Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2404.06196 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916198441025536 |
|---|---|
| author | Frąckiewicz, Piotr Szopa, Marek |
| author_facet | Frąckiewicz, Piotr Szopa, Marek |
| contents | We study the extension of classical games to the quantum domain, generated by the addition of one unitary strategy to two classical strategies of each player. The conditions that need to be met by unitary operations to ensure that the extended game is invariant with respect to the isomorphic transformations of the input game are determined. It has been shown that there are three types of these extensions, two of them are purely quantum. On the other hand, it has been demonstrated that the extensions of two versions of the same classical game by a unitary operator that does not meet these conditions may result in quantum games that are non-equivalent, e.g. having different Nash equilibria. We use the obtained results to extend the classical Prisoner's Dilemma game to a quantum game that has a unique Nash equilibrium closer to Pareto-optimal solutions than the original one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06196 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Permissible extensions of classical to quantum games combining three strategies Frąckiewicz, Piotr Szopa, Marek Quantum Physics Computer Science and Game Theory We study the extension of classical games to the quantum domain, generated by the addition of one unitary strategy to two classical strategies of each player. The conditions that need to be met by unitary operations to ensure that the extended game is invariant with respect to the isomorphic transformations of the input game are determined. It has been shown that there are three types of these extensions, two of them are purely quantum. On the other hand, it has been demonstrated that the extensions of two versions of the same classical game by a unitary operator that does not meet these conditions may result in quantum games that are non-equivalent, e.g. having different Nash equilibria. We use the obtained results to extend the classical Prisoner's Dilemma game to a quantum game that has a unique Nash equilibrium closer to Pareto-optimal solutions than the original one. |
| title | Permissible extensions of classical to quantum games combining three strategies |
| topic | Quantum Physics Computer Science and Game Theory |
| url | https://arxiv.org/abs/2404.06196 |