We study a private-values buyer-seller problem with multiple objects. Valuations are binary and i.i.d. We construct mechanisms that span the set of all Pareto-efficient outcomes. The induced trading rules for objects are linked in a simple way.

We analyze the problem of fully implementing a social choice set in ex post equilibrium. We identify an ex post monotonicity condition that is necessary and--in economic environments--sufficient for full implementation in ex post equilibrium. We also identify an ex post monotonicity no veto...

A social choice function is robustly implemented if every equilibrium on every type space achieves outcomes consistent with it. We identify a robust monotonicity condition that is necessary and (with mild extra assumptions) sufficient for robust implementation. Robust monotonicity is strictly...