Krasovskii-Subbotin approach to mean field type differential games

TL;DR

This paper develops a Krasovskii-Subbotin approach to analyze mean field type differential games, focusing on systems with ODE dynamics and observable agent distributions, establishing suboptimal strategies and the value function.

Contribution

It introduces a novel Krasovskii-Subbotin framework for mean field differential games with observable distributions and proves the existence of the value function.

Findings

Constructed suboptimal strategies for the game

Proved the existence of the value function

Analyzed systems with ODE dynamics and observable distributions

Abstract

A mean field type differential game is a mathematical model of a large system of identical agents under mean-field interaction controlled by two players with opposite purposes. We study the case when the dynamics of each agent is given by ODE and the players can observe the distribution of the agents. We construct suboptimal strategies and prove the existence of the value function.