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

WoS Article

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.

Keywords in English

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

Released

2024-10-01

Publisher

IOP Publishing

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",
  journal="Journal of Physics A-Mathematical and Theoretical",
  year="2024",
  volume="57",
  number="42",
  pages="1--24",
  doi="10.1088/1751-8121/ad7c9c",
  issn="1751-8113",
  url="https://iopscience.iop.org/article/10.1088/1751-8121/ad7c9c"
}