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Many firms use external contests to obtain solutions to their innovation challenges. A central managerial concern is how to screen the population for only the most capable people when the capability of the population is not known. If the manager sets the bar too high, then the contest could fail, leaving the firm to suffer the consequences. Alternatively, if the bar is set too low, then too many people enter, which leads to increased competition, a lack of effort, and diminished performance, again leaving the firm to suffer the consequences. We study a situation in which the number of solvers in a population is known but the ability of each individual is not. At best, the firm can deduce the probability that any number of solvers would enter and the probability that any solver who enters would possess a specific ability. We derive the optimal contest design to maximize the performance of the best submission while accounting for the possibility that the contest receives an insufficient number of entries, resulting in an unproductive contest. Our results provide an alternative rationale for why many contests offer multiple awards: firms want to avoid an unproductive contest and the negative consequences associated with it. We also consider alternative levers available to the firm when facing uncertain participation. These include the establishment of performance thresholds and the decision to expand the potential solver population.

This paper was accepted by Charles Corbett, operations management.

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