Product-Mix Auctions

Nuffield College Working Paper 2018-W07

31 Pages Posted: 1 Feb 2010 Last revised: 13 Jan 2020

See all articles by Paul Klemperer

Paul Klemperer

University of Oxford - Department of Economics; Centre for Economic Policy Research (CEPR)

Multiple version iconThere are 2 versions of this paper

Date Written: 2018


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

Suggested Citation

Klemperer, Paul, Product-Mix Auctions (2018). Nuffield College Working Paper 2018-W07 , Available at SSRN: or

Paul Klemperer (Contact Author)

University of Oxford - Department of Economics ( email )

Manor Road Building
Manor Road
Oxford, OX1 3BJ
United Kingdom
+44 1865 278 588 (Phone)
+44 1865 278 557 (Fax)

Centre for Economic Policy Research (CEPR) ( email )

United Kingdom

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Abstract Views
PlumX Metrics