From infinity to one: The reduction of some mean field games to a global control problem
From infinity to one: The reduction of some mean field games to a global control problem
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从无穷大到一：将一些平均场博弈简化为全局控制问题
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发表时间：
2011
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通讯作者：
Olivier Guéant
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作者：
Olivier Guéant
本文介绍了平均场博弈论的最新结果，该结果基于引入公共噪声，强加于将代理的分布合并为状态变量。从[11,12,13]中引入的通常的平均场博弈方程开始，并将其应用于图上的博弈，我们引入一个偏微分方程，通常被称为主方程（见[14]），从中可以推导出MFG方程。然后，这个主方程可以用一个全局控制问题来重新解释，该问题与非合作初始平均场博弈中的行为相同。
This paper presents recent results from Mean Field Game theory underlying the introduction of common noise that imposes to incorporate the distribution of the agents as a state variable. Starting from the usual mean field games equations introduced in [11 , 12 , 13 ] and adapting them to games on graphs, we introduce a partial differential equation, often referred to as the Master equation (see [14]), from which the MFG equations can be deduced. Then, this Master equation can be reinterpreted using a global control problem inducing the same behaviors as in the non-cooperative initial mean field game.