Elimination Contests with Fatigue

We study the effect of fatigue in all-pay elimination contests with two competing semifinalists and one finalist. Higher effort by the semifinal winner leads to more fatigue in the final which we model by a decreased valuation or, equivalently, higher effort cost. The introduction of fatigue might increase total equilibrium effort and equilibrium effort in each round under the optimal seeding. When the semifinal prize is small, a sufficient, but not necessary condition is given by the exclusion principle (Baye, Kovenock and de Vries, 1993). We analyze the effect of fatigue on winning probabilities and an extension to two semifinals. Our results highlight that a contest designer might use fatigue as an optimal design feature in lobbying, sports, and innovation contests.