Mean Field Models to Regulate Carbon Emissions in Electricity Production

Carmona, René; Dayanıklı, Gökçe; Laurière, Mathieu

doi:10.1007/s13235-021-00422-y

Cited by 10 publications

(2 citation statements)

References 22 publications

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“…We note that another setting with major players has already been explored: Stackelberg MFGs. (Elie, Mastrolia, and Possamaï 2019;Carmona and Wang 2021;Carmona, Dayanıklı, and Laurière 2022) consider a Stackelberg equilibrium instead of a Nash equilibrium, wherein a 'major' principal player chooses their policy first and has priority (like a government or regulator); see (Guo, Hu, and Zhang 2022;Vasal and Berry 2022) for discrete time versions of the problem. Though the Stackelberg setting is of importance, it is distinct from computing Nash equilibria where major and minor players are "on the same level": in the Stackelberg setting, minor players only respond with a Nash equilibrium between themselves after the principal's policy choice.…”

Section: Introductionmentioning

confidence: 99%

Learning Discrete-Time Major-Minor Mean Field Games

Cui,

Dayanıklı,

Laurière

et al. 2024

AAAI

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Recent techniques based on Mean Field Games (MFGs) allow the scalable analysis of multi-player games with many similar, rational agents. However, standard MFGs remain limited to homogeneous players that weakly influence each other, and cannot model major players that strongly influence other players, severely limiting the class of problems that can be handled. We propose a novel discrete time version of major-minor MFGs (M3FGs), along with a learning algorithm based on fictitious play and partitioning the probability simplex. Importantly, M3FGs generalize MFGs with common noise and can handle not only random exogeneous environment states but also major players. A key challenge is that the mean field is stochastic and not deterministic as in standard MFGs. Our theoretical investigation verifies both the M3FG model and its algorithmic solution, showing firstly the well-posedness of the M3FG model starting from a finite game of interest, and secondly convergence and approximation guarantees of the fictitious play algorithm. Then, we empirically verify the obtained theoretical results, ablating some of the theoretical assumptions made, and show successful equilibrium learning in three example problems. Overall, we establish a learning framework for a novel and broad class of tractable games.

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Section: Introductionmentioning

confidence: 99%

Learning Discrete-Time Major-Minor Mean Field Games

Cui,

Dayanıklı,

Laurière

et al. 2024

AAAI

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“…Carmona et al [4] propose a mean field game to model electricity production by many producers. Only once, at the beginning of the game, producers can invest in a renewable production asset; during the game, they can control the rate of electricity produced by nonrenewables.…”

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confidence: 99%

Dynamic Games in Environmental Economics and Management

Wagener

2022

Dyn Games Appl

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Environmental economics thinks about the optimal use of natural resources, like water, oil, the air we breathe, or the physical environment we live in. The fundamental question is the problem of externalities: costs that are generated by one group of actors, which have to be borne by another group. Time scales play an important role: the benefits of the industrial revolution were realised immediately, but we are still dealing with the costs of the concomitant CO 2 pollution. The evolution of underlying stock variables can be influenced to some extent, at a cost, and their management therefore presents an investment problem.Dynamic games come into the story naturally, as they provide the right framework to analyse actions of multiple actors that generate costs and benefits over time. To provide an impetus to research efforts on dynamic issues of competition and cooperation in environmental management, the editors had invited contributions to a Special Issue of Dynamic Games and Applications with exclusive focus on environmental economics and management. Eleven such contributions are collected in the following pages. Six of them can roughly be classified as dealing with pollution problems, while the other five address more general resource problems. The whole spectrum of dynamic games is present: differential games, population games, overlapping generation games, repeated games, and mean-field games.The seminal contribution of Engelbert Dockner and Ngo Van Long [6] analysed a differential game of countries that have to cope with global pollution, and two of the articles in this Special Issue took it as their starting point. Yanase and Kamei [12] extend the Dockner-Van Long model by allowing the two countries to trade. They find that under frictionless trade, the same levels of environmental and social welfare are achieved under international cooperation, open-loop Nash equilibrium, and linear Markov-perfect Nash equilibrium, and these free-trade policies outperform noncooperative environmental policies in the absence of trade. Positive trade costs can reverse this outcome in certain configurations.

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