Common Certainty and Efficiency
with Incomplete Information

• Abstract

Holmstrom-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 do not need to be derived from a prior; (ii) with a notion of common certainty instead of common knowledge. More importantly, we strengthen the Holmstrom-Myerson result 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.

• Old version (2016 Dec) :

Title: Common Knowledge and Efficiency with Incomplete Information

Abstract: Holmstrom-Myerson (1983) show that we need only check for efficiency on common knowledge events to determine that an incentive compatible decision rule is efficient. On adapting the probabilistic version of the definition of common knowledge suggested by Brandenburger-Dekel (1987), we strengthen the Holmstrom-Myerson result by showing that we need only check for efficiency in a strict subset of common knowledge events known as self-evident events and furthermore, that this is the minimal class of events that one needs to inspect.