平均场博弈论(Mean-field Games)简介 (Mean-Field Games)研究的是大量对象之间的博弈,探索在一个竞争的环境中,对象如何选择最优的决策。例如股市里大量根据其他用户行为交易股票的股民,海里游动的鱼群,在世界杯现场看足球赛的观众等。目前,平均场博弈论在经济、金融、机器学习等方面都有应用。那什么是平均场呢?平...
平均场博弈(mean field game) The New Big Fish Called Mean-Field Game Theory 原文链接 http://www.science4all.org/article/mean-field-games/www.science4all.org/article/mean-field-games/ 主要内容 在经典博弈论中,它对附近其他鱼类的行为做出反应。这是非常复杂的,因为不同的鱼类之间会有大量的相互...
Mean-Field Game Theory，被称为新的博弈论大鱼 原文链接 在经典博弈论中，鱼类的行为是对附近其他鱼类的反应。这非常复杂，因为不同的鱼类之间会有大量的相互作用。这意味着经典博弈论对应于一长串高度耦合的方程。如果你不明白我的意思，别担心。本质上，我的观点是，经典博弈论模型几乎不可能用3条鱼...
[27]. However, note that in this case, the mean field game is not potential, which we formally prove in Section 2.5. Thus, the conjecture from the previous paragraph must not be taken too naïvely, as it is clearly false if interpreted too broadly. Monderer and Shapley also prove that...
MeanFieldGames Jean-MichelLASRY (∗)1 Pierre-LouisLIONS (∗)2 (∗) workpartiallysupportedbythechair“Financeandsustainabledevelopment” Abstract:Wesurveyheresomerecentstudiesconcerningwhatwecallmean-fieldmodelsby analogywithStatisticalMechanicsandPhysics.Moreprecisely,wepresentthreeexamplesof...
Mean field games with state constraints: from mild to pointwise solutions of the PDE system. Calc. Var. Partial Differential Equations, 60(3):Paper No. 108, 33, 2021. P. Cannarsa and C. Mendico. Mild and weak solutions of mean field game problems for linear control systems. Minimax ...
The model developed is a mean field game model, which allows for heterogeneity in the productivity of a firm and allows for a novel approach to describing sector-level spillovers. The model is constructed from a network of interacting firms, whose connections represent knowledge transfers. We ...
mean field game; paradigm shift; research dynamics; scientific choice; C61; O39 ABSTRACT This paper analyses the consequences of young researchers' scientific choice on the dynamics of sciences. We develop a simple two state mean field game model to analyse the competition between two paradigms bas...
Mean field games: numerical methods SIAM J. Numer. Anal. (2010) CarliniE. et al. A semi-Lagrangian scheme for a degenerate second order mean field game system Discrete Contin. Dyn. Syst. (2015) CarliniE. et al. On the discretization of some nonlinear Fokker-Planck-Kolmogorov equations and...
Gomes, D.A., Pimentel, E.A., Voskanyan, V.: Regularity Theory for Mean-field Game Systems. SpringerBriefs in Mathematics. Springer, Berlin (2016) Book Google Scholar Gomes, D.A., Pimentel, E., Sánchez-Morgado, H.: Time-dependent mean-field games in the superquadratic case. ESAIM Co...