We examine behavior in a two-stage group contest where intra-group contests are followed by an inter-group contest. Rewards accrue to the winning group, with winners of the intra-group contest within that group receiving a greater reward. The model generates a discouragement effect, where losers from the first stage exert less effort in the second stage than winners. In contrast to the related literature, we show that a prior win may be disadvantageous, generating lower profits for first stage winners as compared to losers. We consider exogenous asymmetry between groups arising from a biased group contest success function. Although the asymmetry occurs in the second stage, its effect plays out in the first stage, with higher intra-group conflict in the advantaged group. Experimental results support the qualitative predictions of the model. However, losers from the first stage bear a higher burden of the group contribution than the theoretical prediction.