n人博弈中的理性与正确性
Rationality and correctness in n-player games
AI总结：
针对双人博弈纳什均衡的两类经典充分条件，本文提出与理性互知（MKR）更契合的“理性与正确性互设”（MARC）概念，证明其在双人零和博弈中普遍成立，但在n人博弈中通常不成立。
摘要：
双人博弈中存在两个众所周知的纳什均衡充分条件：理性互知（MKR）与猜想互知。MKR假设理性概念是被共同知晓的。相比之下，猜想互知假设给定的猜想剖面是被共同知晓的，这长期以来被认为是一个强假设。在本研究短文中，我们引入了“理性与正确性互设”（MARC）的概念，它在概念上与MKR假设更契合。我们提出两项主要结果：第一项结果证明MARC在所有双人零和博弈中均成立；第二项定理表明，MARC在n人博弈中通常不成立。
英文摘要：
There are two well-known sufficient conditions for Nash equilibrium in two-player games: mutual knowledge of rationality (MKR) and mutual knowledge of conjectures. MKR assumes that the concept of rationality is mutually known. In contrast, mutual knowledge of conjectures assumes that a given profile of conjectures is mutually known, which has long been recognized as a strong assumption. In this note, we introduce a notion of "mutual assumption of rationality and correctness" (MARC), which conceptually aligns more closely with the MKR assumption. We present two main results. Our first result establishes that MARC holds in every two-person zero-sum game. In our second theorem, we show that MARC does not in general hold in n-player games.
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。
