buyer case I characterize and prove uniqueness of the equilibrium of hybrid auctions where
the payment is a weighted average of the highest and second-highest bids. A recursive
method to explicitly compute the equilibrium is presented. It is shown that any hybrid auction
yields at least as much revenue as the first-price auction. In particular, the equilibrium of the
second-price auction, obtained in the limit by letting the weight of the highest bid go to zero …