🤖 AI Summary
This study investigates how decision-makers dynamically choose what to explore and when to stop before taking action. By reformulating the dynamic exploration–stopping problem as a static optimization with an information budget constraint, the authors introduce an information shadow price and establish that the optimal policy exhibits a concavified structure of stopping gains net of this shadow price. They precisely characterize, for the first time, the set of attainable joint distributions and uncover the critical role of time preference curvature in shaping exploration: convex preferences induce Poisson-like exploration, whereas concave preferences restrict stopping to specific time windows. The framework also elucidates the emergence of pure exploration phases and is unifiedly applied to real options, speed–accuracy trade-offs, and continuous-time exploration contests, clearly delineating the structural impact of time preferences and information costs on exploration behavior.
📝 Abstract
We study a decision-maker who explores --- dynamically choosing what to learn --- before stopping to act. We first reduce this dynamic control problem to a static one: any exploration-and-stopping strategy is equivalent to a choice of the joint distribution of the stopped state and the stopping time, subject to one information-budget constraint at each date, and we characterize exactly which distributions are attainable. The reduced problem is a convex program with a linear objective; its dual prices information over time, and the optimal policy concavifies the stopping payoff net of these shadow prices. The curvature of the decision-maker's time preference then governs the shape of optimal exploration: convex time preference induces Poisson exploration, concave time preference confines stopping to a window whose length is controlled by the dispersion of the marginal cost of delay --- forcing an initial phase of pure exploration when the window is short --- and the linear case lies at the boundary between them. We apply the framework to real options, to the speed--accuracy tradeoff in information acquisition, and to a continuous-time exploration contest.