The beauty of "bigness" in contest design: merging or splitting?

This paper studies in a multiple-winner contest setting how the total efforts may vary between a grand contest and a set of subcontests. We first show that the rent-dissipation rate increases when the numbers of contestants and prizes are "scaled up". In other words, the total efforts of a contest exhibit a striking "increasing return to scale" property: when the numbers of contestants and prizes scale up proportionally, the total efforts of the contest increase more than proportionally. Thus, the total efforts must increase when a set of identical subcontests are merged into a grand contest. Equivalently, the total efforts decrease when a grand contest is evenly divided. We further allow the grand contest to be split into uneven subcontests. We show that under a mild and plausible condition (regular contest technology), the grand contest generates more efforts as compared to any split contests.