I study endogenous learning dynamics for people expecting systematic reversals from random sequences - the "gambler's fallacy." Biased agents face an optimal-stopping problem. They are uncertain about the underlying distribution and learn its parameters from predecessors. Agents stop when early draws are "good enough," so predecessors' experience contain negative streaks but not positive streaks. Since biased agents understate the likelihood of consecutive below-average draws, society converges to over-pessimistic beliefs about the distribution's mean and stops too early. Agents uncertain about the distribution's variance overestimate it to an extent that depends on predecessors' stopping thresholds. Subsidizing search partially mitigates long-run belief distortions.

中文翻译：

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从截尾数据中错误学习：赌徒在最优停止问题中的谬误

我研究了人们期望从随机序列中系统逆转的内生学习动态——“赌徒谬误”。有偏见的代理面临最优停止问题。他们不确定底层分布并从前辈那里学习其参数。当早期的平局“足够好”时，代理停止，因此前辈的经验包含负连胜但不包含正连胜。由于有偏见的代理人低估了连续低于平均水平的可能性，社会趋于对分布的平均值过于悲观，并过早地停止。不确定分布方差的代理会在一定程度上高估它，这取决于前辈的停止阈值。补贴搜索部分减轻了长期的信念扭曲。