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<p>This work deals with a class of discrete-time mean-field games evolving according to a stochastic difference equation where the random disturbance distribution <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="245_2025_10273_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\theta \)</EquationSource> </InlineEquation> is unknown or difficult to handle. The mean-field game is defined on Borel spaces and it is assumed possibly unbounded costs. Then, by combining suitable statistical estimation process of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="245_2025_10273_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\theta \)</EquationSource> </InlineEquation> with the mean-field games theory, we introduce approximation procedures for the mean-field equilibrium under a discounted optimality criterion.</p>

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Statistical Estimation of Mean-Field Equilibria in a Class of Discounted Mean-Field Games

  • 期刊论文

  • 发表日期：

    2025年6月4日

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  • E. Everardo Martinez-Garcia,
  • Fernando Luque-Vásquez,
  • J. Adolfo Minjárez-Sosa

摘要

This work deals with a class of discrete-time mean-field games evolving according to a stochastic difference equation where the random disturbance distribution \(\theta \) is unknown or difficult to handle. The mean-field game is defined on Borel spaces and it is assumed possibly unbounded costs. Then, by combining suitable statistical estimation process of \(\theta \) with the mean-field games theory, we introduce approximation procedures for the mean-field equilibrium under a discounted optimality criterion.