MFGs for Finite-State Models

  • Vassili N. KolokoltsovEmail author
  • Oleg A. Malafeyev
Part of the Springer Series in Operations Research and Financial Engineering book series (ORFE)


In this chapter, we introduce the MFG framework for discrete state spaces, stressing the points that are most relevant for the models studied in the next chapters. As was already mentioned, the difference between the present MFG setting and the modeling of Part I is that now the small agents themselves become rational optimizers and are not supposed just to follow some prescribed deterministic or stochastic strategies (such as myopic behavior). For simplicity, in treating MFG we will exclusively use finite-state models and will not touch the extensions to countable state spaces, though the results of Chapter  4 allow one to extend large portions of the theory more or less directly to this more general framework.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of WarwickCoventryUK
  2. 2.Faculty of Applied Mathematics and Control ProcessesSaint Petersburg State UniversitySaint PetersburgRussia

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