Abstract

The mean field games equations, consisting of the coupled Kolmogorov–Fokker–Planck and Hamilton–Jacobi–Bellman equations, are studied. The equations are supplemented with initial and terminal conditions. It is shown that for a certain specific choice of data this problem can be reduced to solving a quadratically nonlinear ODE system. This situation occurs naturally in economic applications. As an example, the problem of forming an investor’s opinion on an asset is considered.

中文翻译：

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关于平均场博弈论的某些解析解问题

摘要

研究了由耦合的Kolmogorov-Fokker-Planck方程和Hamilton-Jacobi-Bellman方程组成的平均场博弈方程。这些方程式补充了初始条件和终止条件。结果表明，对于某些特定的数据选择，可以将此问题简化为求解二次非线性ODE系统。这种情况在经济应用中自然会发生。例如，考虑了在资产上形成投资者意见的问题。