scholarly journals Strategic advantages in mean field games with a major player

2020 ◽  
Vol 358 (2) ◽  
pp. 113-118
Author(s):  
Charles Bertucci ◽  
Jean-Michel Lasry ◽  
Pierre-Louis Lions
Keyword(s):  
Mean Field ◽  
Mean Field Games ◽  
Major Player

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

Risks ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 133
Author(s):  
Olivier Féron ◽  
Peter Tankov ◽  
Laura Tinsi
Keyword(s):  
Nash Equilibrium ◽  
Electricity Markets ◽  
Mean Field ◽  
Optimal Strategies ◽  
Price Formation ◽  
Mean Field Games ◽  
Optimal Trading ◽  
Major Player ◽  
Major Producer ◽  
Small Producers

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.

scholarly journals Mean-field games with a major player

2018 ◽  
Vol 356 (8) ◽  
pp. 886-890 ◽  
Author(s):  
Jean-Michel Lasry ◽  
Pierre-Louis Lions
Keyword(s):  
Mean Field ◽  
Mean Field Games ◽  
Major Player

scholarly journals Lax connection and conserved quantities of quadratic mean field games

2021 ◽  
Vol 62 (8) ◽  
pp. 083302
Author(s):  
Thibault Bonnemain ◽  
Thierry Gobron ◽  
Denis Ullmo
Keyword(s):  
Mean Field ◽  
Mean Field Games ◽  
Conserved Quantities ◽  
Quadratic Mean

scholarly journals Quantum Mean-Field Games with the Observations of Counting Type

Games ◽  
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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