This paper deals with a controlled Markov chain in continuous time with a non-exponential discounting and distribution-dependent cost functional. A definition of closed-loop equilibrium is given and its existence and uniqueness are established. Due to the time-inconsistency brought by the non-exponential discounting and distribution dependence, it is proved that the equilibrium is locally optimal in some appropriate sense. Moreover, it is shown that our problem is equivalent to a mean-field game for infinite-many symmetric players with a non-exponential discounting cost.
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Keywords: time inconsistency, distribution dependence, controlled Markov chain
@article{COCV_2021__27_1_A7_0,
author = {Mei, Hongwei and Yin, George},
title = {Controlled {Markov} chains with non-exponential discounting and distribution-dependent costs},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2021},
publisher = {EDP-Sciences},
volume = {27},
doi = {10.1051/cocv/2021003},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2021003/}
}
TY - JOUR AU - Mei, Hongwei AU - Yin, George TI - Controlled Markov chains with non-exponential discounting and distribution-dependent costs JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2021 VL - 27 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2021003/ DO - 10.1051/cocv/2021003 LA - en ID - COCV_2021__27_1_A7_0 ER -
%0 Journal Article %A Mei, Hongwei %A Yin, George %T Controlled Markov chains with non-exponential discounting and distribution-dependent costs %J ESAIM: Control, Optimisation and Calculus of Variations %D 2021 %V 27 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2021003/ %R 10.1051/cocv/2021003 %G en %F COCV_2021__27_1_A7_0
Mei, Hongwei; Yin, George. Controlled Markov chains with non-exponential discounting and distribution-dependent costs. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 5. doi: 10.1051/cocv/2021003
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Cité par Sources :
The research of the second author was supported in part by the Air Force Office of Scientific Research under grant FA9550-18-1-0268.
