Separating Equilibria in Public Auctions

Abstract

We consider two private-value auctions where the prize in one is higher than the prize in the other. We show that a separating equilibrium exists where bidders with a high valuation attend the auction with the higher prize while the weak bidders attend the auction with the lower prize. In addition, we prove that a weak separating equilibrium exists where the strong bidders attend the high prize auction while the weak bidders randomize and may attend either auction, although with a higher probability of attending the low prize auction.