scholarly journals Deterministic Limit of Mean Field Games Associated with Nonlinear Markov Processes

2018 ◽  
Vol 81 (3) ◽  
pp. 711-738
Author(s):  
Yurii Averboukh
Keyword(s):  
Markov Processes ◽  
Mean Field ◽  
Mean Field Games ◽  
Nonlinear Markov Processes ◽  
Deterministic Limit

MICRO-DYNAMIC ASSOCIATED WITH TWO-STATE NONLINEAR MARKOV PROCESSES: WITH AN APPLICATION TO FREE RECALL

2011 ◽  
Vol 10 (01) ◽  
pp. 41-58 ◽  
Author(s):  
T. D. FRANK ◽  
T. RHODES
Keyword(s):  
Free Recall ◽  
Markov Processes ◽  
Dynamic Models ◽  
Mean Field ◽  
Variational Calculus ◽  
State Model ◽  
Recall Data ◽  
Nonlinear Markov Processes ◽  
Many Body Systems ◽  
Two State Model

We examine the relationship between time-discrete nonlinear Markov processes defined in terms of nonlinear Markov chains and corresponding micro-dynamic models describing many-body systems composed of a finite number of units interacting with each other via a mean field. To this end, we consider a two-state model and examine appropriately defined measures for attractor strength and noise amplitude using variational calculus. We focus on a two-state model and demonstrate an application to free recall data from 8 participants.

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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