Alessandro Pavan, Northwestern University

Searching for Arms

Abstract:  We introduce a model of experimentation in which the set of alternatives is endogenously shaped by past search decisions. The environment reflects a tradeoff between exploration of existing alternatives and search for additional ones, in the face of uncertainty about the set of outside alternatives that may be discovered. Despite the effect of search on the future set of alternatives and potential correlation between the types of alternatives found over time, we obtain a simple characterization of the optimal policy. As a special case, the analysis yields a generalization of Weitzman’s (1979) canonical sequential search problem, and its solution, to an environment in which the set of boxes is endogenous. Finally, we extend our analysis to environments in which an irreversible choice may be made among the endogenous set of alternatives, at any time and given any amount of information.