When to stop? A Theoretical and experimental investigation of an individual search task

Information search and opinion formation are central aspects of decision making in consumers choices. Indeed, before taking a decision, the alternatives among which the rational choice will be made should be clearly valued. In standard economic theory, the search dynamics is generally neglected because the process is assumed to be carried out without any cost or without spending time. However, whenever only a significant collection of experience can provide the bulk of relevant information to make the best choice, as it is the case for experience goods (Nelson, 1970), some engendered costs in collecting such information might be considered. Our paper lies on a conceptual framework for the analysis of an individual sequential search task among a finite set of alternatives. This framework is inspired by both the Secretary problem (Ferguson et al., 1989) and the multi-armed bandit problem (Robbins, 1952). We present a model where an individual is willing to locate the best choice among a set of alternatives. The total amount of time for searching is finite and the individual aims at maximizing the expected payoff given by an exploration-exploitation trade-off: a first phase for exploring the value of new alternatives, and a second phase for exploiting her past collected experience. The task involves an iterative exploitation – i.e., where the final payoff does not only depend on the value of the chosen alternative, but also on the remaining time that has not been dedicated to exploration –. Given the finite horizon of time, the optimal stopping strategy can be assimilated to a satisficing behavior (Simon, 1956). We manipulate the degree of certainty of information, and we find that the optimal stopping time is later under the uncertain information condition. We experimentally test the model's predictions and find a tendency to oversearch when exploration is costly, and a tendency to undersearch when exploration is relatively cheap. We also find under the certain information condition that participants learn to converge towards the optimal stopping time, but this learning effect is less present under the uncertain information condition. Regret and anticipation lead to more exploration under both information conditions. A gender effect is also exhibited with women tending to explore more than men.