Perfect Implementation

Abstract

Privacy and trust a effect our strategic thinking, yet they have not been precisely modeled in mechanism design. In settings of incomplete information, traditional implementations of a normal-form mechanism |by disregarding the players' privacy, or assuming trust in a mediator| may fail to reach the mechanism's objectives. We thus investigate implementations of a new type. We put forward the notion of a perfect implementation of a normal-form mechanism M: in essence, a concrete extensive-form mechanism exactly preserving all strategic properties of M, without relying on a trusted mediator or violating the privacy of the players. We prove that any normal-form mechanism can be perfectly implemented by a verifiable mediator using envelopes and an envelope-randomizing device (i.e., the same tools used for running fair lotteries or tallying secret votes). Differently from a trusted mediator, a verifiable one only performs prescribed public actions, so that everyone can verify that he is acting properly, and that he never learns any information that should remain private.