Convergence of Large Population Games to Mean Field Games with Interaction Through the Controls
Convergence of Large Population Games to Mean Field Games with Interaction Through the Controls
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DOI：
10.1137/22m1469328
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发表时间：
2020-04
期刊：
影响因子：
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通讯作者：
M. Laurière;Ludovic Tangpi
中科院分区：
文献类型：
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作者：
M. Laurière;Ludovic Tangpi
这项工作考虑了随机微分博弈与大量的球员，其成本和动态相互作用，通过经验分布的状态和控制。我们开发了一个框架来证明收敛的有限玩家游戏的渐近平均场游戏。我们的方法是基于向前和向后弱相互作用粒子的混沌传播的概念，我们调查完全概率的方法，这似乎是独立的利益。这些传播的混沌参数允许获得的时刻和浓度范围的收敛纳什均衡和社会最优的非合作和合作游戏，分别。顺便说一句，我们还获得了有限维空间上的二阶抛物型偏微分方程系统的收敛到Wasserstein空间上的二阶抛物型偏微分方程。
This work considers stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. We develop a framework to prove convergence of finite-player games to the asymptotic mean field game. Our approach is based on the concept of propagation of chaos for forward and backward weakly interacting particles which we investigate by fully probabilistic methods, and which appear to be of independent interest. These propagation of chaos arguments allow to derive moment and concentration bounds for the convergence of both Nash equilibria and social optima in non-cooperative and cooperative games, respectively. Incidentally, we also obtain convergence of a system of second order parabolic partial differential equations on finite dimensional spaces to a second order parabolic partial differential equation on the Wasserstein space.