DP15018 Sequential Learning with Endogenous Consideration Sets
We study the problem of a decision maker alternating between exploring existing alternatives and searching for new ones. We show that the decision to search depends on the composition of the consideration set only through the information the latter contains about the probability of finding new alternatives. 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. The analysis yields a formula for pricing new alternatives and/or the option to expand the consideration set in the future. We also show how to accommodate for certain irreversible choices that admit as special case a generalization of Weitzman’s (1979) “Pandora’s boxes” problem in which the set of boxes is endogenous and each alternative may require multiple explorations before it can be selected.