Mean-Field-Type Games with Jump and Regime Switching

Alain Bensoussan, Boualem Djehiche, Hamidou Tembine () and Sheung Chi Phillip Yam
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Alain Bensoussan: University of Texas at Dallas
Hamidou Tembine: New York University Abu Dhabi
Sheung Chi Phillip Yam: The Chinese University of Hong Kong

Dynamic Games and Applications, 2020, vol. 10, issue 1, No 2, 19-57

Abstract: 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.

Keywords: Mean-field; McKean–Vlasov; Game theory (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s13235-019-00306-2

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