Endogenous timing in three-player Tullock contests

We study a three-player Tullock contest in an endogenous-timing framework, focusing on the players' decisions on timing of effort exertion. In this model, there are two points in time at which the players may choose their effort levels. The players decide independently and announce simultaneously when they each will expend their effort, and then each player chooses her effort level at the point in time which she announced. We find that, given moderate asymmetries among the players, each of the players announces the first point in time, and thus they all choose their effort levels simultaneously at the first point in time. This finding is in sharp contrast to a well-known result obtained from two-player asymmetric contests with endogenous timing.