This paper obtains finite analogues to propositions that a previous literature obtained about mechanisms whose possible messages form a continuum. Each person's private knowledge of the environment enters her agreement rule. Continuum mechanisms are unrealistic because transmitting every point of a continuum is impossible.
Messages have to be rounded off and the number of possible messages is finite.
Moreover, reaching a continuum mechanism's equilibrium message typically requires infinite time. That difficulty is absent if the number of possible messages is finite. The question therefore arises whether results about continuum mechanisms have finite counterparts. We obtain bounds on error. We apply these results to exchange economies with quasi-linear utilities.