Quantum Mean-Field Games with the Observations of Counting Type

Vassili N. Kolokoltsov
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Vassili N. Kolokoltsov: Department of Statistics, University of Warwick, Coventry CV4 7AL, UK

Games, 2021, vol. 12, issue 1, 1-14

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 ? -Nash equilibrium for the corresponding N -player quantum game. The existence of solutions is suggested as an interesting open problem.

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 (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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