A system of two coupled nonlinear parabolic partial differential equations with two opposite directions of time is considered. In fact, this is the so-called "Mean Field Games System" (MFGS), which is derived in the mean field games (MFG) theory. This theory has numerous applications in social sciences. The topic of Coefficient Inverse Problems (CIPs) in the MFG theory is in its infant age, both in theory and computations. A numerical method for this CIP is developed. Convergence analysis ensures the global convergence of this method. Numerical experiments are presented.

翻译：考虑具有两个相反时间方向的耦合非线性抛物型偏微分方程组。事实上，这就是所谓的“平均场博弈系统”（MFGS），它源于平均场博弈（MFG）理论。该理论在社会科学中具有广泛应用。平均场博弈理论中的系数反问题（CIPs）无论是理论研究还是数值计算均处于初级阶段。本文针对该系数反问题发展了一种数值方法。收敛性分析保证了该方法的全局收敛性。最后给出了数值实验结果。