Quantization of two- and three-player cooperative games based on QRA
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Date
2024-10-01
Authors
Eryganov, Ivan
Hrdina, Jaroslav
Návrat, Aleš
0000-0003-2203-882XAdvisor
Referee
Mark
Journal Title
Journal ISSN
Volume Title
Publisher
IOP Publishing
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Abstract
In 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.
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Citation
Journal of Physics A: Mathematical and Theoretical. 2024, vol. 57, issue 42, p. 1-24.
https://iopscience.iop.org/article/10.1088/1751-8121/ad7c9c
https://iopscience.iop.org/article/10.1088/1751-8121/ad7c9c
Document type
Peer-reviewed
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Published version
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Language of document
en