Bayesian Sequential Search with Censored Observations

2026-08-14

AI Summary

This study addresses the non-monotonicity of continuation values under full information in Bayesian sequential search, which impedes the application of truncation rules. We propose an information censoring mechanism that restores value monotonicity by revealing that one-sided censoring reduces posterior volatility without altering expected learning. Leveraging marginal value decomposition and supermartingale analysis, we derive necessary and sufficient conditions for the optimality of myopic truncation rules and establish a unified framework characterizing expected monotonicity. Furthermore, we prove the optimality of truncation rules under low censoring regimes and demonstrate their successful application to job search and pricing scenarios. Collectively, this work provides a concise yet effective theoretical solution for complex sequential search problems where standard stopping criteria typically fail due to information structure complications.

Abstract

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.

Problem

• Bayesian sequential search
• censored observations
• myopic cutoff rule
• monotonicity
• posterior volatility

Innovation

• Bayesian Sequential Search
• Information Censoring
• Myopic Cutoff Rule
• Monotonicity
• Posterior Volatility