Winners' Efforts in Multi-Battle Team Contests

Multi-battle team contests are ubiquitous in real-life competitions. All temporal structures of multi-battle team contests yield the same total effort, as demonstrated by Fu, Lu, and Pan (2015, American Economic Review, 105(7): 2120-40)'s remarkable temporal-structure independence. Rather than total effort, we focus on winners' efforts, a natural objective in R&D races, elections, and sports. We show that, among all possible temporal structures, winners' efforts are maximized (minimized) by a fully simultaneous (sequential) contest. Furthermore, while total effort is unaffected by battle ordering (sequence independence), we show that winners' efforts are minimized in a fully sequential contest where battles are ordered from hardest to easiest