A probabilistic weak formulation of mean field games and applications

Abstract

Mean field games are studied by means of the weak formulation of stochastic optimal control. This approach allows the mean field interactions to enter through both state and control processes and take a form which is general enough to include rank and nearest-neighbor effects. Moreover, the data may depend discontinuously on the state variable, and more generally its entire history. Existence and uniqueness results are proven, along with a procedure for identifying and constructing distributed strategies which provide approximate Nash equlibria for finite-player games. Our results are applied to a new class of multi-agent price impact models and a class of flocking models for which we prove existence of equilibria.

References in corpus (4)

• Novel type of phase transition in a system of self-driven particles
• Interaction Ruling Animal Collective Behaviour Depends on Topological rather than Metric Distance: Evidence from a Field Study
• Extended deterministic mean-field games
• Forward-Backward Stochastic Differential Equations and Controlled McKean Vlasov Dynamics

Cited by in corpus (29)

• Game-Theoretic Multiagent Reinforcement Learning
• Mean field games via controlled martingale problems: Existence of Markovian equilibria
• On the connection between symmetric $N$-player games and mean field games
• Mean field game model of corruption
• Mean-field-game model for Botnet defense in Cyber-security
• On the mean field games with common noise and the McKean-Vlasov SPDEs
• Discrete Mean Field Games: Existence of Equilibria and Convergence
• On Solutions of Mean Field Games with Ergodic Cost
• Systemic Risk and Interbank Lending
• Large population games with interactions through controls and common noise: convergence results and equivalence between $open$--$loop$ and $closed$--$loop$ controls
• On finite population games of optimal trading
• Existence and Regularity of Solutions to Multi-Dimensional Mean-Field Stochastic Differential Equations with Irregular Drift
• A general characterization of the mean field limit for stochastic differential games
• Connecting GANs, MFGs, and OT
• Systemic Risk and Heterogeneous Mean Field Type Interbank Network
• A Probabilistic Approach to Extended Finite State Mean Field Games
• The Dyson and Coulomb games
• Exploration noise for learning linear-quadratic mean field games
• Nonsmooth mean field games with state constraints
• Extended Mean Field Games with Singular Controls
• Strong Solutions of Mean-Field SDEs with irregular expectation functional in the drift
• Deep Learning for Mean Field Games and Mean Field Control with Applications to Finance
• Probabilistic Approach to Mean Field Games and Mean Field Type Control Problems with Multiple Populations
• Conditional Expectation of Banach Valued Correspondences
• Generalized conditional gradient and learning in potential mean field games
• Robust Mean Field Linear-Quadratic-Gaussian Games with Unknown $L^2$-Disturbance
• Mean Field Contest with Singularity
• Multi-agent interaction and nonlinear Markov games
• A unified approach to mean-field team: homogeneity, heterogeneity and quasi-exchangeability