Intertemporal Effort Provision in Sequential Tournaments

This paper analyzes intertemporal effort provision in two-stage tournaments. A principal with a fixed budget for prizes faces two risk-neutral agents. He observes noisy signals of effort in both periods. His goal is to maximize either total efforts (perfect substitutes) or the product of first- and second-period efforts (imperfect substitutes). He decides (i) how to weigh performance in the two periods when awarding the second period prize, (ii) how to spread prize money across the two periods, and (iii) whether to reveal performance after the first period. Under very general conditions, the principal puts positive weight on both periods in period two. Furthermore, he sets no first-period prize provided the observations in period one are too noisy. The information revelation policy depends on the third derivative of the effort cost function.