Bilateral trade with apositional traders

We study the standard model of bilateral trade under incomplete information dropping the assumption that traders know on which side of the market they are. We consider two mechanisms that differ only in the number of offers that an agent can submit. These mechanisms are realistic and they are ex post individually rational (i.e. regret free), while the usual mechanisms proposed in the literature satisfy the weaker requirement of interim individual rationality. Properties of the Bayesian equilibria are described for the general case. For the case where valuations are uniformly distributed in the unit square, two types of equilibria are derived for each mechanism and their efficiency properties are analyzed. As expected, the equilibria under the double offer mechanism are less inefficient than those under the single offer mechanism.