The interplay of interdependence and correlation in bilateral trade

Crémer and McLean (1988) show that the seller can extract full surplus almost always by an incentive compatible, individually rational mechanism in a single-unit auction model with a finite type space in which agents' beliefs are correlated and their valuations can be interdependent. We first show that this paradoxically positive result can be extended to a model of bilateral trades. To make it more realistic, we investigate when ex-post efficiency and ex-post budget balance in bilateral trades can also be achieved by an incentive compatible, individually rational mechanism. We identify a necessary condition for the existence of such mechanisms and show that it is also sufficient for a two-type model. We next show that the identified condition is not sufficient in general. Through a series of examples, we show that the imposition of ex post budget balance in a bilateral trade model induces a delicate interaction between interdependent values and correlated beliefs, so that the existence of incentive compatible, individually rational mechanisms becomes a very subtle problem. Finally, focusing on a model with linear valuations, we give the precise sense in which a possibility result under interdependent values is more fragile than that under private values.