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Mean-Field-Type Games with Jump and Regime Switching

Author

Listed:
  • Alain Bensoussan

    (University of Texas at Dallas
    City University Hong Kong)

  • Boualem Djehiche

    (KTH Royal Institute of Technology)

  • Hamidou Tembine

    (New York University Abu Dhabi)

  • Sheung Chi Phillip Yam

    (The Chinese University of Hong Kong)

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.

Suggested Citation

  • Alain Bensoussan & Boualem Djehiche & Hamidou Tembine & Sheung Chi Phillip Yam, 2020. "Mean-Field-Type Games with Jump and Regime Switching," Dynamic Games and Applications, Springer, vol. 10(1), pages 19-57, March.
    • Handle: RePEc:spr:dyngam:v:10:y:2020:i:1:d:10.1007_s13235-019-00306-2
    DOI: 10.1007/s13235-019-00306-2
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    References listed on IDEAS

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    1. J. T. Shi & Z. Wu, 2010. "Maximum Principle for Partially-Observed Optimal Control of Fully-Coupled Forward-Backward Stochastic Systems," Journal of Optimization Theory and Applications, Springer, vol. 145(3), pages 543-578, June.
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    4. Bensoussan, A. & Frehse, J. & Yam, S.C.P., 2017. "On the interpretation of the Master Equation," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2093-2137.
    5. Mokhtar Hafayed & Syed Abbas & Abdelmadjid Abba, 2015. "On Mean-Field Partial Information Maximum Principle of Optimal Control for Stochastic Systems with Lévy Processes," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 1051-1069, December.
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    7. Boualem Djehiche & Hamidou Tembine & Raul Tempone, 2014. "A Stochastic Maximum Principle for Risk-Sensitive Mean-Field Type Control," Papers 1404.1441, arXiv.org.
    8. Buckdahn, Rainer & Li, Juan & Peng, Shige, 2009. "Mean-field backward stochastic differential equations and related partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3133-3154, October.
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    Cited by:

    1. Masaaki Fujii, 2020. "Probabilistic Approach to Mean Field Games and Mean Field Type Control Problems with Multiple Populations," CARF F-Series CARF-F-497, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. Zahrate El Oula Frihi & Julian Barreiro-Gomez & Salah Eddine Choutri & Hamidou Tembine, 2020. "Hierarchical Structures and Leadership Design in Mean-Field-Type Games with Polynomial Cost," Games, MDPI, vol. 11(3), pages 1-26, August.
    3. Dianetti, Jodi & Ferrari, Giorgio & Tzouanas, Ioannis, 2023. "Ergodic Mean-Field Games of Singular Control with Regime-Switching (extended version)," Center for Mathematical Economics Working Papers 681, Center for Mathematical Economics, Bielefeld University.
    4. Jun Moon & Wonhee Kim, 2020. "Explicit Characterization of Feedback Nash Equilibria for Indefinite, Linear-Quadratic, Mean-Field-Type Stochastic Zero-Sum Differential Games with Jump-Diffusion Models," Mathematics, MDPI, vol. 8(10), pages 1-23, September.
    5. Adrian Patrick Kennedy & Suresh P. Sethi & Chi Chung Siu & Sheung Chi Phillip Yam, 2021. "Cooperative Advertising in a Dynamic Three‐Echelon Supply Chain," Production and Operations Management, Production and Operations Management Society, vol. 30(11), pages 3881-3905, November.

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