We propose a two-step guessing game to measure the depth of thinking. We apply this method to the P beauty contest game. Using our method, we find that 81% of subjects do not make choice following best response reasoning while the classical method would suggest only 12%. The result suggests that the classical method has the fundamental problem that it cannot distinguish if a submitted number is due to best response reasoning or not. It also suggests that traditional level k analysis falsely attributes some sophistication to random players, and that the degree of false attribution is large. Our procedure provides an alternative way to identify whether the individual has best response reasoning which is essential for any positive level of depth of thinking and differentiates between the depth of thinking and random choice, and hence provides a very different conclusion, which is suggestive of limitations of the classical method.

我们提出了一个两步猜谜游戏来衡量思维深度。我们将这种方法应用到P选美比赛中。使用我们的方法，我们发现 81% 的受试者不会根据最佳反应推理做出选择，而经典方法仅建议 12%。结果表明，经典方法存在根本问题，即它无法区分提交的数字是否是由于最佳响应推理而产生的。它还表明传统的k级分析错误地将一些复杂性归因于随机玩家，并且错误归因的程度很大。我们的程序提供了另一种方法来确定个人是否具有最佳反应推理，这对于任何积极的思维深度水平都是至关重要的，并区分思维深度和随机选择，因此提供了一个非常不同的结论，这表明了局限性的经典方法。