Optimal learning before choice

Abstract

© 2019 Elsevier Inc. A Bayesian decision maker is choosing among two alternatives with uncertain payoffs and an outside option with known payoff. Before deciding which alternative to adopt, the decision maker can purchase sequentially multiple informative signals on each of the two alternatives. To maximize the expected payoff, the decision maker solves the problem of optimal dynamic allocation of learning efforts as well as optimal stopping of the learning process. We show that the decision maker considers an alternative for learning or adoption if and only if the expected payoff of the alternative is above a threshold. Given both alternatives in the decision maker's consideration set, we find that if the outside option is weak and the decision maker's beliefs about both alternatives are relatively low, it is optimal for the decision maker to learn information from the alternative that has a lower expected payoff and less uncertainty, given all other characteristics of the two alternatives being the same. If the decision maker subsequently receives enough positive informative signals, the decision maker will switch to learning the better alternative; otherwise the decision maker will rule out this alternative from consideration and adopt the currently more preferred alternative. We find that this strategy works because it minimizes the decision maker's learning efforts. We also characterize the optimal learning policy when the outside option is relatively high, and discuss several extensions.