Yu Fu Wong

Spatial Experimentation: Optimal Costly Exploration of Correlated Alternatives

Conditionally accepted at Theoretical Economics

I study how a forward-looking decision maker experiments on unknown alternatives of spatially correlated utilities, modeled by a Brownian motion so that similar alternatives yield similar utilities. For example, a firm experiments on its size that yields unknown, spatially correlated profitability. Experimentation trades off the opportunity cost of exploitation for the indirect inference from the explored alternatives to unknown ones. The optimal strategy is to explore unknown alternatives and then exploit the best known alternative when the explored becomes sufficiently worse than the best. The decision maker explores more quickly as the explored alternative worsens. My model predicts the conditional Gibrat's law and linear relation between firm size and profitability.

This paper provides a model of strategic exploration in which competing players independently explore a set of alternatives. The model features a multiple-player multiple-armed bandit problem and captures a strategic tradeoff between preemption—covert exploration of alternatives that the opponent will explore in the future—and prioritization—exploration of the most promising alternatives. Our results explain how the strategic tradeoff shapes equilibrium behaviors and outcomes, e.g., in technology races between superpowers and R&D competitions between firms. We show that players compete on the same set of alternatives, leading to duplicated search from start to finish, and they explore alternatives that are a priori less promising before more promising ones are exhausted. The model also predicts that competition induces players to implement unreliable technologies too early, even though they should wait for the technology to mature. Coordinated exploration is impossible even if the alternatives are equally promising, but it can emerge in equilibrium following a phase of preemptive competition if there is a short deadline. With asymmetric capacities of exploration, the weak player conducts extensive instead of intensive exploration—exploring as many alternatives as the strong player does but never fully exploring any.