Dynamic search models with multiple items

We generalize the classic dynamic single-item search model to a setting with multiple items and vector offers for subsets of items. We first show a computationally feasible way to solve the dynamic optimization problem, and then prove structural results. Although assignment is not generally monotonically increasing in offer value, we show that, in a special case “additive” model, monotonicity holds if costs are submodular. We examine how the thresholds for assignment change with the remaining items, and whether there are gains to grouping searches. Finally, we consider a stopping rule version of the problem with no subsets for sale, showing the optimal policy is myopic.