In an innovation contest, a firm (the seeker) facing an innovation-related problem (e.g., a technical R&D problem) posts this problem to a population of independent agents (the solvers) and then provides an award to the agent that generated the best solution. In this paper, we analyze the interaction between a seeker and a set of solvers. Prior research in economics suggests that having many solvers work on an innovation problem will lead to a lower equilibrium effort for each solver, which is undesirable from the perspective of the seeker. In contrast, we establish that the seeker can benefit from a larger solver population because he obtains a more diverse set of solutions, which mitigates and sometimes outweighs the effect of the solvers' underinvestment in effort. We demonstrate that the inefficiency of the innovation contest resulting from the solvers' underinvestment can further be reduced by changing the award structure from a fixed-price award to a performance-contingent award. Finally, we compare the quality of the solutions and seeker profits with the case of an internal innovation process. This allows us to predict which types of products and which cost structures will be the most likely to benefit from the contest approach to innovation.