Mislearning from censored data: The gambler's fallacy and other correlational mistakes in optimal‐stopping problems

I study endogenous learning dynamics for people who misperceive intertemporal correlations in random sequences. Biased agents face an optimal‐stopping problem. They are uncertain about the underlying distribution and learn its parameters from predecessors. Agents stop when early draws “good enough,” so predecessors' experiences contain negative streaks but not positive streaks. When wrongly expect systematic reversals (the “gambler's fallacy”), they understate likelihood of consecutive below‐average draws, converge to overpessimistic beliefs distribution's mean, too early. variance overestimate it extent that depends on stopping thresholds. also analyze how other misperceptions correlation interact with data censoring.