scholarly journals Mean-Field Games of Optimal Stopping: A Relaxed Solution Approach

2020 ◽  
Vol 58 (4) ◽  
pp. 1795-1821 ◽  
Author(s):  
Géraldine Bouveret ◽  
Roxana Dumitrescu ◽  
Peter Tankov
Keyword(s):  
Optimal Stopping ◽  
Mean Field ◽  
Mean Field Games ◽  
Solution Approach

scholarly journals A remark on Uzawa’s algorithm and an application to mean field games systems

2020 ◽  
Vol 54 (3) ◽  
pp. 1053-1071
Author(s):  
Charles Bertucci
Keyword(s):  
Optimal Stopping ◽  
Impulse Control ◽  
Mean Field ◽  
Numerical Results ◽  
Mean Field Games ◽  
General Situation ◽  
Continuous Control ◽  
The One

In this paper, we present an extension of Uzawa’s algorithm and apply it to build approximating sequences of mean field games systems. We prove that Uzawa’s iterations can be used in a more general situation than the one in it is usually used. We then present some numerical results of those iterations on discrete mean field games systems of optimal stopping, impulse control and continuous control.

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.

Linear–Quadratic Time-Inconsistent Mean Field Games

2013 ◽  
Vol 3 (4) ◽  
pp. 537-552 ◽  
Author(s):  
A. Bensoussan ◽  
K. C. J. Sung ◽  
S. C. P. Yam
Keyword(s):  
Mean Field ◽  
Mean Field Games ◽  
Linear Quadratic ◽  
Time Inconsistent
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