Mean field gamesCommon noisesFBSDEsStochastic maximum principleIn this paper,the authors consider the mean field game with a common noise and allow the state coefficients to vary with the conditional distribution in a nonlinear way.They assume that the cost function satisfies a convexity and a weak...
S. Ahuja. Wellposedness of mean field games with common noise under a weak monotonicity con- dition. SIAM Journal on Control and Optimization, 54(1):30-48, 2016.Saran Ahuja, Wellposedness of Mean Field Games with Common Noise under a Weak Monotonicity Condition,SIAM J. Control Optim., 54...
A theory of existence and uniqueness is developed for general stochastic differential mean field games with common noise. The concepts of strong and weak solutions are introduced in analogy with the theory of stochastic differential equations, and existence of weak solutions for mean field games is ...
A latent Markov chain and a latent Wiener process (common noise) modulate the common process, and agents cannot observe them. We use filtering techniques coupled with a convex analysis approach to (i) solve the mean field game limit of the problem, (ii) demonstrate that the best response ...
继续接着前面的思路来讲解,当多智能体系统中智能体数目特别多时,应该如何来求解。前一个 blog 讲了 weakly coupled MDP 的一系列方法,这里来讲解另一套方法:mean-field games/MARL。 内容 这里考虑的是一个连续时间上的建模,每个智能体有着自己独立的运动学规律,然后它们合起来需要优化一个总体的目标。最后能够得...
Kolokoltsov, V. and Troeva, M. [2015], `On the mean field games with common noise and the mckean-vlasov spdes', arXiv preprint arXiv:1506.04594 .Kolokoltsov, V., Troeva, M.: On the Mean Field Games with Common Noise and the Mckean-Vlasov SPDEs. arXiv:1506.04594...
In this paper, we consider a class of linear quadratic extended mean field games (MFGs) with common noises where the state coefficients and the cost functional vary with the mean field term in a nonlinear way. Based on stochastic maximum principle, solving the mean field game is transformed in...
AppliedMathematics&Optimizationhttps://doi.org/10.1007/s00245-020-09743-7Continuous-TimeMeanFieldGameswithFiniteStateSpaceandCommonNoiseChristoph Belak 1 · Daniel Hof f mann 2 · Frank T. Seifried 2Accepted:26December2020©TheAuthor(s)2021AbstractWe formulate and analyze a mathematical framework for...
【预订】Probabilistic Theory of Mean Field Games with Applications II: Mean Field Games with Common Noise and Master Equations 预订商品,按需印刷,需要1-3个月发货,非质量问题不接受退换货。 进口好书抢先订,点击前往!出版社:Thames&Hudson 手机专享价 ¥ 当当价 降价通知 ¥2131.19 ...
Wellposedness of mean field games with common noise under a weak monotonicity condition SIAM J. Control Optim. (2016) A. Bensoussan et al. Stochastic control on space of random variables A. Bensoussan et al. Control on Hilbert spaces and application to some mean field type control problems C...