Optimal control and zero-sum stochastic differential game problems of mean-field type

TL;DR

This paper investigates optimal control and zero-sum stochastic differential games involving mean-field type dynamics, establishing conditions for optimality, saddle points, and existence of nearly-optimal controls under weak solution frameworks.

Contribution

It provides new theoretical results on the existence of optimal controls and saddle points for mean-field type stochastic differential games and control problems.

Findings

Existence of nearly-optimal controls established.

Conditions for the existence of optimal controls and saddle points derived.

Framework based on weak solutions of mean-field stochastic differential equations.

Abstract

We establish existence of nearly-optimal controls, conditions for existence of an optimal control and a saddle-point for respectively a control problem and zero-sum differential game associated with payoff functionals of mean-field type, under dynamics driven by weak solutions of stochastic differential equations of mean-field type.