Predictions under common knowledge of payoffs may differ from those under arbitrarily, but finitely, many orders of mutual knowledge; Rubinstein's (1989) Email game is a seminal example. Weinstein and Yildiz (2007) showed that the discontinuity in the example generalizes: for all types with multiple rationalizable (ICR) actions, there exist similar types with unique rationalizable action. This paper studies how a wide class of departures from common belief in rationality impact Weinstein and Yildiz's discontinuity. We weaken ICR to ICR-x, where x is a sequence whose n-th term is the probability players attach to (n - 1)th-order belief in rationality. We find that Weinstein and Yildiz's discontinuity holds when higher-order belief in rationality remains above some threshold (constant x), but fails when higher-order belief in rationality eventually becomes low enough (x converging to 0).

中文翻译：

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不完全信息博弈中的不确定性、推理深度和鲁棒性

在收益的共同知识下的预测可能不同于在任意但有限的多阶相互知识下的预测；Rubinstein (1989) 的电子邮件游戏就是一个开创性的例子。Weinstein 和 Yildiz (2007) 表明示例中的不连续性概括了：对于具有多个合理化 (ICR) 操作的所有类型，存在具有唯一合理化操作的相似类型。本文研究了对理性的普遍信念的广泛偏离如何影响韦恩斯坦和耶尔迪兹的不连续性。我们将 ICR 弱化为 ICR-x，其中 x 是一个序列，其第 n 项是玩家依附于 (n - 1) 阶理性信念的概率。我们发现，当理性的高阶信念保持在某个阈值（常数 x）之上时，韦恩斯坦和耶尔迪兹的不连续性成立，