Global-in-Time Well-Posedness for Heterogeneous Mean Field Games

Establish global-in-time well-posedness for the heterogeneous mean field game system—defined by coupled HJB–FPK equations under Lipschitz continuity of drifts in state and mean-field arguments, bounded nondegenerate diffusion coefficients, and compact state space—thereby extending local well-posedness results from time horizons T ≤ δ0 to arbitrary time horizons T.

Background

The paper’s finite-horizon analysis relies on local well-posedness of the HMFG system, ensuring stability and bounded constants over short horizons. Some bounds inherit dependence on the time horizon T, and controlling these for arbitrary T would require global-in-time well-posedness.

The authors explicitly note that extending their results beyond the local horizon demands global well-posedness for HMFG, which remains largely open in the literature. Resolving this would provide theoretical guarantees for long-horizon HMFG models, including those with LEO backhaul dynamics.