Mean field games via controlled martingale problems: Existence of Markovian equilibria
arXiv:1404.2642 · doi:10.1016/j.spa.2015.02.006
Abstract
Mean field games are studied in the framework of controlled martingale problems, and general existence theorems are proven in which the equilibrium control is Markovian. The framework is flexible enough to include degenerate volatility, which may depend on both the control and the mean field. The objectives need not be strictly convex, and the mean field interactions considered are nonlocal and Wasserstein-continuous. When the volatility is nondegenerate, continuity assumptions may be weakened considerably. The proofs first use relaxed controls to establish existence. Then, using a convexity assumption and measurable selection arguments, strict (non-relaxed) Markovian equilibria are constructed from relaxed equilibria.
References in corpus (3)
Cited by in corpus (12)
- Game-Theoretic Multiagent Reinforcement Learning
- Entropy Regularization for Mean Field Games with Learning
- Mean field games with common noise
- A general characterization of the mean field limit for stochastic differential games
- Nonsmooth mean field games with state constraints
- Approximation of N-player stochastic games with singular controls by mean field games
- Regularization of Stationary Second-order Mean Field Game Partial Differential Inclusions
- Controlled Interacting Branching Diffusion Processes: Relaxed Formulation in the Mean-Field Regime
- Controlled superprocesses and HJB equation in the space of finite measures
- Existence of optimal controls for stochastic Volterra equations
- A stochastic maximum principle for partially observed general mean-field control problems with only weak solution
- Generalized entropy minimization under full marginal constraints