Winner's effort in multi-battle team contests

In multi-battle team contests with pairwise battles, how battles are organized—sequentially or (partially) simultaneously—may affect the expected winner's total effort (WE), a natural objective in R&D races, elections, and sports. We focus on noise (modeled via the contest success function's discriminatory power) and across-team heterogeneity, abstracting from player-specific heterogeneity. With sufficient noise, we show that: (1) If teams are symmetric, all temporal structures yield the same WE; and (2) If teams are asymmetric, WE is maximized by a fully simultaneous contest and minimized by a fully sequential one. With no noise, we show that: (3) If teams are symmetric, WE is maximized by a fully sequential contest and minimized by a fully simultaneous one; and (4) If teams are asymmetric, neither the fully sequential nor the fully simultaneous temporal structures maximize or minimize WE. Our results use a novel technique that simplifies temporal structure comparisons: extractions and mergers.