Early contributors, cooperation and fair rewards in crowdfunding

We address the issue of rewarding fairly contributors participating in a funded crowdfunding project. We develop a theoretical non-strategic model of crowdfuding and introduce on a new reward rule, which specifies the individual rewards obtained by the contributors as a function of both their financial contributions and the timing of these contributions. Our model share some similarities with other models of ressource sharing in which the axiomatic method is frequently used. Taking this approach, we characterize this new reward rule by a pair of natural axioms, and it turns out that the resulting rewards coincide with the Shapley value of a suitable cooperative game built from the crowdfunding project. This allocation rule conveys what we call the signaling effect: if two contributors make the same financial contribution, then the earlier of the two obtains a greater reward. In specific but relevant cases, we provide extra properties of this reward rule.