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The Second-Order Master Equation

This chapter investigates the second-order master equation with common noise, which requires the well-posedness of the mean field game (MFG) system. It also defines and analyzes the solution of the master equation. The chapter explains the forward component of the MFG system that is recognized as the characteristics of the master equation. The regularity of the solution of the master equation is explored through the tangent process that solves the linearized MFG system. It also analyzes first-order differentiability and second-order differentiability in the direction of the measure on the same model as for the first-order derivatives. This chapter concludes with further description of the derivation of the master equation and well-posedness of the stochastic MFG system.

Princeton University Press

Pierre Cardaliaguet François Delarue Jean-Michel Lasry Pierre-Louis Lions

The Master Equation and the Convergence Problem in Mean Field Games

2020

Title: The Second-Order Master Equation

Description:

This chapter investigates the second-order master equation with common noise, which requires the well-posedness of the mean field game (MFG) system.

It also defines and analyzes the solution of the master equation.

The chapter explains the forward component of the MFG system that is recognized as the characteristics of the master equation.

The regularity of the solution of the master equation is explored through the tangent process that solves the linearized MFG system.

It also analyzes first-order differentiability and second-order differentiability in the direction of the measure on the same model as for the first-order derivatives.

This chapter concludes with further description of the derivation of the master equation and well-posedness of the stochastic MFG system.

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The Second-Order Master Equation

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