We study a contract design problem between a principal and multiple agents. Each agent participates in an independent task with binary outcomes (success or failure), in which she may exert costly effort towards improving her probability of success, and the principal has a fixed budget which it can use to provide outcome-dependent rewards to the agents. Crucially, each agent's reward may depend not only on whether she succeeds or fails, but also on whether other agents succeed or fail, and we assume the principal cares only about maximizing the agents' probabilities of success, not how much of the budget it expends. A motivating example might be that of a sales manager who is endowed with a fixed budget by the firm and is tasked with incentivizing the salespeople to successfully close sales. The manager can observe whether each salesperson was able to sell the product or not, but now how much effort the salesperson exerted towards making the sale.

Contests are situations in which agents compete with one another by exerting costly effort to win valuable prizes. In this paper, we consider contest environments where participants have private information about their ability and the contest designer can manipulate the values of different prizes to influence the effort exerted by them. In such environments, with the goal of understanding how different contests compare in terms of the effort they induce, we study the effect of two different interventions on effort: