In this paper we present and analyze a model in which users select among, and subsequently compete in, a collection of contests offering various rewards. The objective is to capture the essential features of a crowdsourcing system, an environment in which diverse tasks are presented to a large community. We aim to demonstrate the precise relationship between incentives and participation in such systems.
We model contests as all-pay auctions with incomplete information; as a consequence of revenue equivalence, our model may also be interpreted more broadly as one in which users select among auctions of heterogeneous goods. We present two regimes in which we find an explicit correspondence in equilibrium between the offered rewards and the users’ participation levels. The regimes respectively model situations in which different contests require similar or unrelated skills. Principally, we find that rewards yield logarithmically diminishing returns with respect to participation levels. We compare these results to empirical data from the crowdsourcing site Taskcn.com; we find that as we condition the data on more experienced users, the model more closely conforms to the empirical data.