# Energy transition under scenario uncertainty: a mean-field game of stopping with common noise

arXiv: https://arxiv.org/abs/2210.03554 · HTML: https://mlsanity.com/paper/2210.03554/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Oct 2022.

## Built on by (most cited first, 2 of 2)

- [Population-Aware Imitation Learning in Mean-field Games with Common Noise](https://mlsanity.com/paper/2605.03357/) (2026)
- [Mean field games as a tool for AI safety: a worked example from the July 2026 Hugging Face incident](https://mlsanity.com/paper/2610.00902/) (2026)

## Abstract (arXiv)

We study the impact of transition scenario uncertainty, namely that of future carbon price and electricity demand, on the pace of decarbonization of the electricity industry. To this end, we develop a theory of optimal stopping mean-field games with non-Markovian common noise and partial observation. For mathematical tractability, the theory is formulated in discrete time and with common noise restricted to a finite probability space. We prove the existence of Nash equilibria for this game using the linear programming approach. We then apply the general theory to build a discrete time model for the long-term dynamics of the electricity market subject to common random shocks affecting the carbon price and the electricity demand. We consider two classes of agents: conventional producers and renewable producers. The former choose an optimal moment to exit the market and the latter choose an optimal moment to enter the market by investing into renewable generation. The agents interact through the market price determined by a merit order mechanism with an exogenous stochastic demand. We illustrate our model by an example inspired by the UK electricity market, and show that scenario uncertainty leads to significant changes in the speed of replacement of conventional generators by renewable production.