scholarly journals Positional strategies in mean-field control problems on a finite state space

2018 ◽  
Vol 28 (1) ◽  
pp. 15-21
Author(s):  
A.A. Berezin ◽  
Keyword(s):  
State Space ◽  
Mean Field ◽  
Control Problems ◽  
Field Control ◽  
Finite State ◽  
Finite State Space

scholarly journals Finite state N-agent and mean field control problems

2021 ◽  
Author(s):  
Alekos Cecchin
Keyword(s):  
Control Problem ◽  
Value Function ◽  
Mean Field ◽  
Control Problems ◽  
Value Functions ◽  
Limit Value ◽  
Field Control ◽  
Finite State ◽  
Finite Time Horizon ◽  
Hamilton Jacobi Bellman

We examine mean field control problems  on a finite state space, in continuous time and over a finite time horizon. We characterize the value function of the mean field control problem as the unique viscosity solution of a Hamilton-Jacobi-Bellman equation in the simplex. In absence of any convexity assumption, we exploit this characterization to prove convergence, as $N$ grows, of the value functions of the centralized $N$-agent optimal control problem to the limit mean field control problem  value function, with a convergence rate of order $\frac{1}{\sqrt{N}}$. Then, assuming convexity, we show that the limit value function is smooth and establish propagation of chaos, i.e.  convergence of the $N$-agent optimal trajectories to the unique limiting optimal trajectory, with an explicit rate.

scholarly journals Discrete time, finite state space mean field games

2010 ◽  
Vol 93 (3) ◽  
pp. 308-328 ◽  
Author(s):  
Diogo A. Gomes ◽  
Joana Mohr ◽  
Rafael Rigão Souza
Keyword(s):  
State Space ◽  
Discrete Time ◽  
Mean Field ◽  
Mean Field Games ◽  
Finite State ◽  
Finite State Space
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