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 poolqualities 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 loopbetween 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 .
I study endogenous learning dynamics for people expecting systematic reversals from random sequences -- the "gambler's fallacy . " Biased agents face an optimal-stopping problem, such as managers conducting sequential interviews. They are uncertain about the underlying distribution (e.g. talent distribution in the labor pool) and must learn its parameters from previous agents' histories. Agents stop when early draws are deemed "good enough," so predecessors' histories contain negative streaks but not positive streaks. Since biased learners understate the likelihood of consecutive below-average draws, histories induce pessimistic beliefs about the distribution's mean. When early agents decrease their acceptance thresholds due to pessimism, later learners will become more surprised by the lack of positive reversals in their predecessors' histories, leading to even more pessimistic inferences and even lower acceptance thresholds -- a positive-feedback loop. Agents who are additionally uncertain about the distribution's variance believe in fictitious variation (exaggerated variance) to an extent depending on the severity of data censoring. When payoffs are convex in the draws (e.g. managers can hire previously rejected interviewees), variance uncertainty provides another channel of positive feedback between past and future thresholds .
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In the context of a sequential search problem, I explore large-generations
I study endogenous
R
agents who suffer from
people expecting systematic reversals from random sequences --
A
.
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- the statistical bias of anticipating too much regression to the mean for realizations of independent random events. Searchers
Biased agents face an optimal-stopping problem, such as managers conducting sequential interviews. They
R
search poolqualities 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 loopbetween 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
the underlying distribution (e.g. talent distribution in the labor pool) and must learn its parameters from previous agents' histories. Agents stop when early draws are deemed "good enough," so predecessors' histories contain negative streaks but not positive streaks. Since biased learners understate the likelihood of consecutive below-average draws, histories induce pessimistic beliefs about the distribution's mean. When early agents decrease their acceptance thresholds due to pessimism, later learners will become more surprised by the lack of positive reversals in their predecessors' histories, leading to even more pessimistic inferences and even lower acceptance thresholds -- a positive-feedback loop. Agents who are additionally uncertain about the distribution's variance believe in fictitious variation (exaggerated variance) to an extent depending on the severity of data censoring. When payoffs are convex in the draws (e.g. managers can hire previously rejected interviewees), variance uncertainty provides another channel of positive feedback between past and future thresholds