A Simple Model of Crowdfunding Dynamics

Abstract

This paper develops a dynamic game with endogenous inspection costs to explain empirically salient bidding profiles in crowdfunding and to characterize how success rates vary with design parameters. In the baseline, bidders arrive at a constant rate and face an inspection cost to learn if they like the crowdfunder's product. The average funding profile is weakly decreasing over time for any fixed inspection cost. Heterogeneity and a relatively high threshold can generate an increasing bid profile: only low inspection cost types inspect at first but their bids tend to convince higher types to start inspecting over time. The addition of a group of contacts who can bid on the project at the start of the campaign can give rise to a bimodal or U-shaped profile. We also derive a U-shape without this but the conditions are more restrictive. Moreover, to explain a more pronounced final peak or upturn in the U-shape, we extend to allow for endogenous timing by letting some bidders choose to wait before inspecting. We also study how conditioning on project success or fail- ure affects funding profiles and solve a continuous-time version of the model. We conclude with implications for success rates and lessons for optimal design.