Price Dynamics for Electricity in Smart Grid Via Mean-Field-Type Games

Djehiche, Boualem; Barreiro-Gómez, Julian; Tembiné, Hamidou

doi:10.1007/s13235-020-00367-8

Cited by 14 publications

(7 citation statements)

References 14 publications

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“…In [12], [24], Stackelberg games modeled price formation under revenue optimization. To study price dynamics in the electricity market in [14], the authors considered a Cournot model and showed that their model is a MFG problem with common noise and a jump-diffusion. The paper [5] modeled the transition to renewable energies by an optimal switching MFG.…”

Section: Prior Workmentioning

confidence: 99%

The potential method for price-formation models

Ashrafyan

Bakaryan

Gomes

et al. 2022

2022 IEEE 61st Conference on Decision and Control (CDC)

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We consider the mean-field game price formation model introduced by Gomes and Sa úde. In this MFG model, agents trade a commodity whose supply can be deterministic or stochastic. Agents maximize profit, taking into account current and future prices. The balance between supply and demand determines the price. We introduce a potential function that converts the MFG into a convex variational problem. This variational formulation is particularly suitable for machine learning approaches. Here, we use a recurrent neural network to solve this problem. In the last section of the paper, we compare our results with known analytical solutions.

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Section: Prior Workmentioning

confidence: 99%

The potential method for price-formation models

Ashrafyan

Bakaryan

Gomes

et al. 2022

2022 IEEE 61st Conference on Decision and Control (CDC)

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show abstract

“…In [37] and [7], Stackelberg games to maximize the producer's revenue were used. A Cournot model was introduced in [16], which specifies the price dynamics with noise from a Brownian motion and a jump process. A model with finitely many agents was presented in [1], where the demand includes common noise.…”

Section: Introductionmentioning

confidence: 99%

Machine Learning architectures for price formation models

Gomes¹,

Gutiérrez²,

Laurière³

2022

Preprint

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Here, we study machine learning (ML) architectures to solve a mean-field games (MFGs) system arising in price formation models. We formulate a training process that relies on a min-max characterization of the optimal control and price variables. Our main theoretical contribution is the development of a posteriori estimates as a tool to evaluate the convergence of the training process. We illustrate our results with numerical experiments for a linear-quadratic model.

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“…In [4], the price equilibrium is obtained for a finite number of agents who optimally control their production and trading rates in order to satisfy a demand subjected to common noise. Stackelberg games for price formation under revenue optimization were proposed in [13] and [40], and Cournot models in [21]. A MFG of optimal switching was presented in [5] to model the transition to renewable energies.…”

Section: Introductionmentioning

confidence: 99%

A Variational Approach For Price Formation Models In One Dimension

Ashrafyan¹,

Bakaryan²,

Gomes³

et al. 2022

Preprint

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In this paper, we study a class of first-order mean-field games (MFGs) that model price formation. Using Poincaré Lemma, we eliminate one of the equations and obtain a variational problem for a single function. This variational problem offers an alternative approach for the numerical solution of the original MFGs system. We show a correspondence between solutions of the MFGs system and the variational problem. Moreover, we address the existence of solutions for the variational problem using the direct method in the calculus of variations. We end the paper with numerical results for a linear-quadratic model.

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Price Dynamics for Electricity in Smart Grid Via Mean-Field-Type Games

Cited by 14 publications

References 14 publications

The potential method for price-formation models

The potential method for price-formation models

Machine Learning architectures for price formation models

A Variational Approach For Price Formation Models In One Dimension

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