Fostering collaboration

We study project selection and development by a principal, interacting with two agents each of whom wants their respective project selected. When the best choice is uncertain, keeping both projects alive gives the principal the ability to adapt its choice in the future, but implies an efficiency loss of effort being spent on the project finally not chosen. We show a time-varying threshold rule is uniquely optimal: the principal selects the first project to achieve a sufficient lead. The optimum entails initial competition, always followed by permanent collaboration. Our proof uses martingale time-change methods applying weak solutions.