Mean field models provide a framework for understanding complex energy market decisions.
• Cooperative strategies can lead to a social optimum, potentially mitigating climate change impacts more effectively.
• Regulatory intervention, through carbon tax policy, can influence market equilibria and drive sustainable energy transitions.