A characterization of sub-game perfect Nash equilibria for SDEs of mean field type

TL;DR

This paper develops a stochastic maximum principle to characterize subgame perfect Nash equilibria in mean field type stochastic differential games with time-inconsistent costs, and extends the approach to construct decentralized strategies.

Contribution

It introduces a novel stochastic maximum principle for mean field games with time inconsistency and provides a method to construct decentralized strategies with performance estimates.

Findings

Derived a stochastic maximum principle for mean field games.

Extended the approach to construct decentralized strategies.

Provided performance estimates for strategies.

Abstract

We study a class of dynamic decision problems of mean field type with time inconsistent cost functionals, and derive a stochastic maximum principle to characterize subgame perfect Nash equilibrium points. Subsequently, this approach is extended to a mean field game to construct decentralized strategies and obtain an estimate of their performance.