Time-Inconsistent Problems for Controlled Markov Chains with Distribution-Dependent Costs: Equilibrium Solutions
Optimization and Control
2019-09-26 v1 Probability
Abstract
This paper focuses on a class of continuous-time controlled Markov chains with time-inconsistent and distribution-dependent cost functional (in some appropriate sense). A new definition of time-inconsistent distribution-dependent equilibrium in closed-loop sense is given and its existence and uniqueness have been established. Because of the time-inconsistency, it is proved that the equilibrium is locally optimal in an appropriate sense. Moreover, it has been shown that our problem is essentially equivalent to an infinite-player mean-field game with time-inconsistent cost.
Keywords
Cite
@article{arxiv.1909.11584,
title = {Time-Inconsistent Problems for Controlled Markov Chains with Distribution-Dependent Costs: Equilibrium Solutions},
author = {Hongwei Mei and George Yin},
journal= {arXiv preprint arXiv:1909.11584},
year = {2019}
}