When Less Information is Good for Efficiency: Private Information in Bilateral Trade and in Markets

We consider a simple bilateral trading game between a seller and a buyer who have private valuations for an indivisible good. The seller makes a price offer which the buyer can either accept or reject. If the seller can observe the valuation of the buyer (if information is symmetric), then the trading outcome is trivially efficient. If the seller can not observe the valuation (if information is asymmetric), then the outcome must be inefficient, as is known from the Myerson-Satterthwaite Impossibility Theorem. We embed this bilateral trading game between a single buyer and a single seller into a matching market with a continuum of traders. We show that in this market the relation between information and efficiency is reversed. In particular, if information is symmetric, trading in the market is, in fact, inefficient.