Searching for Arms

Abstract

We study a model of experimentation in which the set of alternatives is endogenously shaped by past search decisions. The environment reflects a tradeoff between exploring existing alternatives and search for additional ones, in the face of uncertainty about what outside alternatives may be found. We characterize the optimal policy, and show that despite the effect of search on future competition among the alternatives, and potential correlation between the types of alternatives found over time, a simple index policy is optimal. The characterization is used to shed light on the dynamics that arise as a function of the evolution of the search technology. We also apply our results to a class of problems in which an irreversible choice is to be made among the endogenous set of alternatives, and environments with asymmetric information, in which the alternatives correspond to strategic agents. Joint with Alessandro Pavan.