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<p>Finite-population games (FPGs) provide a unified paradigm for modeling strategic interactions among anonymous players, where interactions depend on other players only through their aggregate distribution. However, as the population size increases, computing Nash equilibria of FPGs becomes computationally intractable. As the limiting framework of FPGs when the population size tends to infinity, mean field games (MFGs) constitute a viable method for tackling this challenge. This review summarizes recent progress in the study of FPGs with a focus on MFG-based theoretical connections. First, the fundamental concepts of static and dynamic FPGs are introduced. Then, attention is devoted to the construction of their MFG counterparts. This review of recent research leads to the following conclusion: The mean field equilibria of the MFGs correspond to the <i>ε</i>-symmetric Nash equilibria of the associated FPGs. Finally, to demonstrate the foundation of a physical application with MFG-based approaches, a decentralized charging/discharging mode decision problem for large-scale electric vehicles influenced by collective behaviour is taken as an illustration. It will be shown that the formulation is carried out in the fashion of a multi-valued logical system using the semi-tensor product framework.</p>

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Recent Progress in Finite-Population Games: Mean Field Game-Based Approaches

  • 期刊论文

  • 发表日期：

    2026年4月28日

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  • Yingying Chai,
  • Yuexi Zhang,
  • Wanying Guo,
  • Tielong Shen,
  • Yuhu Wu

摘要

Finite-population games (FPGs) provide a unified paradigm for modeling strategic interactions among anonymous players, where interactions depend on other players only through their aggregate distribution. However, as the population size increases, computing Nash equilibria of FPGs becomes computationally intractable. As the limiting framework of FPGs when the population size tends to infinity, mean field games (MFGs) constitute a viable method for tackling this challenge. This review summarizes recent progress in the study of FPGs with a focus on MFG-based theoretical connections. First, the fundamental concepts of static and dynamic FPGs are introduced. Then, attention is devoted to the construction of their MFG counterparts. This review of recent research leads to the following conclusion: The mean field equilibria of the MFGs correspond to the ε-symmetric Nash equilibria of the associated FPGs. Finally, to demonstrate the foundation of a physical application with MFG-based approaches, a decentralized charging/discharging mode decision problem for large-scale electric vehicles influenced by collective behaviour is taken as an illustration. It will be shown that the formulation is carried out in the fashion of a multi-valued logical system using the semi-tensor product framework.