Dynamic Models for Selling Multiple Items∗

We study the optimal strategy for selling multiple items in a setting where bidders can bid for individual items and for subsets of items. There is a large literature examining search problems with a single good, but few papers that generalize the problem to vector offers for subsets of items. One of the challenges in extending to multiple goods is that, as the state space expands, the problem can become computationally intractable. We show how to solve the dynamic optimization problem so that it becomes computationally feasible when the number of items is not too large. We also consider special cases of the model, including an “additive” case and a “single item” case, and present several intuitive structural results about the optimal policy and value functions for these specialized cases. Finally, we consider extensions to a stopping rule problem. JEL Classification Numbers: C61, D83.