We propose and study a threshold utility model (TUM) where consumers buy any product whose net utility exceeds a non-negative, product-specific threshold. The thresholds are selected to maximize the expected surplus of the representative consumer subject to a bound on the expected number of...

In the k-prophet problem, a decision maker observes n items sequentially and selects up to k n items without recourse to maximize the total expected reward of the selected items. We consider a soft version of the problem where the decision maker can select up to k items in expectation rather...