Searching for Arms: Experimentation with Endogenous Consideration Sets

Abstract: We study the problem of a decision maker alternating between exploring existing alternatives in the consideration set and searching for new ones. We characterize the optimal policy and its key properties, and identify implications for search and exploration dynamics. When the search technology is stationary, or improves over time, search is equivalent to replacement. With deteriorating technologies, instead, alternatives are revisited after search is launched and each expansion is treated as if it were the last one. A key consequence of the endogeneity of the consideration set is that an improvement in the desirability of a category of alternatives may lead

to a reduction in the exploration of the category as well as in the eventual selection of an alternative from that category. We apply the analysis to clinical trials, experimentation toward regulatory approval, and consumer search.