Optimal tree contest design and winner-take-all

This paper investigates the effort-maximizing design of multi-stage contests with tree-like architectures, focusing on both contest architecture and prize structure. Given the architecture, we show that the whole budget should be assigned to a single match. This match must be the final if the architecture is symmetric. Moreover, the winner-take-all rule proves to be optimal if the contest organizer can jointly design the architecture and prize structure. To determine the optimal contest architecture, we use dynamic programming and induction to provide a tight upper bound for the optimized total effort level. Our new approach extends the findings of Gradstein and Konrad (1999), offering new insights into how the optimal architecture hinges on the noise level of matches.