A Very Silent Auction

In celebration of what would have been Jim Mirrlees' 90th birthday, we are auctioning a number of special items and books generously donated in his memory by Fiona and Patricia Mirrlees. All proceeds go to the endowed scholarship newly established in Jim's name.^*

The auction will end on 4 July 2026 at 2pm BST (9am ET).

How the bidding works

No one will know whether or what you have bid, with the exception that Lottie Madden in the development office will know who has won what objects, and the prices they have to pay.

Rules: You can make as many bids as you like, of any or all of the following kinds.

Simple bids: You can make one or more bids for a single object each. For example, you might £100 for the soap statue, and independently bid £150 for the bronze statue.

"OR" bids: You can also make bids of the form "I will pay £X for object A, or £Y for object B, or £Z for object C, or ...". In this case, at most one of these offers will be successful. For example, one OR bid might offer £200 for the soap statue or £300 for the bronze statue; it could win either statue, but not both. Similarly, an OR bid across several of Jim's books can win at most one of those books. If you submit separate bids that cover overlapping objects, however, those separate bids can each win one object.

"Any book" bids: "Any book" is a convenient shorthand for an OR bid that places the same value on every book in the auction. If you bid £40 for "Any book", the auction may allocate you any one book at a price up to £40, but this bid will never win more than one book. You can also combine "Any book" with named books in the same bid: for example, you might bid £40 for any book but £75 for a particular book you especially want. The bid remains an OR bid, so it can still win at most one book.

Outcome: The auction computes competitive-equilibrium prices and allocations, specifically the unique lowest prices that balance supply and demand.

For more background and why truthful bidding is generally the best strategy, see below. Paul Klemperer and Edwin Lock will be happy to answer any questions.

Packaging and shipping costs will be covered by Nuffield College.

Start bidding

More about the (Product-Mix) Auction

Many of you will recognise that this auction is similar to a Vickrey auction—named after Jim's co-Nobel prize winner—but the Vickrey auction does not find competitive equilibrium. The auction is in fact a simplification of the Product-Mix Auction that Paul Klemperer (Nuffield Fellow 1995-current) designed in 2007-8 at the beginning of the financial crisis for the Bank of England to auction repos. The Bank still uses it, although with far fewer different qualities of collateral for the repos than the number of different objects that Patricia and Fiona have generously supplied.

This version has been programmed by Prof. Edwin Lock (Nuffield Research Fellow, 2021-24) who (along with Prof. Elizabeth Baldwin, Nuffield Research Fellow 2016-2017) has been involved with Paul in the further development of the Product-Mix Auction.

For more on the origins of this auction, see this paper, or this 5-minute film published by the Guardian newspaper.

Equilibrium and truthful bidding

Each bidder's demand in this auction is captured by their bids, as described above. The auction will find the unique lowest competitive equilibrium prices. That is, it will find the unique lowest prices that balance supply and demand, assuming everyone has made bids that accurately reflect their true preferences. It will also allocate the goods according to competitive equilibrium.^† It follows that if your bids accurately reflect your true preferences, you will be allocated whatever is best for you at the prices set by the auction: that is, whatever you would have chosen if you had known the final prices in advance. More generally, you are unlikely to gain much, if anything, by choosing bids that misrepresent your preferences.^‡ If any bidders are indifferent about whether, or what, they are allocated at the final prices, these ties are broken randomly.

Simple example: Suppose Paul bids £100 for the wax statue of Jim, and Lottie bids £150. Lottie wins: her bid is high enough to beat Paul's, and she pays £100. If Edwin also bids £125, Lottie still wins, but now pays £125. (With many OR bids, of course, the calculation is considerably more complex.) In this simple single-item case, if these bids are the bidders' true values, no bidder could have gained by choosing a different bid.

For more details, read this paper.

Why we are using this auction

The “Very Silent Auction” is not intended to maximise expected revenue--the aim is that people who wish can have something of Jim's, in celebration of what would have been his 90th birthday weekend, and to make the allocation efficiently. Our rules mean:

1. Those unable to be physically present can participate on the same terms as others.
2. No one feels under any social pressure to participate. (And nor need anyone feel embarrassed by their bids showing publicly just how much they hero worship Jim!)
3. The auction should be more efficient, i.e., achieve higher “social welfare”, than standard “silent” or “live” auctions.