带有删失观测的贝叶斯序贯搜索
Bayesian Sequential Search with Censored Observations
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中文总结 AI 辅助
本文研究信息删失对贝叶斯序贯搜索的影响，发现单侧删失可恢复单调性使短视截断规则最优，并将框架应用于求职、价格搜索等场景。
中文摘要 AI 辅助
本文研究信息删失如何使贝叶斯序贯搜索中的短视截断规则成为可能。在完全信息下，贝叶斯学习通常会破坏延续价值的单调性，阻碍简单截断规则的应用。我们表明，单侧删失通过限制后验波动恢复了单调性，从而使短视截断规则成为最优选择。通过将搜索边际价值的跨期变化分解为保留价值效应和学习效应，我们推导了在低删失下单调性的必要充分条件，并刻画了最优截断规则。相比之下，在完全披露下，单调性需要非常严格的条件。我们进一步证明，期望单调性（即上鞅性质）在低删失和完全披露下由相同条件刻画，这归因于贝叶斯合理性和问题的仿射结构。因此，删失并非通过改变期望学习，而是通过降低后验波动来恢复单调性。最后，我们将该框架应用于求职、消费者价格搜索和产品实验。
英文摘要
This paper studies how information censoring enables a myopic cutoff rule in Bayesian sequential search. Under full information, Bayesian learning generally destroys the monotonicity of continuation values, preventing simple cutoff rules. We show that one-sided censoring restores monotonicity by limiting posterior fluctuations, thereby making a myopic cutoff rule optimal. By decomposing the intertemporal change in the marginal value of search into a fallback-value effect and a learning effect, we derive necessary and sufficient conditions for monotonicity under lower censoring and characterize the optimal cutoff rule. In contrast, under full revelation, monotonicity requires highly restrictive conditions. We further show that expected monotonicity (i.e., the supermartingale property) is characterized by the same conditions under both lower censoring and full revelation, owing to Bayes plausibility and the affine structure of the problem. Thus, censoring restores monotonicity not by altering expected learning, but by reducing posterior volatility. Finally, we apply our framework to job search, consumer price search, and product experimentation.
