Contingent stimulus in crowdfunding

Archimedes once said "give me a fulcrum, and I shall move the world." In this paper, we study the optimal timing of contingently placing a "fulcrum" in the context of crowdfunding, with the potential of tilting the random pledging process from failure to success. Specifically, we consider a model where backers arrive sequentially at a crowdfunding project. Upon arrival, a backer makes her pledging decision by taking into account the expected success of the project. We characterize the dynamics of a project's pledging process. In particular, we show that there exists a "cascade effect" on backers' pledging, which is mainly driven by the all-or-nothing nature of crowdfunding projects. According to our data collected from the most popular online crowdfunding platform, the majority of projects fail to achieve their goals. To address this issue, we propose three contingent stimulus policies, namely, seeding, feature upgrade and limited-time offer. We show that the optimal stimulus policies have a cutoff-time structure, and that the benefit of contingent policies is greatest in the middle of crowdfunding campaigns. Testing with the data set of Kickstarter, we obtain empirical evidence that the projects' success rates improve by 14.6% on average with updates in the middle of the campaign and when the pledging progress is lagging