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Quantum Mean-Field Games with the Observations of Counting Type

1
Department of Statistics, University of Warwick, Coventry CV4 7AL, UK
2
Higher School of Economics, 109028 Moscow, Russia
Received: 4 November 2020 / Revised: 28 December 2020 / Accepted: 6 January 2021 / Published: 14 January 2021
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. View Full-Text
Keywords: quantum dynamic law of large numbers; quantum filtering; observation of counting type; Belavkin equation; nonlinear stochastic Schrödinger equation; quantum interacting particles; quantum control; quantum mean field games; mean field games of jump type on manifolds quantum dynamic law of large numbers; quantum filtering; observation of counting type; Belavkin equation; nonlinear stochastic Schrödinger equation; quantum interacting particles; quantum control; quantum mean field games; mean field games of jump type on manifolds
MDPI and ACS Style

Kolokoltsov, V.N. Quantum Mean-Field Games with the Observations of Counting Type. Games 2021, 12, 7. https://0-doi-org.brum.beds.ac.uk/10.3390/g12010007

AMA Style

Kolokoltsov VN. Quantum Mean-Field Games with the Observations of Counting Type. Games. 2021; 12(1):7. https://0-doi-org.brum.beds.ac.uk/10.3390/g12010007

Chicago/Turabian Style

Kolokoltsov, Vassili N. 2021. "Quantum Mean-Field Games with the Observations of Counting Type" Games 12, no. 1: 7. https://0-doi-org.brum.beds.ac.uk/10.3390/g12010007

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