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We investigate a stochastic differential game in which a major player has a private information (the knowledge of a random variable), which she discloses through her control to a population of small players playing in a Nash Mean Field Game equilibrium.
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Carmona, R., Delarue, F., and Lacker, D. (2016). Mean field games with common noise. The Annals of Probability, Vol. 44, No. 6, 3740-3803
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Carmona, R., Wang, P. (2017). An alternative approach to mean field game with major and minor players, and applications to herders impacts. Applied Mathematics & Optimization, 76(1), 5-27
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Firoozi, D., and Caines, P. E. (2020). ϵ \epsilon -Nash Equilibria for Major-Minor LQG Mean Field Games With Partial Observations of All Agents. IEEE Transactions on Automatic Control, 66(6), 2778-2786
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Bertucci, C. (2022). Mean field games with incomplete information. arXiv preprint arXiv:2205.07703
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Cardaliaguet, P., and Souganidis, P. E. (2022). On first order mean field game systems with a common noise. The Annals of Applied Probability, 32(3), 2289-2326
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2023
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