Product-Mix Auctions

Abstract

This paper adds new material about the implementations of, and the Bidding Languages used in, the Product-Mix Auction to Klemperer (2008).

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.

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; it uses it more often at times of potential stress (e.g., it used the auction weekly after the 2016 "Brexit" vote). The Bank’s first implementation corresponds closely to the description in section 2, below. The current implementation permits more dimensions (i.e., more “varieties” of goods), and also allocates an endogenous total quantity. We now use simple linear-programming methods to solve the auction. The Corporate Bond Purchase Scheme that the Bank ran in 2016-17 also has some features in common with the auction we describe.

The then-Governor, Mervyn King, told the Economist that “[the Product-Mix Auction] is a marvelous application of theoretical economics to a practical problem of vital importance to financial markets”. The current Governor, Mark Carney, announced plans for greater use of the auction. The Guardian newspaper published a 5 minute video including an interview with then-Deputy Governor, Paul Tucker.

(pro bono) software to run Product-Mix Auctions is available on my website.

Note: This Paper adds New Material, Including about Implementations of the Product-Mix Auction and More Detail about The Bidding Languages, to Klemperer(2008).

Keywords: Multi-Object Auction, TARP, Central Banking, Simultaneous Ascending Auction, Treasury Auction, Term Auction, Toxic Assets, Simultaneous Multiple Round Auction, Product-Mix Auction

JEL Classification: D44, E58