博弈论II的一种新的数学表示
A new mathematical representation of Game Theory II
摘要：
在另一篇同名的论文\cite{frame}中，我们提出了一种新的博弈论表示，但大多数结果都是通过具体的例子和论证给出的。在本文中，我们试图证明的结论，我们可以，包括一个新的表示和传统的博弈论之间的等价性证明，并在新的表示的经典纳什定理的证明。给出了量子博弈的操纵定义，并证明了该定义与一般抽象表示的等价性。提出了一个量子纳什命题，但没有给出一般的证明。然后，对纳什均衡（NE）和伪动态均衡（PDE）进行了比较。最后，我们探讨了这种表示是否会导致真正的量子博弈，以及这种新的表示是否有助于经典博弈，作为对\cite{enk}中问题的回答。对连续策略博弈也进行了一些讨论。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
