Mean-Field-Type Games with Jump and Regime Switching

Alain Bensoussan, Boualem Djehiche, Hamidou Tembine, Sheung Chi Phillip Yam

Research output: Contribution to journalArticle

Abstract

In this article, we study mean-field-type games with jump–diffusion and regime switching in which the payoffs and the state dynamics depend not only on the state–action profile of the decision-makers but also on a measure of the state–action pair. The state dynamics is a measure-dependent process with jump–diffusion and regime switching. We derive novel equilibrium systems to be solved. Two solution approaches are presented: (i) dynamic programming principle and (ii) stochastic maximum principle. Relationship between dual function and adjoint processes are provided. It is shown that the extension to the risk-sensitive case generates a nonlinearity to the adjoint process and it involves three other processes associated with the diffusion, jump and regime switching, respectively.

Original languageEnglish (US)
Pages (from-to)19-57
Number of pages39
JournalDynamic Games and Applications
Volume10
Issue number1
DOIs
StatePublished - Mar 1 2020

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Keywords

  • Game theory
  • McKean–Vlasov
  • Mean-field

ASJC Scopus subject areas

  • Statistics and Probability
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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