Contiguous Search: Exploration and Ambition on Uncharted Terrain

We provide a framework for analyzing search across correlated samples. The agent—a mineral prospecting team, a drug company, a politician—tracks observations over a Brownian path. The agent chooses the search speed and retrospectively picks the best observation when deciding to complete the search. We show that the optimal search speed is U-shaped: it is highest when approaching a breakthrough or when nearing search termination. Unlike search across independent samples, search optimally stops when observations are sufficiently discouraging, following a drawdown stopping boundary. We also show the tractability and features of optimal search contracts in our setting.