The Influence of Valuation Estimation on

This paper examines a two-stage price-discrimination game inspired by eBay’s second chance offer. An item, with private valuation X, is offered to the highest bidder in the first stage. In the second stage, a take-it-or-leave-it offer for an item with valuation Y = h(X), h ′> 0, h(0) = 0, is offered to the highest bidder from the first stage. This pa-per shows that, if an equilibrium in invertible strategies exists, then it is revenue-equivalent to two independent Vickrey auctions. This equiva-lence result is very useful in explicitly computing optimal strategies for both first-price and second-price auctions in the first stage for given parametric forms. A comparison with classical auctions shows that price discrimination leads bidders to additionally “shade ” their bids. The equivalence result also helps to bound the second stage discrim-inatory price for which an equilibrium in invertible strategies exists. We are also able to generalize results on non-existence of equilibrium in invertible strategies in other auction models incorporating price dis-crimination or resale