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

TL;DR

This paper proves the existence of mean-field type Markov chains with unbounded jump intensities and explores optimal control and saddle-point solutions for related zero-sum games using backward SDE methods.

Contribution

It introduces a fixed point approach for unbounded jump intensities and establishes conditions for optimal controls and saddle points in mean-field Markov chain games.

Findings

Existence of mean-field Markov chains with unbounded jumps

Conditions for optimal control existence

Existence of saddle points in zero-sum games

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.