Equilibrium Voluntary Disclosures when Firms Possess Random Multi-Dimensional Private Information

Abstract

This paper presents an equilibrium model of voluntary disclosures for the seller of an asset who receives a random sample of information of random size about the asset’s value. Even though (a) antifraud rules prevent the seller from making false statements about the value of the items in his random sample, (b) all potential purchasers of the asset know that the seller’s random sample always contains at least one sample element, (c) all potential purchasers of the asset interpret the seller’s disclosure or nondisclosure in the same way, and (d) disclosure of any or all of the seller’s sample information generates no proprietary costs, we show that in equilibrium there is a positive probability that the seller will make no disclosure at all, and that, when the seller makes no disclosure, the nondisclosed information is not the worst possible sample information the seller could have had about the asset’s value. These results are contrasted with the “unravelling” result of [Grossman [1981]], [Grossman and Hart [1980]], and [Milgrom [1981]]. We show that, were potential purchasers of the asset to know the size of the seller’s random sample, “unravelling” (i.e., full disclosure) would occur. We conclude that the randomness of the seller’s sample size is key to determining the seller’s equilibrium voluntary disclosure strategy.