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Dynamic Games and Applications

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28-02-2019

Mean-Field-Type Games with Jump and Regime Switching

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

Published in: Dynamic Games and Applications | Issue 1/2020

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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.

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Title: Mean-Field-Type Games with Jump and Regime Switching
Authors: Alain Bensoussan
Boualem Djehiche
Hamidou Tembine
Sheung Chi Phillip Yam
Publication date: 28-02-2019
Publisher: Springer US
Published in: Dynamic Games and Applications / Issue 1/2020
Print ISSN: 2153-0785
Electronic ISSN: 2153-0793
DOI: https://doi.org/10.1007/s13235-019-00306-2

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