## Friday, February 22, 2008

### How much would you pay for a £10 note - The Economics of Rationality

Suppose there is a game where I am selling a £10 note. I will sell it to the highest bidder. The only problem is that if you make the second highest bid, you have to forfeit that amount to me.

The first bidder could offer 1p for the £10. He has nothing to lose and the chance to make £9.99 profit. However, a second person may then think that they might as well bid 2p. It is still remarkable value for a £10. Furthermore, if he ends up losing 2p, it doesn't matter, as it is not worth anything.

However, the bidding process may keep going on. In one sense it is rational to keep offering a higher bid, when there is chance to buy a £10 note for less than £10.

However, when you get to £9.99 what happens next?

Well the person who bid £9.98 is on the verge of losing £9.98 something he doesn't want to do. The rational thing for him to do is to bid £10. As this will save him losing £9.98. However, the person who bid £9.99 doesn't want to lose his £9.99 either. Therefore, it is rational for him to bid £10.01. The problem is then that neither bidder wants to lose their stake, therefore, the rational thing is to keep bidding higher, hoping that the other person will drop out. It is always best to win, because you at least get £10. It makes no sense to drop out because you will have to pay the losing bid and not get the £10.

The question is who will drop out first? At Sometime people will make a seemingly irrational decision to drop out. They can see the problem will escalate and so they might as well cut their losses. The question is when do you drop out of the bidding process at 2p, £9.99 or £19.99? From an economic point of view it represents an interesting investigation of human behaviour because ultimately people will choose to do something which is seemingly irrational, but from their perspective makes sense.

Is there any point in getting involved in the game at all?

But, if nobody else joins, you might be able to win a £10 with a 1p offer.

Will this tempt others to join in?

It becomes a little like poker, who has the greatest nerve? In economics we can analyse decisions like this through game theory. The important thing here is your decision whether to bid higher, depends on how others respond. If you think others will soon drop out, you should bid higher, if you think someone will be determined to get the £10 note there is no point in continuing.

OK, who would like to start the bidding at 1p for a brand new £10 note?