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A mean-field game model of electricity market dynamics

Alicia Bassière, Roxana Dumitrescu, Peter Tankov

TL;DR

The paper tackles long-term dynamics in electricity markets under energy-transition pressures by modeling a large population of producers with mean-field games of optimal stopping, incorporating endogenous fuel prices and invest/divest decisions. It extends prior two-technology MF models to multiple conventional and renewable technologies, allows for investment and divestment, and introduces endogenized fuel pricing while ensuring deterministic price paths via a fixed-point scheme. The authors prove existence and uniqueness of equilibrium price trajectories and present a tractable numerical method (linear-programming fictitious play) to compute equilibria, delivering insights into how gas, coal, and renewables substitute over time and how market design and build times affect the transition. The approach yields interpretable outputs (price paths, installed capacity, energy mix, emissions) and provides a framework for policy analysis and market design under realistic energy-transition scenarios, including the 2022 price crisis context.

Abstract

We develop a model for the long-term dynamics of electricity market, based on mean-field games of optimal stopping. Our paper extends the recent contribution [Aïd, René, Roxana Dumitrescu, and Peter Tankov, ``The entry and exit game in the electricity markets: A mean-field game approach." Journal of Dynamics \& Games 8.4 (2021): 331] in several ways, making the model much more realistic, especially for describing the medium-term impacts of energy transition on electricity markets. In particular, we allow for an arbitrary number of technologies with endogenous fuel prices and enable the agents to both invest and divest. This makes it possible to describe the role of gas generation as a medium-term substitute for coal, to be replaced by renewable generation in the long term, and enables us to model the events like the 2022 energy price crisis.

A mean-field game model of electricity market dynamics

TL;DR

The paper tackles long-term dynamics in electricity markets under energy-transition pressures by modeling a large population of producers with mean-field games of optimal stopping, incorporating endogenous fuel prices and invest/divest decisions. It extends prior two-technology MF models to multiple conventional and renewable technologies, allows for investment and divestment, and introduces endogenized fuel pricing while ensuring deterministic price paths via a fixed-point scheme. The authors prove existence and uniqueness of equilibrium price trajectories and present a tractable numerical method (linear-programming fictitious play) to compute equilibria, delivering insights into how gas, coal, and renewables substitute over time and how market design and build times affect the transition. The approach yields interpretable outputs (price paths, installed capacity, energy mix, emissions) and provides a framework for policy analysis and market design under realistic energy-transition scenarios, including the 2022 price crisis context.

Abstract

We develop a model for the long-term dynamics of electricity market, based on mean-field games of optimal stopping. Our paper extends the recent contribution [Aïd, René, Roxana Dumitrescu, and Peter Tankov, ``The entry and exit game in the electricity markets: A mean-field game approach." Journal of Dynamics \& Games 8.4 (2021): 331] in several ways, making the model much more realistic, especially for describing the medium-term impacts of energy transition on electricity markets. In particular, we allow for an arbitrary number of technologies with endogenous fuel prices and enable the agents to both invest and divest. This makes it possible to describe the role of gas generation as a medium-term substitute for coal, to be replaced by renewable generation in the long term, and enables us to model the events like the 2022 energy price crisis.
Paper Structure (25 sections, 8 theorems, 100 equations, 4 figures)

This paper contains 25 sections, 8 theorems, 100 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Literature review
  3. Optimization models
  4. Market equilibrium models
  5. Simulation models
  6. Entry and exit models for electricity market
  7. Mean-field games and their applications to economic and financial modeling
  8. The model
  9. Power plants
  10. Conventional producers
  11. Renewable producers
  12. Price formation
  13. Entry and exit mean-field game
  14. Definition of the mean-field setting
  15. Price formation
  16. ...and 10 more sections

Key Result

Proposition 1

Let $\overline \Phi_k(x) := \int_0^x \Phi_k(y) dy$ for $k=1,\dots,K$ and $G_0(x):=\int_0^x F_0(y) dy$. Assume that the functions $\overline \Phi_1,\dots,\overline \Phi_K$ and $G_0$ are strongly convex. Then, for each $t\in [0,T]$, there exists a unique solution of the system fprice-eprice.

Figures (4)

  • Figure 1: Left: exogenous peak and off-peak electricity demand. Right: gas and coal price trajectories, computed by the model.
  • Figure 2: Left: peak and off-peak electricity price (euros per MWh). Right: installed capacity for the three technologies (GW).
  • Figure 3: Peak (left) and off-peak electricity supply (GW).
  • Figure 4: Comparison of the model with zero and nonzero construction time. Left: peak and off-peak electricity price (euros per MWh). Right: installed capacity for the three technologies (GW).

Theorems & Definitions (15)

  • Proposition 1
  • proof
  • Definition 1
  • Theorem 1
  • Proposition 2
  • Lemma 1
  • proof
  • Lemma 2: A bounded variation property
  • proof
  • Lemma 3
  • ...and 5 more