[Paul Klemperer:] When I was 16 the thing that I was really obsessed about was geometry.
Well, actually of course, I was really obsessed about girls,
but my social skills were such that about 99% of my time could be spent on geometry.
I'm excited by both the theory and by the practical application.
The interface between the two is a lot of fun.
I got a phone call from the Governor saying,
"Was there some way in which I could help by designing an auction
which would more effectively get money out to the banks and building societies that really needed it?"
[Paul Tucker:] I think the Bank of England was imaginative in saying...
"We need to get hold of one of the best academics in the world
and get him to help us solve this problem.
[Paul Klemperer:] One of the nice things about working in university,
is that I can feel comfortable giving some of my time for free
to institutions like the Bank of England, to government departments and to charities etc.
There's always a tension between the very beautiful, precise theory of mathematics
and how you take that to a much messier real world.
But the excitement is trying to understand the real world
-- what are the underlying forces? --
then seeing how you can mathematically model those,
and actually doing something with them.
[Paul Tucker:] As the crisis that began in 2007 got worse,
nearly all central banks found that they were lending money to the banking system,
not just against the collateral of very low risk securities and government bonds,
but also against risky securities.
[Paul Klemperer:] So I originally started working for the Bank of England
because the central bank was having trouble getting funds to
the banks and building societies that needed them.
It was the fear that these banks didn't have enough funds that was leading to bankrupts.
[Paul Tucker:] If we were planning to lend £100 billion in total, we needed to decide:
How much would we lend against gilts?
How much would we lend against the riskier securities?
This was a complicated problem in the design of auctions.
[Sounds of auctioning...]
[Paul Klemperer:] This is a class of problem that we've studied before.
For example, 7 years earlier with Ken Binmore
I had run the UK's 3G auction.
We took 7 weeks on that occasion.
When you're worried about bank runs you've got more like 7 seconds than 7 weeks.
So the question then became:
How can we collapse that kind of process into a very tiny amount of time?
[Auctioneer:] "550 with you..."
[Paul Tucker:] Trying to take a lot of bids from a lot of different people
and pare them down to a simple aggregate decision.
[Paul Klemperer:] The answer that I came up with for that was to ask the bidders
-- that is the banks and building societies --
to tell us something about their preferences,
in fact, enough about their preferences that I could then work out
how a long, multi-round process would work.
I could then plug their preferences into a system
-- a very simple computer model --
and it would spit out the answers and tell us
what would have happened if we had the full 7 week process.
So what we do is:
we can represent those preferences in graphs
and then we can work with those graphs.
What's really exciting is that geometry
turns out to be very valuable in solving problems like the Bank of England's
and many other problems of resource allocation.
If I am allocating a bowl of fruit and there's
oranges, apples, bananas, grapefruit and grapes
-- that's 5 different kinds of fruit --
I'm going to need to work in 5 dimensions
in order to cope with the fact that I need to express trade-offs,
preferences between five different things.
[Auctioneer:] "90 I'm bid at... 90 in front...100..."
[Paul Klemperer:] I would then be asking you questions like, "how many grapes is an apple worth to you?...
Are you happy to have 1 orange on its own...
or would you insist on having a pair of oranges if you have them at all?
Because you happen to have two kids and you really want have the same pieces of fruit,
because if you take home different pieces of fruit they'll fight over them..."
[Auctioning...]
[Paul Klemperer:] So I'm starting off in 5 dimensions.
Nevertheless we have a clearly defined set of rules
by which we can transform these pictures of people's preferences
and understand, in the end, how to efficiently divide up this bowl of fruit.
[Auctioneer:] "600...I have 600... all done at 600, thank you."
[Paul Klemperer:] I am now, with my colleague Elizabeth Baldwin,
taking tropical geometry -- which mathematicians only invented about 10 years ago --
and using it, now, to work out how to more efficiently allocate resources to the Bank of England.
The Department of Energy & Climate Change has asked us to look into
how they can do what they're doing better
and we'll be using these techniques there, we hope.
It'd be nice if the government now further understood
the value of fundamental academic research
and how really valuable it can be, almost immediately, in the real world.