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In Sect. 2.6.14 , a mean-field game problem with an infinite number of players was introduced. The mean-field term which was a population mean-field (distribution of states of all other players) was not affected by a single agent’s individual state. This chapter examines the case where an individual state of a player may affect a mean-field term: The probability distribution of own-state appears in the dynamics and/or the payoff functional. This is a continuation of the formulation in Chap. 1 where the expected payoff is nonlinear in the measure \(P_{x_{t+1}}.\) We analyze the existence of optimal strategies in games associated with payoff functionals of mean-field type, under a dynamics driven by a class of Markov chains of mean-field type.

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Mean-Field-Type Games With Discrete State Spaces

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  • 发表日期：

    2026年

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  • Tamer Başar,
  • Boualem Djehiche,
  • Hamidou Tembine

摘要

In Sect. 2.6.14 , a mean-field game problem with an infinite number of players was introduced. The mean-field term which was a population mean-field (distribution of states of all other players) was not affected by a single agent’s individual state. This chapter examines the case where an individual state of a player may affect a mean-field term: The probability distribution of own-state appears in the dynamics and/or the payoff functional. This is a continuation of the formulation in Chap. 1 where the expected payoff is nonlinear in the measure \(P_{x_{t+1}}.\) We analyze the existence of optimal strategies in games associated with payoff functionals of mean-field type, under a dynamics driven by a class of Markov chains of mean-field type.