Approximation of deterministic mean field games under polynomial growth conditions on the data

IF 1.1 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Justina Gianatti, Francisco J. Silva, Ahmad Zorkot
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引用次数: 1

Abstract

We consider a deterministic mean field game problem in which a typical agent solves an optimal control problem where the dynamics is affine with respect to the control and the cost functional has a growth which is polynomial with respect to the state variable. In this framework, we construct a mean field game problem in discrete time and finite state space that approximates equilibria of the original game. Two numerical examples, solved with the fictitious play method, are presented.
数据多项式增长条件下确定性平均场博弈的逼近
我们考虑了一个确定性的平均场博弈问题,其中一个典型的智能体解决了一个最优控制问题,其中动力学是仿射的,而成本函数是一个多项式增长的状态变量。在此框架下,我们构造了一个离散时间有限状态空间的平均场博弈问题,该问题近似于原博弈的平衡点。给出了用虚拟游戏法求解的两个数值算例。
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来源期刊
Journal of Dynamics and Games
Journal of Dynamics and Games MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-
CiteScore
2.00
自引率
0.00%
发文量
26
期刊介绍: The Journal of Dynamics and Games (JDG) is a pure and applied mathematical journal that publishes high quality peer-review and expository papers in all research areas of expertise of its editors. The main focus of JDG is in the interface of Dynamical Systems and Game Theory.
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