Control systems of interacting objects modeled as a game against nature under a mean field approach

Carmen G. Higuera-Chan, Héctor Jasso-Fuentes, J. Adolfo Minjárez-Sosa*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


This paper deals with discrete-time stochastic systems composed of a large number of N interacting objects (a.k.a. agents or particles). There is a central controller whose decisions, at each stage, affect the system behavior. Each object evolves randomly among a finite set of classes, according to a transition law which depends on an unknown parameter. Such a parameter is possibly non observable and may change from stage to stage. Due to the lack of information and to the large number of agents, the control problem under study is rewritten as a game against nature according to the mean field theory; that is, we introduce a game model associated to the proportions of the objects in each class, whereas the values of the unknown parameter are now considered as "actions" selected by an opponent to the controller (the nature). Then, letting N → ∞ (the mean field limit) and considering a discounted optimality criterion, the objective for the controller is to minimize the maximum cost, where the maximum is taken over all possible strategies of the nature.

Original languageEnglish
Pages (from-to)59-74
Number of pages16
JournalJournal of Dynamics and Games
Issue number1
StatePublished - 2017

Bibliographical note

Publisher Copyright:
© 2017, American Institute of Mathematical Sciences.


  • Discounted criterion
  • Games against nature
  • Mean field theory
  • Minimax control
  • Systems of interacting objects


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