Common certainty and efficiency with incomplete information

Holmström and Myerson (1983) show that we need only check for efficiency on common knowledge events to determine that an incentive compatible decision rule is efficient. In this paper, we show that this result still holds in a more general setup: (i) in a type space where the agents’ type does not need to be derived from a prior; (ii) with a notion of common certainty instead of common knowledge. More importantly, we strengthen the Holmström–Myersonresult by showing that we need only check for efficiency in a strict subset of common certainty events known as self-evident events and furthermore, that this is the minimal class of events that one needs to check. When applied to the original setup of HM (a finite state space model with a prior), our result provides a rationale for assuming a strictly positive prior in such a model as it is often observed in applications.