Price Formation and Optimal Trading in Intraday Electricity Markets with a Major Player

We study price formation in intraday electricity markets in the presence of intermittent renewable generation. We consider the setting where a major producer may interact strategically with a large number of small producers. Using stochastic control theory, we identify the optimal strategies of agents with market impact and exhibit the Nash equilibrium in a closed form in the asymptotic framework of mean field games with a major player.

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Quantum Mean-Field Games with the Observations of Counting Type

Games ◽

10.3390/g12010007 ◽

2021 ◽

Vol 12 (1) ◽

pp. 7

Author(s):

Vassili N. Kolokoltsov

Keyword(s):

Game Theory ◽

Nash Equilibrium ◽

Open Problem ◽

Existence And Uniqueness ◽

Existence Of Solutions ◽

Mean Field ◽

Mean Field Games ◽

Quantum Game ◽

Quantum Games ◽

Interesting Open Problem

Quantum games and mean-field games (MFG) represent two important new branches of game theory. In a recent paper the author developed quantum MFGs merging these two branches. These quantum MFGs were based on the theory of continuous quantum observations and filtering of diffusive type. In the present paper we develop the analogous quantum MFG theory based on continuous quantum observations and filtering of counting type. However, proving existence and uniqueness of the solutions for resulting limiting forward-backward system based on jump-type processes on manifolds seems to be more complicated than for diffusions. In this paper we only prove that if a solution exists, then it gives an ϵ-Nash equilibrium for the corresponding N-player quantum game. The existence of solutions is suggested as an interesting open problem.

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A Novel Mean Field Game-Based Strategy for Charging Electric Vehicles in Solar Powered Parking Lots

Energies ◽

10.3390/en14248517 ◽

2021 ◽

Vol 14 (24) ◽

pp. 8517

Author(s):

Samuel M. Muhindo ◽

Roland P. Malhamé ◽

Geza Joos

Keyword(s):

Nash Equilibrium ◽

Solar Energy ◽

Electric Vehicles ◽

Large Population ◽

Mean Field ◽

Mean Field Games ◽

Parking Lot ◽

Equal Sharing ◽

Solar Powered ◽

Energy Forecast

We develop a strategy, with concepts from Mean Field Games (MFG), to coordinate the charging of a large population of battery electric vehicles (BEVs) in a parking lot powered by solar energy and managed by an aggregator. A yearly parking fee is charged for each BEV irrespective of the amount of energy extracted. The goal is to share the energy available so as to minimize the standard deviation (STD) of the state of charge (SOC) of batteries when the BEVs are leaving the parking lot, while maintaining some fairness and decentralization criteria. The MFG charging laws correspond to the Nash equilibrium induced by quadratic cost functions based on an inverse Nash equilibrium concept and designed to favor the batteries with the lower SOCs upon arrival. While the MFG charging laws are strictly decentralized, they guarantee that a mean of instantaneous charging powers to the BEVs follows a trajectory based on the solar energy forecast for the day. That day ahead forecast is broadcasted to the BEVs which then gauge the necessary SOC upon leaving their home. We illustrate the advantages of the MFG strategy for the case of a typical sunny day and a typical cloudy day when compared to more straightforward strategies: first come first full/serve and equal sharing. The behavior of the charging strategies is contrasted under conditions of random arrivals and random departures of the BEVs in the parking lot.

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Mean Field Games Flock! The Reinforcement Learning Way

Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2021/50 ◽

2021 ◽

Author(s):

Sarah Perrin ◽

Mathieu Laurière ◽

Julien Pérolat ◽

Matthieu Geist ◽

Romuald Élie ◽

...

Keyword(s):

Reinforcement Learning ◽

Nash Equilibrium ◽

Population Distribution ◽

Mean Field ◽

High Dimensional ◽

Mean Field Games ◽

Fictitious Play ◽

Mean Field Game ◽

Best Response

We present a method enabling a large number of agents to learn how to flock. This problem has drawn a lot of interest but requires many structural assumptions and is tractable only in small dimensions. We phrase this problem as a Mean Field Game (MFG), where each individual chooses its own acceleration depending on the population behavior. Combining Deep Reinforcement Learning (RL) and Normalizing Flows (NF), we obtain a tractable solution requiring only very weak assumptions. Our algorithm finds a Nash Equilibrium and the agents adapt their velocity to match the neighboring flock’s average one. We use Fictitious Play and alternate: (1) computing an approximate best response with Deep RL, and (2) estimating the next population distribution with NF. We show numerically that our algorithm can learn multi-group or high-dimensional flocking with obstacles.

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