Pandora{'}s Box Problem with Correlations: Some Results for the Case of Stochastic Dominance

We consider a version of Pandora’s box problem in which the distributions of the various alternatives’ utilities are ranked by first-order stochastic dominance and possibly correlated. Under independence, Weitzman’s optimal search rule prescribes inspecting the dominant alternative first. We show that, with correlation, this sampling order remains optimal if there are two alternatives, each with only two possible utility levels. Next, we show that, with three possible utility levels for each alternative, inspecting the dominated alternative first can be optimal: we provide sufficient conditions for this to happen.