Splitting methods and short time existence for the master equations in mean field games

DOI10.4171/jems/1227zbMath1522.35511arXiv2001.10406OpenAlexW3003914912MaRDI QIDQ6172669

Marco Cirant, Alessio Porretta, Pierre Cardaliaguet

Publication date: 20 July 2023

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.10406

zbMATH Keywords

master equationmean field gamesMFG with major player contents

Mathematics Subject Classification ID

Differential games and control (49N70) Nonlinear parabolic equations (35K55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) PDEs with measure (35R06) PDEs in connection with mean field game theory (35Q89)

Related Items

Well-posedness of mean field games master equations involving non-separable local Hamiltonians, Density of subalgebras of Lipschitz functions in metric Sobolev spaces and applications to Wasserstein Sobolev spaces, Minimal solutions of master equations for extended mean field games, The Convergence Problem in Mean Field Games with Neumann Boundary Conditions, Remarks on Nash equilibria in mean field game models with a major player

Cites Work

• Unnamed Item
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• A probabilistic approach to mean field games with major and minor players
• Mean field games with a dominating player
• Existence of a solution to an equation arising from the theory of mean field games
• Mean field games with common noise
• Mean field games. I: The stationary case
• Mean field games. II: Finite horizon and optimal control
• Mean field games
• Analysis and geometry on configuration spaces
• Mass transportation problems. Vol. 1: Theory. Vol. 2: Applications
• Mean-field games with a major player
• An alternative approach to mean field game with major and minor players, and applications to herders impacts
• Short time solution to the master equation of a first order mean field game
• Translation invariant mean field games with common noise
• Large-Population LQG Games Involving a Major Player: The Nash Certainty Equivalence Principle
• Wellposedness of Mean Field Games with Common Noise under a Weak Monotonicity Condition
• The Master Equation and the Convergence Problem in Mean Field Games
• Remarks on Nash equilibria in mean field game models with a major player
• Probabilistic Theory of Mean Field Games with Applications I
• The Master Equation for Large Population Equilibriums
• Nonlinear Stochastic Differential Games Involving a Major Player and a Large Number of Collectively Acting Minor Agents
• Mean Field Stackelberg Games: Aggregation of Delayed Instructions
• Optimal Transport