Publication detail

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

ERYGANOV, I. HRDINA, J. NÁVRAT, A.

Original Title

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

Type

journal article in Web of Science

Language

English

Original 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.

Keywords

quantum games; cooperative games; quantum computing; shapley value; quantum register algebra

Authors

ERYGANOV, I.; HRDINA, J.; NÁVRAT, A.

Released

1. 10. 2024

Publisher

IOP Publishing Ltd

Location

BRISTOL

ISBN

1751-8121

Periodical

Journal of Physics A: Mathematical and Theoretical

Year of study

57

Number

42

State

United Kingdom of Great Britain and Northern Ireland

Pages from

1

Pages to

24

Pages count

24

URL

https://www.google.iopscience.iop.org/article/10.1088/1751-8121/ad7c9c

BibTex

@article{BUT189790,
  author="Ivan {Eryganov} and Jaroslav {Hrdina} and Aleš {Návrat}",
  title="Quantization of two- and three-player cooperative games based on QRA",
  journal="Journal of Physics A: Mathematical and Theoretical",
  year="2024",
  volume="57",
  number="42",
  pages="1--24",
  doi="10.1088/1751-8121/ad7c9c",
  issn="1751-8121",
  url="https://www.google.iopscience.iop.org/article/10.1088/1751-8121/ad7c9c"
}