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A probabilistic approach to mean field games with major and minor players
16 references·16 citing·29 second hopsampled
A probabilistic approach to mean field games with major and minor players (2016)A probabilistic approach to mean field ga…On well-posedness of forward–backward SDEs—A unified approach (2015)On well-posedness of forward–…Mean Field Games and systemic risk (2015)Mean Field Games and systemic…Forward–backward stochastic differential equations and controlled McKean–Vlasov dynamics (2015)Forward–backward stochastic d…A probabilistic weak formulation of mean field games and applications (2015)A probabilistic weak formulat…Probabilistic Analysis of Mean-Field Games (2013)Probabilistic Analysis of Mea…Mean field forward-backward stochastic differential equations (2013)Mean field forward-backward s…$\epsilon$-Nash Mean Field Game Theory for Nonlinear Stochastic Dynamical Systems with Major and Minor Agents (2013)$\epsilon$-Nash Mean Field Ga…Control of McKean–Vlasov dynamics versus mean field games (2012)Control of McKean–Vlasov dyna…Large-Population LQG Games Involving a Major Player: The Nash Certainty Equivalence Principle (2010)Large-Population LQG Games In…Mean field games (2007)Mean field gamesForward-Backward Stochastic Differential Equations and their Applications (2007)Forward-Backward Stochastic D…Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle (2006)Large population stochastic d…Jeux à champ moyen. II – Horizon fini et contrôle optimal (2006)Jeux à champ moyen. II – Hori…Jeux à champ moyen. I – Le cas stationnaire (2006)Jeux à champ moyen. I – Le ca…On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case (2002)On the existence and uniquene…Stochastic controls : Hamiltonian systems and HJB equations (1999)Stochastic controls : Hamilto…McKean–Vlasov optimal control: The dynamic programming principle (2022)McKean–Vlasov optimal control…Mean-Field Leader-Follower Games with Terminal State Constraint (2020)Mean-Field Leader-Follower Ga…From the master equation to mean field game limit theory: Large deviations and concentration of measure (2020)From the master equation to m…An Introduction to Mean Field Game Theory (2020)An Introduction to Mean Field…Quadratic mean field games (2019)Quadratic mean field gamesLinear Quadratic Mean Field Games: Asymptotic Solvability and Relation to the Fixed Point Approach (2019)Linear Quadratic Mean Field G…Linear quadratic mean field games with a major player: The multi-scale approach (2019)Linear quadratic mean field g…From the master equation to mean field game limit theory: a central limit theorem (2019)From the master equation to m…Linear-Quadratic-Gaussian Mixed Mean-Field Games with Heterogeneous Input Constraints (2018)Linear-Quadratic-Gaussian Mix…Convergence, fluctuations and large deviations for finite state mean field games via the Master Equation (2018)Convergence, fluctuations and…A Mean Field Game of Optimal Portfolio Liquidation * (2018)A Mean Field Game of Optimal …Mean Field Games (2017)Mean Field GamesMean Field Games with Singular Controls (2017)Mean Field Games with Singula…An Alternative Approach to Mean Field Game with Major and Minor Players, and Applications to Herders Impacts (2017)An Alternative Approach to Me…A mean-field stochastic control problem with partial observations (2017)A mean-field stochastic contr…Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications (2016)Linear quadratic optimal cont…Adapted solution of a backward stochastic differential equation (1990)The Master Equation and the Convergence Problem in Mean Field Games (2019)Large-Population Cost-Coupled LQG Problems With Nonuniform Agents: Individual-Mass Behavior and Decentralized $\varepsilon$-Nash Equilibria (2007)Mean Field Games Models—A Brief Survey (2013)Dynamic Noncooperative Game Theory (1982)Evolution and the Theory of Games (1988)Social Optima in Mean Field LQG Control: Centralized and Decentralized Strategies (2012)Linear-Quadratic Mean Field Games (2015)Theory of games and economic behavior (2019)The Malliavin Calculus and Related Topics (1995)Second‐order backward stochastic differential equations and fully nonlinear parabolic PDEs (2006)The Malliavin Calculus and Related Topics (2006)Brownian Motion and Stochastic Calculus (2007)The Theory of Learning in Games (1998)Games with Incomplete Information Played by “Bayesian” Players, I–III: Part I. The Basic Model (2004)A Maximum Principle for SDEs of Mean-Field Type (2010)Linear-Quadratic Optimal Control Problems for Mean-Field Stochastic Differential Equations (2013)Markets with a Continuum of Traders (1964)Mean Field Games and Applications (2010)The Pricing of Options and Corporate Liabilities (1973)Theory of Rational Option Pricing (1973)Continuous Auctions and Insider Trading (1985)Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach (2021)Continuous-Time Mean-Variance Portfolio Selection: A Stochastic LQ Framework (2000)G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Itô Type (2007)Nonlinear Expectations and Stochastic Calculus under Uncertainty (2019)A numerical scheme for BSDEs (2004)Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations (2004)Stochastic Differential Equations (2014)
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References

  • 2007Mean field games2,638 cited
  • 1999Stochastic controls : Hamiltonian systems and HJB equations1,780 cited
  • 2006Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle1,574 cited
  • 2006Jeux à champ moyen. I – Le cas stationnaire965 cited
  • 2006Jeux à champ moyen. II – Horizon fini et contrôle optimal810 cited
  • 2007Forward-Backward Stochastic Differential Equations and their Applications675 cited
  • 2013Probabilistic Analysis of Mean-Field Games435 cited
  • 2010Large-Population LQG Games Involving a Major Player: The Nash Certainty Equivalence Principle326 cited
  • 2002On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case267 cited
  • 2015Forward–backward stochastic differential equations and controlled McKean–Vlasov dynamics244 cited
  • 2015Mean Field Games and systemic risk244 cited
  • 2012Control of McKean–Vlasov dynamics versus mean field games238 cited
  • 2013$\epsilon$-Nash Mean Field Game Theory for Nonlinear Stochastic Dynamical Systems with Major and Minor Agents188 cited
  • 2015A probabilistic weak formulation of mean field games and applications178 cited
  • 2015On well-posedness of forward–backward SDEs—A unified approach

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151 cited
  • 2013Mean field forward-backward stochastic differential equations124 cited
  • Cited by

    • 2017Mean Field Games107 cited
    • 2019From the master equation to mean field game limit theory: a central limit theorem84 cited
    • 2019Linear Quadratic Mean Field Games: Asymptotic Solvability and Relation to the Fixed Point Approach72 cited
    • 2022McKean–Vlasov optimal control: The dynamic programming principle67 cited
    • 2020An Introduction to Mean Field Game Theory67 cited
    • 2016Linear quadratic optimal control of conditional McKean-Vlasov equation with random coefficients and applications62 cited
    • 2017A mean-field stochastic control problem with partial observations59 cited
    • 2018Linear-Quadratic-Gaussian Mixed Mean-Field Games with Heterogeneous Input Constraints57 cited
    • 2020From the master equation to mean field game limit theory: Large deviations and concentration of measure57 cited
    • 2018Convergence, fluctuations and large deviations for finite state mean field games via the Master Equation56 cited
    • 2019Quadratic mean field games41 cited
    • 2018A Mean Field Game of Optimal Portfolio Liquidation *41 cited
    • 2017Mean Field Games with Singular Controls39 cited
    • 2017An Alternative Approach to Mean Field Game with Major and Minor Players, and Applications to Herders Impacts35 cited
    • 2019Linear quadratic mean field games with a major player: The multi-scale approach34 cited
    • 2020Mean-Field Leader-Follower Games with Terminal State Constraint32 cited