Mean Field Game systems describe equilibrium configurations in differential
games with infinitely many infinitesimal interacting agents. We introduce a
learning procedure (similar to the Fictitious Play) for these games and show
its convergence when the Mean Field Game is potential.

本文介绍了一种类似于虚构判断游戏的学习过程用于求解 Mean Field Game 系统，并证明了该方法在 Mean Field Game 系统为 potential 时的收敛性。

均场博弈中的学习：虚假博弈

Learning in Mean Field Games: the Fictitious Play

It has recently been shown that the Helmholtz free energy difference between
two equilibrium configurations of a system may be obtained from an ensemble of
finite-time (nonequilibrium) measurements of the work performed in switching an
external parameter of the system. Here this result is established, as an
identity, within the master equation formalism. Examples are discussed and
numerical illustrations provided.

该论文应用主方程式的形式建立了一个等式，以固定的时间段（非平衡态）的工作量测量来获得系统两个平衡构型之间的 Helmholtz 自由能差值，并提供了例证和数值说明。