Three-player contests with a potential inactive player: Endogenous timing of effort exertion

We study a contest where there are two active players in equilibrium when three players expend effort simultaneously to win a prize. We look at how endogenous timing of effort exertion affects the players' behavior. The players play the following game. First, they announce simultaneously whether they each will expend effort in period 1 or in period 2. Then, after knowing when they expend effort, each player expends effort in the period which he announced. We find interesting results, focusing on the players' decisions on when to expend effort, the identities of active players, and the effort levels in a subgame-perfect equilibrium.