Mean-field risk sensitive control and zero-sum games for Markov chains

TL;DR

This paper develops a theoretical framework for risk-sensitive control and zero-sum games involving mean-field Markov chains with unbounded jump intensities, establishing existence results using fixed point and backward SDE methods.

Contribution

It introduces a fixed point approach for mean-field Markov chains with unbounded jumps and provides conditions for optimal controls and saddle points in risk-sensitive settings.

Findings

Existence of controlled mean-field Markov chains with unbounded jumps.

Conditions for optimal control and saddle points in risk-sensitive mean-field games.

Application of Wasserstein distance and entropic backward SDEs in the analysis.

Abstract

We establish existence of controlled Markov chain of mean-field type with unbounded jump intensities by means of a fixed point argument using the Wasserstein distance. Using a Markov chain entropic backward SDE approach, we further 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 risk sensitive payoff functionals of mean-field type.