This paper explores price formation when sellers are privately informed about their preferences and the quality of their asset. There are many equilibria, including a semi-separating one in which each seller's price depends on a one-dimensional index of her preferences and asset quality. This multiplicity does not rely on off-the-equilibrium path beliefs and so is not amenable to standard signaling game refinements. The semi-separating equilibrium may not be Pareto efficient, even if it is not Pareto dominated by any other equilibrium. Instead, efficient allocations may require transfers across uninformed buyers, inconsistent with any equilibrium.
Guerrieri, Veronica, and Robert Shimer.
"Markets with Multidimensional Private Information."
American Economic Journal: Microeconomics,
Consumer Economics: Theory
Asymmetric and Private Information; Mechanism Design