Two-stage contests with effort-dependent values of winning

We study two-stage all-pay contests in which synergy exists between the stages. The value of winning for each contestant is fixed in the first stage while it is effort-dependent in the second one. We assume that a player’s effort in the first stage either increases (positive synergy) or decreases (negative synergy) his value of winning in the second stage. The subgame perfect equilibrium of this contest is analyzed with either positive or negative synergy. We show, in particular, that whether the contestants are symmetric or asymmetric their expected payoffs may be higher under negative synergy than under positive synergy. Consequently, they prefer smaller values of winning (negative synergy) over higher ones (positive synergy).