Quantum mean-field games with the observations of counting type
type: Item
instance of: scholarly article
title: Quantum mean-field games with the observations of counting type
zbMATH Open document ID: 1478.91044
author: Vassili Kolokoltsov
published in: Games
publication date: 2021-11-26T00:00:00Z
review text: Summary: 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 \(\epsilon\)-Nash equilibrium for the corresponding \(N\)-player quantum game. The existence of solutions is suggested as an interesting open problem.
Mathematics Subject Classification ID: 91A81
Mathematics Subject Classification ID: 91A16
Mathematics Subject Classification ID: 91A05
Mathematics Subject Classification ID: 81Q05
Mathematics Subject Classification ID: 81Q93
zbMATH DE Number: 7434006
zbMATH Keywords: quantum dynamic law of large numbers
zbMATH Keywords: quantum filtering
zbMATH Keywords: observation of counting type
zbMATH Keywords: Belavkin equation
zbMATH Keywords: nonlinear stochastic Schrödinger equation
zbMATH Keywords: quantum interacting particles
zbMATH Keywords: quantum control
zbMATH Keywords: quantum mean field games
zbMATH Keywords: mean field games of jump type on manifolds
MaRDI profile type: Publication
full work available at URL: g12010007
OpenAlex ID: W3119888456
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DOI: 10.3390/G12010007
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description: scientific article; zbMATH DE number 7434006