Efficient crowdsourcing contests

A principal seeks production of a good within a limited timeframe with a hard deadline, after which any good procured has no value. There is inherent uncertainty in the production process, which in light of the deadline may warrant simultaneous production of multiple goods by multiple producers despite there being no marginal value for extra goods beyond the maximum quality good produced. This motivates a crowdsourcing model of procurement. We address efficient execution of such procurement from a social planner's perspective, taking account of and optimally balancing the value to the principal with the costs to producers (modeled as effort expenditure) while, crucially, contending with self-interest on the part of all players. A solution to this problem involves both an algorithmic aspect that determines an optimal effort level for each producer given the principal's value, and also an incentive mechanism that achieves equilibrium implementation of the socially optimal policy despite the principal privately observing his value, producers privately observing their skill levels and effort expenditure, and all acting selfishly to maximize their own individual welfare. In contrast to popular "winner take all" contests, the efficient mechanism we propose involves a payment to every producer that expends non-zero effort in the efficient policy.