What happens when a buyer and a seller each have private information about the value of an item for trade, as is particularly common in real estate? We solve for the equilibrium price under both public information, where the seller shares his information with the buyer, and private information, where the seller is constrained to be unable to credibly share. Our main results are 1) even under public information, the equilibrium price differs from the expected value of the item, 2) under private information, prices follow a step function, with small changes in information generically having no effect on price, and 3) equilibrium price is more sensitive to informational changes under private information than public information. This under-studied game of 2-sided asymmetric information reasonably describes real estate transactions.