意外考试悖论的博弈分析

摘要

本文从博弈的角度分析了意外考试悖论，指出了以往解决方案的不足，给出了一种新的方案。根据这个新方案，考试悖论的推理中使用了倒推法和弱下策反复剔除法。本文接着讨论了这些博弈推理方法的不足。然后把这个新的博弈方案用到卡片悖论和方格悖论这些考试悖论的变种里。最后指出，在考试悖论里，比起倒推法，弱下策剔除法是引起悖论的更根本的原因。%We discuss the surprise examination paradox from the point of view of game theory, pointing out the defects of resolutions offered before, and propose a new resolution. According to this new resolution, two methods, i.e., backward induction and iterated elimination of weakly dominated strategies, are used in the reasoning of the surprise examination paradox. Then the flaws of these two methods are discussed. In addition, we apply the new resolution to the unexpected Ace paradox and the undiscoverable position paradox which are the variants of the examination paradox, and then find that the iterated elimination of weakly dominated strategies is more fundamental for causing these paradoxes than the backward induction.