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C. Higuera-Chan, J. Minjárez‐Sosa (2021)
A Mean Field Approach for Discounted Zero-Sum Games in a Class of Systems of Interacting ObjectsDynamic Games and Applications, 11
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[We deal with a class of discrete-time stochastic controlled systems composed by a large population of N interacting individuals. Given that N is large and the cost function is possibly unbounded, the problem is studied by means of a limit model ℳ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal {M}$$ \end{document}, known as the mean field model, which is obtained as limit as N →∞ of the model ℳN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal {M}_N$$ \end{document} corresponding to the system of N individuals in combination with an approximate algorithm for the cost function.]
Published: Aug 5, 2021
Keywords: Systems of interacting individuals; Mean field theory; Approximation algorithm; Discounted criterion
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