Incentive Compatibility: Everywhere vs. Almost Everywhere∗

A risk neutral buyer observes a private signal s ∈ [a, b], which informs her that the mean and variance of a normally distributed risky asset are s and σ s respectively. She then sets a price at which to acquire the asset owned by risk averse “outsiders”. Assume σ s ∈ { 0, σ } for some σ > 0 and let B = { s ∈ [a, b] | σ s = 0 } . If B = ∅, then there exists a fully revealing equilibrium in which trade occurs. If B = ∅, no such equilibrium can exist, even if B is of measure zero. ∗We thank Roger Myerson, George Mailath and Drew Fudenberg for helpful remarks. †Economics Discipline, SEPS , University of Sydney, Sydney NSW 2006, AUSTRALIA. [email protected] ‡MIT Sloan, 50 Memorial Drive E52-410, Cambridge MA 02142. [email protected] 1