Dynamic contests with resource constraints

We study a dynamic contest between two players who compete against each other in n different stages. The players have winning values for each stage of the contest that may vary across the stages as well as heterogeneous resource budgets that decrease from a given stage to the next proportionally to the resources allocated in that stage. We characterize a subgame perfect equilibrium of this dynamic contest and show that when the winning value is equal between the stages, the players' resource allocations are weakly decreasing over the stages. We also study the effect of several distributions of winning values on the players' resource allocations. We show both the distribution of winning values that balances the players' resource allocations and the distribution of winning values that maximizes the players' total resource allocations.