Existence of optimal auctions in general environments

We provide a unified approach to the problem of existence of optimal auctions for a wide variety of auction environments. We accomplish this by first establishing a general existence result for a particular Stackelberg revelation game. By systematically specializing our revelation game to cover various types of auctions, we are able to deduce the existence of optimal Bayesian auction mechanisms for single and multiple unit auctions, as well as for contract auctions with moral hazard and adverse selection. In all cases, we allow for risk aversion and multidimensional, stochastically dependent types.