Separating equilibria in auctions with two types of bidders

We consider two simultaneous, private value, second-price auctions with identical objects for sale and two types of bidders, strong and weak, in the sense of hazard rate stochastic dominance. We show that if the strong bidders are not too strong with respect to the weak bidders, then, by setting an appropriate reserve price, a separating equilibrium exists in which strong bidders will participate in the auction with only strong bidders, and weak bidders will participate in the auction with only weak bidders.