Abstract
A principal may know the interim distribution of agent types rather than the ex-ante distribution. For example, she may have information about types but not be permitted to discriminate due to anonymity or legal restrictions. This setting is rarely studied in mechanism design because full surplus extraction is trivial. However, this setting is frequently studied in contest design where functional form assumptions prevent trivial results. We model contest design as a general allocation rule without any functional form assumptions. Instead, we impose efficiency, the requirement that the entire prize budget must be allocated in response to any bid profile. This condition holds in all popular contest forms. We find that efficiency is sufficient to prevent full surplus extraction when there is only one marginal player. In the two-player case, the overall optimal contest is one of two popular models: an all-pay auction with bid caps when heterogeneity is low or a difference-form contest when heterogeneity is high.