Publication detail

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

ERYGANOV, I. HRDINA, J. NÁVRAT, A.

English title

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

Type

journal article in Web of Science

Language

en

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.

English 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 in English

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

Released

01.10.2024

Publisher

IOP Publishing Ltd

Location

BRISTOL

ISSN

1751-8121

Volume

57

Number

42

Pages from–to

1–24

Pages count

24

BIBTEX


@article{BUT189790,
  author="Ivan {Eryganov} and Jaroslav {Hrdina} and Aleš {Návrat},
  title="Quantization of two- and three-player cooperative games based on QRA",
  year="2024",
  volume="57",
  number="42",
  month="October",
  pages="1--24",
  publisher="IOP Publishing Ltd",
  address="BRISTOL",
  issn="1751-8121"
}