Locally robust implementation of efficient bilateral trade with correlated beliefs

We identify the ex ante welfare (EAW) condition as a necessary requirement to implement ex post efficient bilateral trade in any finite type space with interdependent values and correlated beliefs. As these finite settings become finer to approximate a continuous type space, we derive a limit EAW condition by taking the EAW condition in finite settings to its limit. We show that this limit condition trivially holds in the benchmark continuous setting admitting a full-support density function. We then insist on locally robust implementation by requiring efficient trade to be implemented uniformly across all finite type spaces that approximate the benchmark continuous type space. Our main result shows that under high interdependence, locally robust implementation of efficient trade is impossible. We thus show that the negative results of Myerson and Satterthwaite (1983) and Fieseler, Kittsteiner, and Moldovanu (2003) under independent beliefs can also emerge as the robust limit of discrete environments even when beliefs are correlated.