Optimal control and zero-sum games for Markov chains of mean-field type

Salah Eddine Choutri; Boualem Djehiche; Hamidou Tembine

doi:10.3934/mcrf.2019026

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2019, Volume 9, Issue 3: 571-605. Doi: 10.3934/mcrf.2019026

This issue Previous Article A non-exponential discounting time-inconsistent stochastic optimal control problem for jump-diffusion Next Article

Optimal control and zero-sum games for Markov chains of mean-field type

1.
Department of Mathematics, KTH Royal Institute of Technology, 100 44, Stockholm, Sweden
2.
Learning & Game Theory Laboratory, New York University, 19 Washington Square North New York, NY 10011, USA

^* Corresponding author: H. Tembine
^* Corresponding author: H. Tembine

Received: September 30, 2017

Revised: October 31, 2018

Published: September 2019

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Abstract

We establish existence of Markov chains of mean-field type with unbounded jump intensities by means of a fixed point argument using the total variation distance. We further show existence of nearly-optimal controls and, using a Markov chain backward SDE approach, we suggest conditions for existence of an optimal control and a saddle-point for respectively a control problem and a zero-sum differential game associated with payoff functionals of mean-field type, under dynamics driven by such Markov chains of mean-field type.

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Mathematics Subject Classification: Primary: 60H10, 60H07; Secondary: 49N90.

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