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Quantum Mean-Field Games with the Observations of Counting Type

Author

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  • Vassili N. Kolokoltsov

    (Department of Statistics, University of Warwick, Coventry CV4 7AL, UK
    Higher School of Economics, 109028 Moscow, Russia)

Abstract

Quantum games and mean-field games (MFG) represent two important new branches of game theory. In a recent paper the author developed quantum MFGs merging these two branches. These quantum MFGs were based on the theory of continuous quantum observations and filtering of diffusive type. In the present paper we develop the analogous quantum MFG theory based on continuous quantum observations and filtering of counting type. However, proving existence and uniqueness of the solutions for resulting limiting forward-backward system based on jump-type processes on manifolds seems to be more complicated than for diffusions. In this paper we only prove that if a solution exists, then it gives an ϵ -Nash equilibrium for the corresponding N -player quantum game. The existence of solutions is suggested as an interesting open problem.

Suggested Citation

  • Vassili N. Kolokoltsov, 2021. "Quantum Mean-Field Games with the Observations of Counting Type," Games, MDPI, vol. 12(1), pages 1-14, January.
    • Handle: RePEc:gam:jgames:v:12:y:2021:i:1:p:7-:d:480221
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    References listed on IDEAS

    as
    1. A. Bensoussan & K. Sung & S. Yam, 2013. "Linear–Quadratic Time-Inconsistent Mean Field Games," Dynamic Games and Applications, Springer, vol. 3(4), pages 537-552, December.
    2. Belavkin, Viacheslav P., 1992. "Quantum stochastic calculus and quantum nonlinear filtering," Journal of Multivariate Analysis, Elsevier, vol. 42(2), pages 171-201, August.
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    Cited by:

    1. Vassili N. Kolokoltsov, 2022. "Dynamic Quantum Games," Dynamic Games and Applications, Springer, vol. 12(2), pages 552-573, June.

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