dorsal/arxiv
View SchemaClassification of Quantum Symmetric Non-zero Sum 2x2 Games in the Eisert Scheme
| Authors | Álvaro Francisco Huertas-Rosero |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0402117 |
| URL | https://arxiv.org/abs/quant-ph/0402117 |
Abstract
A quantum game in the Eisert scheme is defined by the payoff matrix, plus some quantum entanglement parameters. In the symmetric nonzero-sum 2x2 games, the relevant features of the game are given by two parameters in the payoff matrix, and only one extra entanglement parameter is introduced by quantizing it in the Eisert scheme. The criteria adopted in this work to classify quantum games are the amount and characteristics of Nash equilibria and Pareto-optimal positions. A new classification based on them is developed for symmetric nonzero-sum classical 2x2 games, as well as classifications for quantum games with different restricted subsets of the total strategy set. Finally, a classification is presented taking the whole set of strategies into account, both unitary strategies and nonunitary strategies studied as convex mixures of unitary strategies. The classification reproduces features which have been previously found in other works, like appearance of multiple equilibria, changes in the character of equilibria, and entanglement regime transitions.
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"abstract": "A quantum game in the Eisert scheme is defined by the payoff matrix, plus\nsome quantum entanglement parameters. In the symmetric nonzero-sum 2x2 games,\nthe relevant features of the game are given by two parameters in the payoff\nmatrix, and only one extra entanglement parameter is introduced by quantizing\nit in the Eisert scheme.\n The criteria adopted in this work to classify quantum games are the amount\nand characteristics of Nash equilibria and Pareto-optimal positions. A new\nclassification based on them is developed for symmetric nonzero-sum classical\n2x2 games, as well as classifications for quantum games with different\nrestricted subsets of the total strategy set. Finally, a classification is\npresented taking the whole set of strategies into account, both unitary\nstrategies and nonunitary strategies studied as convex mixures of unitary\nstrategies.\n The classification reproduces features which have been previously found in\nother works, like appearance of multiple equilibria, changes in the character\nof equilibria, and entanglement regime transitions.",
"arxiv_id": "quant-ph/0402117",
"authors": [
"\u00c1lvaro Francisco Huertas-Rosero"
],
"categories": [
"quant-ph"
],
"title": "Classification of Quantum Symmetric Non-zero Sum 2x2 Games in the Eisert Scheme",
"url": "https://arxiv.org/abs/quant-ph/0402117"
},
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"source": {
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