Procedurally Fair Implementation: The Cost of Insisting on Symmetry

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 [Nash equilibrium and welfare optimality, Rev. Econ. Stud. 66 (1999) 23-38.], 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.