So when you go out to dinner with a friend in this modern age I'm sure that despite wondering about all of the food and wine and polite conversation the one question that must really bother us all is did the Dutch really invent sharing?

I am assuming for the purposes of this that, in fact, you dispensed with all the wonders of the dinner table before the modern age or at least during dinner. The problem with the fabled equality of the Dutch during bill paying scenarios is that it will tend to happen right there at the end of a meal so that there is seldom time to make points and counter-points in an argument about the origin of the term "going Dutch". So did they really invent sharing ?

In a word; no. In 147 words; The phrase "going Dutch" is actually a much more modern version of "Dutch treat" as in "it's not a real treat as you'll be paying too". During one of Britain's more difficult times with the Dutch the Brits decided that it would be a good idea to make fun of their enemies they added Dutch to the front of lots of different words for example "Dutch courage" and so the "Dutch treat" was born of a similar insult the idea that a Dutch person was cheap. The reason the phrases became so popular in the states is due to a historical version of that recent mob in Britain who graffitied obscenities all over a paediatrician's car because they thought she was a paedophile because they couldn't read very well - the Americans hated the German immigrants and decided that Deutsch sounded a bit like Dutch so it stuck.

There's actually another "Dutch" thing which is becoming more relevant with each passing year and that's the "Dutch Auction". This was originally an insult because in Dutch tulip auctions the prices start high and go down which seems rather counter intuitive. In fact there is a very sensible reason for why you would want to run an auction this way and understanding the process has won a few people some Nobel prizes, so lets see if I can rustle myself up a Nobel prize by explaining the principles of auctions in an easy to understand way. This topic brings me back to somebody I've written about twice before John Nash and game theory. Firstly I spoke about board games in relation to him (I'm fascinated by board games) and then about the time somebody thought I was him - sort of (Mathematical biography).

Up until recently there were three main types of auction. The main one is the one where you see an object you want and people keep outdoing each other to bid on the item as the price goes up, this is known as a British Auction (or if somebody just says auction this is probably what they mean). The second type of Auction is a sealed envelope auction. Each party sends in a bid in and the person who has the highest number is the winner. Both of these auctions work really well if you want to sell a single item. The Dutch Auction was designed to deal with getting rid of all of the tulips that had been picked. If they didn't all go then they would be wasted and all of the items were effectively interchangeable. In this type of auction the seller would start with a very high price for his lot and then gradually reduce the price until somebody took the lot.

The fourth type of Auction was brought to fame by a guy called William Vickrey. Vickrey didn't invent the Vickrey Auction he just popularised it. He became interested in the three auction types above and applied to them Nash equilibrium maths to each of them. He proved that logically the British Auction was the superior one. Effectively the Dutch Auction and the sealed bid auction are identical mathematically as in each case the person willing to pay the most will win. And although one is held in public the point at which the winner makes their bid is when they have no information about the desire of their competitors - all they know is what they are willing to pay.

What Vickrey wanted was a version of the Dutch Auction which dealt well with selling lots of identical things in a situation where you wanted to get rid of all of them. Two key areas for this are things like treasury bills where a fixed number are issued and a price needs to be found where all of them can be sold or in an IPO situation where a company is issuing shares for the first time. A price needs to be found so that all of the shares are taken - the traditional methodology for this is that a company makes up a price (on the back of advice) and the broker buys the difference to make the price stick.

The model he found for this is called the second-price auction. It starts off akin to a sealed bid auction. Everyone suggests how much of the item they want and at how much they want it. Lets stick with tulips for this example. I want 10 tulips at $10 a tulip. You want 5 tulips at $5 a tulip. And Jeff wants 5 tulips at $2 a tulip. There are 20 tulips for sale and we all get all of the tulips we want for $2 each. Regardless of how much we were willing to pay we get the tulips for the lowest price required to shift all of the tulips. Say we were all offering the same quantities and prices but there were only 15 tulips then you and I would get all of the tulips we wanted for $5 a tulip and Jeff would get nothing.

What's happening here is you are telling the auctioneer your ultimate desire, how far you are willing to go to get the tulips. Then the auction is happening mathematically without you having to be in the room and a single price is emerging to shift the tulips.

There is one extra twist to make the thing fair. I would never ever in this situation pay $10 a tulip. I would only ever pay $6 a tulip. The reason this is called a second-price auction is because the final price is set at the second highest price plus the minimum bid. This is a little complicated but if you imagine it like a British Auction it suddenly becomes easier. If it were a British Auction and I want this tulip enough that I'm willing to pay $10 for it but you only want it enough that you are willing to pay $5 for it I wouldn't have to bid $10. I would only have to bid $6. Once I had bid $6 you wouldn't bother to beat me because I'd have gone over your maximum bid. So I'd be able to stick at $6 even though I was willing to pay $10.

And to make this system fair for the people buying and the people selling this element has to be introduced. The seller should not be able to profit from knowing my desire level otherwise the balance would be too much in their favour.

Although this seems like a very useful method of running an auction the reason that they haven't always been so successful is that people tend to feel like revealing their desire to the auctioneer is likely to cause the auctioneer to stiff them. Perhaps they will finally find their time now as perhaps people are willing to believe that a computer calculating the maths will be fair. Attempts to make the system more transparent have seen all the bids exposed at the end but with the names of the bidders obscured. But this leads to problems in situations where the number of bidders are unknown because there is nothing to stop somebody inventing another anonymous bidder to drive the secondary price up.

Google is currently running a Vickrey auction in their IPO. An interesting experiment which I for one will be following with interest.