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

Salah Eddine Choutri, Boualem Djehiche, Tembine Hamidou

Research output: Contribution to journalArticle

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 1 2019

Fingerprint

Zero sum game
Mean Field
Markov processes
Markov chain
Optimal Control
Total Variation Distance
Differential Games
Saddlepoint
Control Problem
Jump
Fixed point

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

Cite this

Optimal control and zero-sum games for markov chains of mean-field type. / Choutri, Salah Eddine; Djehiche, Boualem; Hamidou, Tembine.

In: Mathematical Control and Related Fields, Vol. 9, No. 3, 01.09.2019, p. 571-605.

Research output: Contribution to journalArticle

Choutri, Salah Eddine ; Djehiche, Boualem ; Hamidou, Tembine. / Optimal control and zero-sum games for markov chains of mean-field type. In: Mathematical Control and Related Fields. 2019 ; Vol. 9, No. 3. pp. 571-605.
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