Artikel
Quantum mean-field games with the observations of counting type
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.
- Sprache
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Englisch
- Erschienen in
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Journal: Games ; ISSN: 2073-4336 ; Volume: 12 ; Year: 2021 ; Issue: 1 ; Pages: 1-14 ; Basel: MDPI
- Klassifikation
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Wirtschaft
- Thema
-
Belavkin equation
mean field games of jump type on manifolds
nonlinear stochastic Schrödinger equation
observation of counting type
quantum control
quantum dynamic law of large numbers
quantum filtering
quantum interacting particles
quantum mean field games
- Ereignis
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Geistige Schöpfung
- (wer)
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Kolokolʹcov, Vassilij N.
- Ereignis
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Veröffentlichung
- (wer)
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MDPI
- (wo)
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Basel
- (wann)
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2021
- DOI
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doi:10.3390/g12010007
- Handle
- Letzte Aktualisierung
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10.03.2025, 11:43 MEZ
Datenpartner
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Objekttyp
- Artikel
Beteiligte
- Kolokolʹcov, Vassilij N.
- MDPI
Entstanden
- 2021
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