| Issue |
ESAIM: COCV
Volume 27, 2021
|
|
|---|---|---|
| Article Number | 5 | |
| Number of page(s) | 18 | |
| DOI | https://doi.org/10.1051/cocv/2021003 | |
| Published online | 03 March 2021 | |
Controlled Markov chains with non-exponential discounting and distribution-dependent costs*
1
Department of Statistics, Rice University,
Houston,
TX
77005, USA.
2
Department of Mathematics, University of Connecticut,
Storrs,
CT
06269, USA.
** Corresponding author: hongwei.mei@rice.edu
Received:
8
June
2020
Accepted:
2
January
2021
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.
Mathematics Subject Classification: 93E20 / 60J27 / 90C40
Key words: time inconsistency / distribution dependence / controlled Markov chain
© EDP Sciences, SMAI 2021
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