On a typical crowdsourcing platform solvers can self-select which (if any) of the concurrently running contests to participate in. Thus, firms which offer prizes and organize contests on these platforms are competing among themselves (for solver participation and effort). We formalize and model this competition among contests and examine the equilibrium outcomes. Our analysis reveals that, in general, there is a unique dominant strategy for each firm to offer multiple identical prizes. Moreover, when the quality of submitted solutions is sufficiently noise-driven (as opposed to effort-driven), we find that a single winner-take-all reward is the unique equilibrium allocation. Our analytical framework integrates and extends prior results of the monopolistic contest.