Optimal control and zero-sum games for markov chains of mean-field type

Salah Eddine Choutri, Boualem Djehiche, Hamidou Tembine

Research output: Contribution to journalArticlepeer-review

Abstract

We establish existence of Markov chains of mean-field type with unbounded jump intensities by means of a fixed point argument using the total variation distance. We further show existence of nearly-optimal controls and, using a Markov chain backward SDE approach, we suggest conditions for existence of an optimal control and a saddle-point for respectively a control problem and a zero-sum differential game associated with payoff functionals of mean-field type, under dynamics driven by such Markov chains of mean-field type.

Original languageEnglish (US)
Pages (from-to)571-605
Number of pages35
JournalMathematical Control and Related Fields
Volume9
Issue number3
DOIs
StatePublished - Sep 2019

Keywords

  • Backward SDEs
  • Mean-field
  • Nonlinear Markov chain
  • Optimal control
  • Saddle point
  • Stochastic maximum principle
  • Thinning
  • Zero-sum game

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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