We develop a splitting method to prove the well-posedness, in short time, of solutions for two master equations in mean field game (MFG) theory: the second order master equation, describing MFGs with a common noise, and the system of master equations associated with MFGs with a major player. Both problems are infinite-dimensional equations stated in the space of probability measures. Our new approach simplifies and generalizes previous existence results for second order master equations and provides the first existence result for systems associated with MFG problems with a major player.
Cardaliaguet, P., Cirant, M., Porretta, A. (2022). Splitting methods and short time existence for the master equations in mean field games. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 25(5), 1823-1918 [10.4171/JEMS/1227].
Splitting methods and short time existence for the master equations in mean field games
Porretta, Alessio
2022-01-01
Abstract
We develop a splitting method to prove the well-posedness, in short time, of solutions for two master equations in mean field game (MFG) theory: the second order master equation, describing MFGs with a common noise, and the system of master equations associated with MFGs with a major player. Both problems are infinite-dimensional equations stated in the space of probability measures. Our new approach simplifies and generalizes previous existence results for second order master equations and provides the first existence result for systems associated with MFG problems with a major player.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.