Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle

By Peter E. Caines, Minyi Huang, Roland P. Malhamé. 2006

1,911 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Economics and Econometrics, Statistical and Nonlinear Physics

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Citations in the corpus

Mean Field Multi-Agent Reinforcement Learning (2018, background): “ine which actions are benecial or not, as we have demonstrated from one of our experiments. Our work is also closely related to the recent development of mean eld game (MFG) (Lasry & Lions, 2007; Huang et al., 2006; Weintraub et al., 2006). MFG studies population behaviors resulting from the agg”
Mean Field Games (2020, background): “The original works by Lasry and Lions give a certain number of conditions under which equation (1) has a solution, discuss its uniqueness and its stability (see also Huang-Caines-Malhamé [32, 33, 34, 35]).”
Finite Mean Field Games: Fictitious play and convergence to a first order continuous mean field game (2018, background): “1 Introduction Mean Field Games (MFGs) were introduced by Lasry and Lions in [21, 22, 23] and, independently, by Huang, Caines and Malhamé in [20].”
A Maximum Principle for SDEs of Mean-Field Type (2011, methodology): “Due to time inconsistency of the control problem, [ 9 ] and [4] need to specify a definition of admissible controls that involves the Nash Certainty Equivalent Principle and the notion of Nash Equilibrium, respectively, to turn the problem into a time consistent one and solve it using Bellman’s dyna”
Hierarchies, entropy, and quantitative propagation of chaos for mean field diffusions (2021, background): “This short introduction can hardly do justice to the vast literature, but we mention two notable and active recent directions beyond those discussed in [74, 35]: McKean-Vlasov models feature prominently in recent work on neural networks, as scaling limits of stochastic gradient descent algorithms [5”
Optimal control of path-dependent McKean–Vlasov SDEs in infinite-dimension (2020, background): “The control of such equations has attracted an increasing interest since the emergence of mean-field game theory initiated independently in [40] and [37], aiming at describing control of large systems or population of interacting particles, and has generated over the last few years numerous contribu”
Existence of a solution to an equation arising from the theory of Mean Field Games (2015, methodology): “Similar ideas were independently introduced at the same time and studied in the engineering literature by Huang–Caines–Malhamé [36, 37, 38, 40].”
The Master Equation and the Convergence Problem in Mean Field Games (2015, background): “Since its simultaneous introduction by Lasry and Lions [50] and by Huang, Caines and Malhamé [32], this system has been thoroughly investigated: existence, under various assumptions, can be found in [11, 17, 33, 34, 35, 40, 50, 52].”
A probabilistic weak formulation of mean field games and applications (2013, background): “ch depend on the rank (Example 5.9 in Section 5), or on the mean ﬁeld of the individual’s nearest neighbors (Section 2.2). Our framework also includes models with diﬀerent types of agents, similar to [25]. Moreover, fdoes not need to be strictly convex, and may in fact be identically zero. A ﬁnal no”
A general characterization of the mean field limit for stochastic differential games (2014, methodology): “M. Huang, R. Malhamé, and P. Caines, Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle, Communications in Information and Systems 6 (2006), no. 3, 221–252.”
Weak Solutions to Fokker–Planck Equations and Mean Field Games (2015, methodology): “The theory of mean field games, initiated by Lasry and Lions [27–29] and, simultaneously, by Huang, Caines andMalamhé [24], leads to the study of systems of PDEs where a backward viscous Hamilton–Jacobi equation is coupled with a forward Fokker–Planck equation.”
Bellman equation and viscosity solutions for mean-field stochastic control problem (2015, positive): “This topic is closely related to the mean-ﬁeld game (MFG) problem as originally formulated by Lasry and Lions in [27] and simultaneously by Huang, Caines and Malham´e in [24].”
Mean field and n‐agent games for optimal investment under relative performance criteria (2017, methodology): “Moreover, the manner in which we incorporate different types of agents, by randomizing ζ = (ξ, δ, θ, μ, ν, σ) as described above, seems to be novel; several works on MFGs have incorporated finitely many types [25] by tracking a vector of mean field interactions, one for each type, but our approach h”
Smoothing properties of McKean–Vlasov SDEs (2017, background): “As MVSDEs can be interpreted as limiting equations for large systems, they are widely used as models in statistical physics [7, 31] as well as in the study of large-scale social interactions within the theory of mean-field games [26, 27, 28, 19, 20, 10, 11].”
McKean–Vlasov optimal control: The dynamic programming principle (2019, background): “Though many authors have worked on this equation following these initial papers, there has been a drastic surge of interest in the topic in the past decade, due to the connection that it shares with the so–called mean–field game (MFG for short) theory, introduced independently and simultaneously on ”