Searching for Arms: Experimentation with Endogenous Consideration Sets

Abstract: A decision-maker alternates between exploring alternatives in a consideration set and searching for new ones. The problem admits an index solution, featuring a novel recursive index for the expansion of the consideration set. When the expansion technology is stationary or improving, newly discovered alternatives replace existing ones. When it deteriorates, previously discovered alternatives are revisited, and each expansion is effectively treated as the last. We apply the results to the design of procurement mechanisms in environments where a buyer faces uncertainty about the number, costs, and quality of potential suppliers, and must trade off learning about existing suppliers against soliciting new ones. On the positive side, the analysis shows that firms discovered later in the process enjoy higher expected profits, all else equal, and it identifies primitive conditions under which the buyer becomes more (or less) lenient with incumbents after each expansion. On the normative side, the analysis reveals that low-cost firms contribute to inefficient entrenchment with incumbents, whereas high-cost firms contribute to excessive solicitation. Joint work with Alessandro Pavan.