Two-stage elimination games

We study two-stage elimination games with four heterogeneous players. In the first stage, the players are allocated into two contests, each of which includes two players competing against each other in an all-pay auction. The winners of the two contests then interact with each other in the second stage. The outcomes of the interaction in the second stage are given by a general form of the players’ payoffs as functions of their types (abilities). Then, we examine the effect of the timing of the competitions in the first stage on the players’ expected payoffs and their total effort. In particular, we show that if the players’ payoff functions in the second stage are separable in the players’ types, then the timing of play in the first stage of either simultaneous or sequential contests has no effect on the players’ expected payoff as well as their total effort in the elimination games.