Procedurally fair implementation under complete information

We derive a necessary and a sufficient condition for Nash implementation with a procedurally fair mechanism. Our result has a nice analogue with the path-braking result of Maskin (1999), and therefore, it allows us to give a simple characterization of those choice rules that are implementable, but not in a procedurally fair way. This reveals the constraints that insisting on procedural fairness impose on the collective.