Optimizing successive incentives: Rewarding the past or motivating the future?

We study sequential processes where agents create value through costly and uncertain investments, with success triggering further investment decisions by others. Our paper focuses on designing optimal allocation rules that distribute the total value generated among agents, balancing the recognition of past contributions with incentives for future investments. We prove the existence of equilibrium in the game induced by any such rule and identify a unique investment profile that maximizes the overall expected welfare in the sequential process. This profile can be supported in equilibrium by a simple rule. Additionally, we show that there is a unique investment profile maximizing the initiator's expected payoff and provide a method for the initiator to design a rule supporting it. We extend the model to scenarios where agents' investments are constrained by the value generated within the process. Our findings demonstrate that relatively simple reward structures that prioritize short-term incentives can effectively achieve long-term systemic goals.