Mean-Field-Type Games with Jump and Regime Switching

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 wi...

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Bibliographic Details
Published inDynamic games and applications Vol. 10; no. 1; pp. 19 - 57
Main Authors Bensoussan, Alain, Djehiche, Boualem, Tembine, Hamidou, Yam, Sheung Chi Phillip
Format Journal Article
LanguageEnglish
Published New York Springer US 01.03.2020
Springer Nature B.V
Subjects
Communications Engineering
Computer Systems Organization and Communication Networks
Decision making
Diffusion
Dynamic programming
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Game Theory
Games
Management Science
Mathematics
Mathematics and Statistics
Maximum principle
McKean-Vlasov
Mean-field
Networks
Operations Research
Social and Behav. Sciences
Switching
Mean-field
McKean–Vlasov
Game theory
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Summary: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.
ISSN:2153-0785
2153-0793
2153-0793
DOI:10.1007/s13235-019-00306-2