  We study competition among contests in a general model that allows for an
arbitrary and heterogeneous space of contest design, where the goal of the
contest designers is to maximize the contestants' sum of efforts. Our main
result shows that optimal contests in the monopolistic setting (i.e., those
that maximize the sum of efforts in a model with a single contest) form an
equilibrium in the model with competition among contests. Under a very natural
assumption these contests are in fact dominant, and the equilibria that they
form are unique. Moreover, equilibria with the optimal contests are
Pareto-optimal even in cases where other equilibria emerge. In many natural
cases, they also maximize the social welfare.
