The Product-Mix Auction: A New Auction Design for Differentiated Goods

Abstract

The “Product-Mix Auction” is a single-round auction that can be used whenever an auctioneer wants to sell (or buy) multiple differentiated goods. It allows all participants to express their preferences between varieties, as well as for alternative quantities of specific varieties. Bidders simultaneously make sets of bids. Each of a bidder’s bids can be an OR” bid that offers a different price for each different variety, and the auction then accepts at most one of the offers from each bid (whichever is best for the bidder given the prices that the auction sets). The graphical solution method makes the operation and merits of the auction easy to explain. The auction is more efficient, and less sensitive to market power, than either running a separate auction for each different variety or running a combined auction with predetermined price differences between varieties. It is also faster, less vulnerable to collusion, and can be easier to use and understand than a simultaneous multiple round auction (SMRA). Moreover, unlike in an SMRA, the auctioneer can specify how the quantities to be sold will depend on the auction prices, by choosing supply functions across varieties. Related material is at www.paulklemperer.org.I invented the auction for the Bank of England when it consulted me at the beginning of the financial crisis in 2007. It now uses it regularly to auction loans of funds secured against different varieties of collateral. The Bank’s first implementation corresponds closely to the description in section 2; the then-Governor, Mervyn King, told the Economist that “[the Product-Mix Auction] is a marvellous application of theoretical economics to a practical problem of vital importance to financial markets” I also advised the Bank on the updated version it introduced in 2014. This permits more dimensions (i.e., more “varieties” of goods), and also allocates an endogenous total quantity. Simple linear-programming methods are now used to solve the auction.The current Governor, Mark Carney, announced plans for greater use of the auction.Future auctions may use others of the enhancements described in section 3.The Guardian newspaper published a 5 minute video including an interview with then-Deputy Governor, Paul Tucker.