Abstract: We consider a variant of the standard Bayesian mechanism, where players evaluate their outcomes and constraints in an {\em ex-ante} manner. Such a model captures a major form of modern online advertising where an advertiser is concerned with her/his expected utility over a time period and her/his type may change over time. We are interested in the incentive compatibility (IC) problem of such Bayesian mechanism. Under very mild conditions on the mechanism environments, we give a full characterization of IC via the {\em taxation principle} and show, perhaps surprisingly, that such IC mechanisms are fully characterized by the so-called {\em auto-bidding} mechanisms, which are pervasively fielded in the online advertising industry.