Mislearning from Censored Data: Gambler's Fallacy in a Search Problem
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In the context of a sequential search problem, I explore large-generations learning dynamics for agents who suffer from the "gambler's fallacy" - the statistical bias of anticipating too much regression to the mean for realizations of independent random events. Searchers are uncertain about search pool qualities of different periods but infer these fundamentals from search outcomes of the previous generation. Searchers' stopping decisions impose a censoring effect on the data of their successors, as the values they would have found in later periods had they kept searching remain unobserved. While innocuous for rational agents, this censoring effect interacts with the gambler's fallacy and creates a feedback loop between distorted stopping rules and pessimistic beliefs about search pool qualities of later periods. In general settings, the stopping rules used by different generations monotonically converge to a steady-state rule that stops searching earlier than optimal. In settings where true pool qualities increase over time - so there is option value in rejecting above-average early draws - learning is monotonically harmful and welfare strictly decreases across generations.
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