Fetching the paper…

Reading the bibliography…

2022

Mean Field Game Master Equations with Anti-monotonicity Conditions

Mou, Chenchen, Zhang, Jianfeng

Original
PDF
Post on X

Understand

It is well known that the monotonicity condition, either in Lasry-Lions sense or in displacement sense, is crucial for the global well-posedness of mean field game master equations, as well as for the uniqueness of mean field equilibria and solutions to mean field game systems.

In the literature, the monotonicity conditions are always taken in a fixed direction.
In this paper we propose a new type of monotonicity condition in the opposite direction, which we call the anti-monotonicity condition, and establish the global well-posedness for mean field game master equations with nonseparable Hamiltonians.
Our anti-monotonicity condition allows our data to violate both the Lasry-Lions monotonicity and the displacement monotonicity conditions.

Mean Field Game Master Equations with Anti-monotonicity Conditions · Around

Built on

Bensoussan, A., Graber, P.J. and Yam, S. C. P., Stochastic control on space of random variables, preprint, arXiv:1903.12602
Original
1903
Earlier work this paper cites.
Mou, C. and Zhang, J., Wellposedness of second order master equations for mean field games with nonsmooth data, accepted in Mem. Amer. Math. Soc
Original
1903
Earlier work this paper cites.
Cardaliaguet, P., Cirant M. and Porretta, A., Splitting methods and short time existence for the master equations in mean field games, accepted in J. Eur. Math. Soc
Original
2001
Earlier work this paper cites.
Gangbo, W. and Mészáros, A.R., Global well-posedness of master equations for deterministic displacement convex potential mean field games, accepted in Comm. Pures Appl. Math
Original
2004
Earlier work this paper cites.
Bensoussan, A., Graber, P.J. and Yam, S. C. P., Control on Hilbert spaces and application to mean field type control theory, preprint, arXiv:2005.10770
Original
2005
Earlier work this paper cites.
Cecchin A. and Delarue, F., Selection by vanishing common noise for potential finite state mean field games, accepted in Commun. Partial Differ. Equ
2005
Earlier work this paper cites.
Caines, P. E., Huang, M. and Malhamé, R. P., Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle, Commun. Inf. Syst
2006
Earlier work this paper cites.
Lasry, J.-M. and Lions, P.-L., Mean field games, Jpn. J. Math
2007
Earlier work this paper cites.
Cardaliaguet, P., Notes on mean field games
2010
Earlier work this paper cites.
Bayraktar, E., Cecchin, A., Cohen, A. and Delarue, F., Finite state mean field games with Wright-Fisher common noise as limits of N N -player weighted games, accepted in Math. Oper. Res
Original
2012
Earlier work this paper cites.
Bensoussan, A., Frehse, J., and Yam, S. C. P., Mean Field Games and Mean Field Type Control Theory
2013
Earlier work this paper cites.
Gangbo, W. and Swiech, A., Existence of a solution to an equation arising from the theory of mean field games, J. Differential Equations
2015
Earlier work this paper cites.
Ahuja, S., Wellposedness of mean field games with common noise under a weak monotonicity condition, SIAM J. Control Optim
2016
Earlier work this paper cites.

Similar

Lacker, D., A general characterization of the mean field limit for stochastic differential games, Probab. Theory Relat. Fields
2016
Cited alongside, same era.
Buckdahn, R., Li, J., Peng, S. and Rainer, C., Mean-field stochastic differential equations and associated PDEs, Ann. Probab
2017
Cited alongside, same era.
Lacker, D., Limit theory for controlled McKean-Vlasov dynamics, SIAM J. Control Optim
2017
Cited alongside, same era.
Bayraktar, E. and Cohen, A., Analysis of a finite state many player using its master equation, SIAM J. Control Optim
2018
Cited alongside, same era.
Carmona, R. and Delarue, F., Probabilistic theory of mean field games with applications I - Mean field FBSDEs, control, and games
2018
Cited alongside, same era.

Then

Cecchin A., Dai Pra P., Fischer M. and Pelino G., On the convergence problem in mean field games: a two state model without uniqueness, SIAM J. Control Optim
2019
Later among the works it cites.
Delarue, F., Lacker, D. and Ramanan, K., From the master equation to mean field game limit theory: A central limit theorem, Electron. J. Probab
2019
Later among the works it cites.
Bayraktar, E. and Zhang, X., On non-uniqueness in mean field games, Proc. Amer. Math. Soc
2020
Later among the works it cites.
Cardaliaguet, P. and Porretta, A., An introduction to mean field game theory
2020
Later among the works it cites.
Delarue, F. and Foguen Tchuendom, R., Selection of equilibria in a linear quadratic mean-field game. Stochastic Process. Appl
2020
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Carmona, R. and Delarue, F., Probabilistic theory of mean field games with applications II - Mean field games with common noise and master equations

2018

Cited alongside, same era.

Foguen Tchuendom, R., Uniqueness for linear-quardratic mean field games with common noise, Dyn. Games Appl

2018

Cited alongside, same era.

Lacker, D., On a strong form of propagation of chaos for McKean-Vlasov equations, Electron. Commun. Probab

2018

Cited alongside, same era.

Ahuja, S., Ren, W., and Yang, T.-W., Forward-backward stochastic differential equations with monotone functionals and mean field games with common noise, Stoch. Proc. Appl

2019

Cited alongside, same era.

Bensoussan, A. and Yam, S. C. P., Control problem on space of random variables and master equation, ESAIM Control Optim. Calc. Var

2019

Cited alongside, same era.

Bertucci, C., Lasry, J.M. and Lions, P.L., Some remarks on mean field games, Comm. Partial Differential Equations

2019

Cited alongside, same era.

Cardaliaguet, P., Delarue, F., Lasry, J.M. and Lions, P.L., The master equation and the convergence problem in mean field games

2019

Cited alongside, same era.

Delarue, F., Lacker, D. and Ramanan, K., From the master equation to mean field game limit theory: Large deviations and concentration of measure, Ann. Probab

2020

Later among the works it cites.

Lacker, D., On the convergence of closed-loop Nash equilibria to the mean field game limit, Ann. Appl. Probab

2020

Later among the works it cites.

Mayorga, S., Short time solution to the master equation of a first order mean field game system, J. Differential Equations

2020

Later among the works it cites.

Nutz, M., San Martin, J. and Tan, X., Convergence to the mean field game limit: a case study, Ann. Appl. Probab

2020

Later among the works it cites.

Bayraktar, E., Cecchin, A., Cohen, A. and Delarue, F., Finite state mean field games with Wright-Fisher common noise, J. Math. Pures et Appliquées

2021

Later among the works it cites.

Bertucci, C., Monotone solutions for mean field games master equations: finite state space and optimal stopping, J. Éc. polytech. Math

2021

Later among the works it cites.

Gangbo, W., Mészáros, A.R., Mou, C. and Zhang, J., Mean field games master equations with non-separable Hamiltonians and displacement monotonicity, Ann. Probab

2022

Closest in time.