Theoretical Economics, Volume 16, Number 4 ( 2021)

Theoretical Economics 16 (2021), 1431–1470

Robust sequential search

Karl H. Schlag, Andriy Zapechelnyuk


We study sequential search without priors. Our interest lies in decision rules that are close to being optimal under each prior and after each history. We call these rules robust. The search literature employs optimal rules based on cutoff strategies, and these rules are not robust. We derive robust rules and show that their performance exceeds 1/2 of the optimum against binary i.i.d. environments and 1/4 of the optimum against all i.i.d. environments. This performance improves substantially with the outside option value, for instance, it exceeds 2/3 of the optimum if the outside option exceeds 1/6 of the highest possible alternative.

Keywords: Sequential search, search without priors, robustness, dynamic consistency, competitive ratio

JEL classification: D83, D81, C44

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