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    This study explores open-loop and feedback strategies for leader-follower mean field games. Both approaches yield equilibrium solutions, with costs determined by Riccati equations and performance compared via simulation.

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    Area of Science:

    • Game Theory
    • Stochastic Differential Equations
    • Control Theory

    Background:

    • Investigates leader-follower linear quadratic mean field games.
    • Focuses on optimizing social cost with cooperative followers.

    Purpose of the Study:

    • To derive and compare open-loop and feedback control strategies.
    • To establish equilibrium conditions for mean field games.

    Main Methods:

    • Variational analysis and mean field approximations.
    • Mean field forward-backward stochastic differential equations (FBSDEs).
    • Matrix maximum principle for decentralized feedback strategies.

    Main Results:

    • Obtained open-loop controls as solutions to MF-FBSDEs, forming an asymptotic Stackelberg-team equilibrium.
    • Constructed decentralized feedback strategies for all players.
    • Explicitly determined player costs using solutions to two Riccati equations.

    Conclusions:

    • Both open-loop and feedback strategies provide valid equilibrium solutions.
    • Numerical simulations demonstrate performance comparisons between the two solution types.