Quantization of two- and three-player cooperative games based on QRA

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dc.contributor.authorEryganov, Ivancs
dc.contributor.authorHrdina, Jaroslavcs
dc.contributor.authorNávrat, Alešcs
dc.coverage.issue42cs
dc.coverage.volume57cs
dc.date.accessioned2025-04-04T11:56:46Z
dc.date.available2025-04-04T11:56:46Z
dc.date.issued2024-10-01cs
dc.description.abstractIn this paper, a novel quantization scheme for cooperative games is proposed. The circuit is inspired by the Eisert-Wilkens-Lewenstein protocol, which was modified to represent cooperation between players and extended to 3-qubit states. The framework of Clifford algebra is used to perform necessary computations. In particular, we use a direct analogy between Dirac formalism and Quantum Register Algebra (QRA) to represent circuits. This analogy enables us to perform automated proofs of the circuit equivalence in a simple fashion. The expected value of the Shapley value concerning quantum probabilities is employed to distribute players' payoffs after the measurement. We study how entanglement, representing the level of pre-agreement between players, affects the final utility distribution. The paper also demonstrates how the QRA and GAALOP software can automate all necessary calculations.en
dc.formattextcs
dc.format.extent1-24cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationJournal of Physics A: Mathematical and Theoretical. 2024, vol. 57, issue 42, p. 1-24.en
dc.identifier.doi10.1088/1751-8121/ad7c9ccs
dc.identifier.issn1751-8121cs
dc.identifier.orcid0000-0003-2203-882Xcs
dc.identifier.orcid0000-0003-2460-7571cs
dc.identifier.orcid0000-0002-8100-4032cs
dc.identifier.other189790cs
dc.identifier.researcheridHNR-5985-2023cs
dc.identifier.researcheridK-7147-2019cs
dc.identifier.scopus57219437840cs
dc.identifier.scopus14044864000cs
dc.identifier.urihttps://hdl.handle.net/11012/250781
dc.language.isoencs
dc.publisherIOP Publishingcs
dc.relation.ispartofJournal of Physics A: Mathematical and Theoreticalcs
dc.relation.urihttps://iopscience.iop.org/article/10.1088/1751-8121/ad7c9ccs
dc.rightsCreative Commons Attribution 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/1751-8121/cs
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/cs
dc.subjectquantum gamesen
dc.subjectcooperative gamesen
dc.subjectquantum computingen
dc.subjectshapley valueen
dc.subjectquantum register algebraen
dc.titleQuantization of two- and three-player cooperative games based on QRAen
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-189790en
sync.item.dbtypeVAVen
sync.item.insts2025.04.04 13:56:45en
sync.item.modts2025.04.02 14:32:10en
thesis.grantorVysoké učení technické v Brně. Fakulta strojního inženýrství. Ústav matematikycs
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