Quantum mean-field games with the observations of counting type

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Quantum mean-field games with the observations of counting type. / Kolokoltsov, Vassili N.

In: Games, Vol. 12, No. 1, 7, 03.2021.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{c45eb9f0eb174b7c9385788d1fe383af,

title = "Quantum mean-field games with the observations of counting type",

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

keywords = "Belavkin equation, Mean field games of jump type on manifolds, Nonlinear stochastic Schr{\"o}dinger equation, Observation of counting type, Quantum control, Quantum dynamic law of large numbers, Quantum filtering, Quantum interacting particles, Quantum mean field games, quantum mean field games, quantum interacting particles, nonlinear stochastic Schrodinger equation, quantum filtering, observation of counting type, mean field games of jump type on manifolds, quantum control, quantum dynamic law of large numbers",

author = "Kolokoltsov, {Vassili N.}",

year = "2021",

month = mar,

doi = "10.3390/g12010007",

language = "English",

volume = "12",

journal = "Games",

issn = "2073-4336",

publisher = "MDPI AG",

number = "1",

}

RIS

TY - JOUR

T1 - Quantum mean-field games with the observations of counting type

AU - Kolokoltsov, Vassili N.

PY - 2021/3

Y1 - 2021/3

N2 - 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 ɛ-Nash equilibrium for the corresponding N-player quantum game. The existence of solutions is suggested as an interesting open problem.

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

KW - Belavkin equation

KW - Mean field games of jump type on manifolds

KW - Nonlinear stochastic Schrödinger equation

KW - Observation of counting type

KW - Quantum control

KW - Quantum dynamic law of large numbers

KW - Quantum filtering

KW - Quantum interacting particles

KW - Quantum mean field games

KW - quantum mean field games

KW - quantum interacting particles

KW - nonlinear stochastic Schrodinger equation

KW - quantum filtering

KW - observation of counting type

KW - mean field games of jump type on manifolds

KW - quantum control

KW - quantum dynamic law of large numbers

UR - http://www.scopus.com/inward/record.url?scp=85099444250&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/0346d435-4016-33b9-a1d5-d4b06adf1ee1/

U2 - 10.3390/g12010007

DO - 10.3390/g12010007

M3 - Article

AN - SCOPUS:85099444250

VL - 12

JO - Games

JF - Games

SN - 2073-4336

IS - 1

M1 - 7

ER -

ID: 76068412