dorsal/arxiv
View SchemaA new mathematical representation of Game Theory II
| Authors | Jinshan Wu |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0405183 |
| URL | https://arxiv.org/abs/quant-ph/0405183 |
Abstract
In another paper with the same name\cite{frame}, we proposed a new representation of Game Theory, but most results are given by specific examples and argument. In this paper, we try to prove the conclusions as far as we can, including a proof of equivalence between the new representation and the traditional Game Theory, and a proof of Classical Nash Theorem in the new representation. And it also gives manipulation definition of quantum game and a proof of the equivalence between this definition and the general abstract representation. A Quantum Nash Proposition is proposed but without a general proof. Then, some comparison between Nash Equilibrium (NE) and the pseudo-dynamical equilibrium (PDE) is discussed. At last, we investigate the possibility that whether such representation leads to truly Quantum Game, and whether such a new representation is helpful to Classical Game, as an answer to the questions in \cite{enk}. Some discussion on continuous-strategy games are also included.
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"abstract": "In another paper with the same name\\cite{frame}, we proposed a new\nrepresentation of Game Theory, but most results are given by specific examples\nand argument. In this paper, we try to prove the conclusions as far as we can,\nincluding a proof of equivalence between the new representation and the\ntraditional Game Theory, and a proof of Classical Nash Theorem in the new\nrepresentation. And it also gives manipulation definition of quantum game and a\nproof of the equivalence between this definition and the general abstract\nrepresentation. A Quantum Nash Proposition is proposed but without a general\nproof. Then, some comparison between Nash Equilibrium (NE) and the\npseudo-dynamical equilibrium (PDE) is discussed. At last, we investigate the\npossibility that whether such representation leads to truly Quantum Game, and\nwhether such a new representation is helpful to Classical Game, as an answer to\nthe questions in \\cite{enk}. Some discussion on continuous-strategy games are\nalso included.",
"arxiv_id": "quant-ph/0405183",
"authors": [
"Jinshan Wu"
],
"categories": [
"quant-ph"
],
"title": "A new mathematical representation of Game Theory II",
"url": "https://arxiv.org/abs/quant-ph/0405183"
},
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