Robust Possibility and Impossibility Results

In a general setting of private information, the possibility (impossibility) theorem is said to be valid, if a balanced and ex post efficient mechanism exists (does not exist) which agents voluntarily participate at. Possibility and impossibility results are called robust if they hold for all priors with independently distributed private information. The following papers, among others, implicitely contain such results: Myerson and Satterthwaite (1983), Gth and Hellwig (1986), Cramton, Gibbons and Klemperer (1987), McAfee (1991), Makowski and Mezzetti (1993), Williams (1994) and Schmitz (1998). The present paper introduces a criterion which does not depend on the prior distribution of information. This criterion allows, not only, to simplify drastically earlier proofs, but also to generalize the existing results in a substantial way.Impossibility theorems, possibility theorems, Bayesian implementation under voluntary participation