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This chapter covers foundations of mean-field-type games in discrete time with scalar states via illustrative variance-aware examples. We start with linear-quadratic discrete-time mean-field games in Sect. 14.1. Section 14.1.2 collects several results on discrete-time risk-neutral linear-quadratic mean-field games. In Sect. 14.1.3, we formulate risk-sensitive discrete-time game problem, carefully explaining the difference between risk-sensitive and risk-neutral Riccati equations. Section 14.1.4 is devoted to the study of robust mean-field difference games. Section 14.1.5 focuses on social optima of linear-quadratic mean-field difference games using mean-field-type control.

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Difference Games of Mean-Field Type

  • 章节

  • 发表日期：

    2026年

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  • Tamer Başar,
  • Boualem Djehiche,
  • Hamidou Tembine

摘要

This chapter covers foundations of mean-field-type games in discrete time with scalar states via illustrative variance-aware examples. We start with linear-quadratic discrete-time mean-field games in Sect. 14.1. Section 14.1.2 collects several results on discrete-time risk-neutral linear-quadratic mean-field games. In Sect. 14.1.3, we formulate risk-sensitive discrete-time game problem, carefully explaining the difference between risk-sensitive and risk-neutral Riccati equations. Section 14.1.4 is devoted to the study of robust mean-field difference games. Section 14.1.5 focuses on social optima of linear-quadratic mean-field difference games using mean-field-type control.