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We study a model of retrospective search in which an agent—a researcher, an online shopper, or a politician—tracks the value of a product. Discoveries beget discoveries and their observations are correlated over time, which we model using a Brownian motion. The agent decides both how ambitiously, or broadly, to search, and for how long. We fully characterize the optimal search policy and show that it entails constant scope of search and a simple stopping boundary. We also show the special features that emerge from contracting with a retrospective searcher.
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