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Remarks on Nash equilibria in mean field game models with a major player
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-07-20 , DOI: 10.1090/proc/15135 P. Cardaliaguet , M. Cirant , A. Porretta
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-07-20 , DOI: 10.1090/proc/15135 P. Cardaliaguet , M. Cirant , A. Porretta
Abstract:For a mean field game model with a major and infinite minor players, we characterize a notion of Nash equilibrium via a system of so-called master equations, namely a system of nonlinear transport equations in the space of measures. Then, for games with a finite number 
of minor players and a major player, we prove that the solution of the corresponding Nash system converges to the solution of the system of master equations as 
tends to infinity.
中文翻译：
关于具有主要参与者的均值野外游戏模型中的纳什均衡的评论
摘要：对于具有主要参与者和无限次要参与者的均值博弈模型，我们通过所谓的主方程组（即度量空间中的非线性传输方程组）来刻画纳什均衡的概念。然后，对于具有有限数量的次要参与者和主要参与者的游戏，我们证明了相应的Nash系统的解趋于无穷大而收敛到主方程组的解。
更新日期：2020-08-20
of minor players and a major player, we prove that the solution of the corresponding Nash system converges to the solution of the system of master equations as tends to infinity. 中文翻译：
关于具有主要参与者的均值野外游戏模型中的纳什均衡的评论
摘要：对于具有主要参与者和无限次要参与者的均值博弈模型，我们通过所谓的主方程组（即度量空间中的非线性传输方程组）来刻画纳什均衡的概念。然后，对于具有有限数量
的次要参与者和主要参与者的游戏，我们证明了相应的Nash系统的解趋于无穷大而收敛到主方程组的解。
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