  We consider a variant of the standard Bayesian mechanism, where players
evaluate their outcomes and constraints in an 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 taxation principle
and show, perhaps surprisingly, that such IC mechanisms are fully characterized
by the so-called auto-bidding mechanisms, which are pervasively fielded in the
online advertising industry.
