Fatigue accumulation in dynamic contests

We study a dynamic contest model where efforts exerted in previous periods accumulate as fatigue. As an individual's fatigue level increases, it becomes more costly to exert one unit of effort in the future. This creates a trade-off between exerting high efforts today to collect winning prizes sooner and exerting low efforts today to gain a cost advantage in the future. We characterize the steady state conditions for open-loop equilibrium and analyze equilibrium efforts in the presence of accumulated fatigue.