On minimal ascending auctions with payment discounts

The literature on ascending combinatorial auctions yields conflicting insights regarding the possibility to implement the Vickrey payoffs for general valuations. We introduce the class of minimal ascending auctions, a class which allows one to disconnect the final payments from the final bids but which prohibits the raising of the price vector of a provisionally winning bidder. We first establish the impossibility of implementing the Vickrey payoffs for general valuations. Second, we propose a minimal ascending auction that yields a bidder-optimal competitive equilibrium thanks to payment discounts.