Linear quadratic mean-field game-team analysis: a mixed coalition approach

TL;DR

This paper introduces a mixed mean-field framework for large-scale systems with cooperative inner layers and competitive outer layers, proposing a new asymptotic equilibrium concept for distributed game-team strategies.

Contribution

It develops a novel mixed mean-field analysis and equilibrium concept for systems with layered cooperation and competition, extending traditional mean-field models.

Findings

Proposes a mixed mean-field framework for layered systems.

Introduces an asymptotic mixed-equilibrium-optima.

Validates the proposed approach through theoretical analysis.

Abstract

Mean-field theory has been extensively explored in decision analysis of {large-scale} (LS) systems but traditionally in ``pure" cooperative or competitive settings. This leads to the so-called mean-field game (MG) or mean-field team (MT). This paper introduces a new class of LS systems with cooperative inner layer and competitive outer layer, so a ``mixed" mean-field analysis is proposed for distributed game-team strategy. A novel asymptotic mixed-equilibrium-optima is also proposed and verified.