Large-Population LQG Games Involving a Major Player: The Nash Certainty Equivalence Principle

By Minyi Huang. SIAM Journal of Control and Optimization, 2009

370 citations recorded by the source corpus.

Subfields: Finance, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e3a92acd0eacbf994edffc2c15ee44f9fbf05aca

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Citations in the corpus

Mean field games via controlled martingale problems: Existence of Markovian equilibria (2014, background): “This stochastic approach leads to a notably clean solution of linear-quadratic mean field games, as in [4, 13], as well as an interesting generalization of mean field games involving one dominant agent competing with a mean field of minor agents [27, 8].”
Mean Field Games Models—A Brief Survey (2013, background): “Problems motivated by applications with mixed populations or with a major player were studied in [58, 59].”
Nonlinear Markov Games on a Finite State Space (Mean-field and Binary Interactions) (2012, neutral): “Related equilibrium concept was called the Nash certainty equivalence principle, see (Lasry & Lions, 2006; Achdou & Capuzzo-Dolcetta, 2010; Gomes, Mohr, & Souza, 2010; Huang, Caines, & Malhamé, 2003; Huang, Malhamé, & Caines, 2006; Huang, 2010; Kolokoltsov, Li, & Yang, 2011) and references therein.”
Mean Field Games with a Dominating Player (2014, background): “M. Huang, R.P. Malhamé and P.E. Caines.”
Existence of a solution to an equation arising from the theory of Mean Field Games (2015, methodology): “This manuscript version is made available under the Elsevier user license http://www.elsevier.com/open-access/userlicense/1.0/”
Splitting methods and short time existence for the master equations in mean field games (2020, background): “Mean field games with a major player have been first discussed by Huang in [20] and several notions of equilibria, in different contexts, have been proposed in the literature since then: see [5, 6, 7, 8, 11, 13, 14, 15, 26].”
The Master Equation and the Convergence Problem in Mean Field Games (2015, background): “In the same spirit, we may notice that the original MFG system (6) does not accommodate with mean field games with a major player and infinitely many small players, see [31].”
Linear-Quadratic Mean Field Games (2014, background): “Huang [34] considered a MFG where a major player exists which affects the state of minor agents in a linear-quadratic setting which is later generalized by Nourian and Caines into nonlinear case in [35].”