Hierarchical Mean Field Games for Multiagent Systems With Tracking-Type Costs: Distributed $\varepsilon $-Stackelberg Equilibria

Bing‐Chang Wang · Ji‐Feng Zhang

52 citations0/0 files storedIEEE Transactions on Automatic Control

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Game Theory and Applications Stochastic processes and financial applications Distributed Control Multi-Agent Systems

Abstract

In this technical note, hierarchical games are investigated for multi-agent systems involving a leader and a large number of followers with infinite horizon tracking-type costs. By jointly analyzing dynamic equations and index functions of all agents, a set of centralized Stackelberg equilibrium strategies is given. Then, by using the mean field approach and the brute force method, a set of distributed strategies is designed. Under mild conditions, it is shown that the closed-loop system is uniformly stable and the set of distributed strategies is an ε-Stackelberg equilibrium.

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References

2007Mean field games 1995Dynamic noncooperative game theory 2007Large-Population Cost-Coupled LQG Problems With Nonuniform Agents: Individual-Mass Behavior and Decentralized $\varepsilon$-Nash Equilibria 2006Jeux à champ moyen. I – Le cas stationnaire 2010Large-Population LQG Games Involving a Major Player: The Nash Certainty Equivalence Principle 2008Markov Perfect Industry Dynamics With Many Firms 2013$\epsilon$-Nash Mean Field Game Theory for Nonlinear Stochastic Dynamical Systems with Major and Minor Agents 2002A Stackelberg Network Game with a Large Number of Followers

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