Whether or not to open Pandora's box

Weitzman's [15] search model requires that, conditional on stopping, the agent only takes boxes which have already been inspected. We relax this assumption and allow the agent to take any uninspected box without inspecting its contents when stopping. Thus, each uninspected box is now a potential outside option. This introduces a new trade-off: every time the agent inspects a box, he loses the value of the option to take it without inspection. Nevertheless, we find that, under conditions common in the search and information acquisition literature, boxes are inspected following the same order as in Weitzman's rule; however, the stopping rule is different, and we characterize it. Moreover, we provide additional results that partially characterize the optimal policy when these conditions fail.