Consumer's Dilemma
2007-09-15
It's game theory: who said maths wasn't practical!
You may or may not be familiar with the Prisoner's Dilemma, a game theoretic scenario with surprisingly many real-life applications. While you could go and read up on it at Wikipedia, regular readers will realise that I'm about to explain it anyway...
Two people are in custody pending trial for some crime. Each is offered a plea bargain: testify against the other and you can go free - unless he gives evidence against you. If they get that testimony against one person, he'll get ten years. If they have sufficient evidence to get both, they'll get five years each. If they can't get one to implicate the other, they'll only be able to bring minor charges against each; a few months. Each must make his decision without the opportunity to talk to the other.
Clearly, best overall pay off is when both players cooperate. However, since one player cannot know the other's strategy, the numbers are much better if he betrays the other: 0 - 5 years over 0.5 - 10 years. It's true if you assume the other player will choose [uniformly] randomly, more so when you credit him with the sense to play optimally in his own right.
Game theory ignores the idea that the players might have faith in one another. Which is fine, because in most of the real world applications, they don't.
I've been familiar with the Prisoner's Dilemma for a while now. I did a little game theory at university, and the dilemma has some interesting properties, not least that the combination of optimum plays is a sub-optimal solution for the game at large. But that wasn't the point: the point was that I was reminded of it by the news yesterday of Northern Rock approaching the Bank of England for emergency funds.
Now, Northern Rock is a little unusual as mortgage lender in that although it has some investors with savings accounts, mainly it borrows the money to make its loans from other financial institutions. At first I thought that was a bit odd, but I suppose they're just doing the same as many other businesses: buying something wholesale and passing it on with a cut for themselves.
The claim was made ('experts and officials', the BBC calls the source) that Northern Rock is not in danger of going bust. After all, a certain degree of stability when you have £113 billion of assets. Hands up if you can honestly way you have any idea what £133 billion even is in real terms: I haven't a clue. (If you have your hand up, feel free to comment below with some ideas of large and impressive things one might buy with that much).
It's stable and it's not going anywhere soon, because it's got lots of assets. So the customers are safe. In fact, the only I can think of that might threaten that stability would be a sudden loss of assets. And that isn't going to happen. Unless...
Unless everyone with money in savings tries to get it out. Which of course they are, because once there's even a whisper that your savings institution might go under, trusting them with your money is a Prisoner's Dilemma. It's big and multiplayer, granted, but still relatively simple in principle. If everyone leaves their money in, the institution is likely to be fine: small risk. If you get your money out quick enough, you'll have it all, but you'll be increasing the risk of those who still have an investment. Because of the time aspect, an all-defect scenario is unlikely: there's almost guaranteed to be some poor bugger with his money still in play when the ship sinks.
Although it's the first time I've mentioned the Prisoner's Dilemma by name, it's not my first post about games with the best mutual solution ruled out by individual distrust. During the last bout of fuel 'strikes' I was moaning about panic buying: it was claimed that supplies were fine for normal use, but of course as soon as there's a danger of anyone trying to stockpile, everyone needs to do so so that they aren't the one left without fuel.
With regards panic, Northern Rock may be lucky: their 'resale' nature limits the extent of their assets that panicked investors could take away. Their reliance on financial institutions has made them the first institution to make the news in what could be quite the epidemic of squeezing in the financial sector, but it also gives them less to fear from the selfishness of human nature.
You may or may not be familiar with the Prisoner's Dilemma, a game theoretic scenario with surprisingly many real-life applications. While you could go and read up on it at Wikipedia, regular readers will realise that I'm about to explain it anyway...
Two people are in custody pending trial for some crime. Each is offered a plea bargain: testify against the other and you can go free - unless he gives evidence against you. If they get that testimony against one person, he'll get ten years. If they have sufficient evidence to get both, they'll get five years each. If they can't get one to implicate the other, they'll only be able to bring minor charges against each; a few months. Each must make his decision without the opportunity to talk to the other.
Clearly, best overall pay off is when both players cooperate. However, since one player cannot know the other's strategy, the numbers are much better if he betrays the other: 0 - 5 years over 0.5 - 10 years. It's true if you assume the other player will choose [uniformly] randomly, more so when you credit him with the sense to play optimally in his own right.
Game theory ignores the idea that the players might have faith in one another. Which is fine, because in most of the real world applications, they don't.
I've been familiar with the Prisoner's Dilemma for a while now. I did a little game theory at university, and the dilemma has some interesting properties, not least that the combination of optimum plays is a sub-optimal solution for the game at large. But that wasn't the point: the point was that I was reminded of it by the news yesterday of Northern Rock approaching the Bank of England for emergency funds.
Now, Northern Rock is a little unusual as mortgage lender in that although it has some investors with savings accounts, mainly it borrows the money to make its loans from other financial institutions. At first I thought that was a bit odd, but I suppose they're just doing the same as many other businesses: buying something wholesale and passing it on with a cut for themselves.
The claim was made ('experts and officials', the BBC calls the source) that Northern Rock is not in danger of going bust. After all, a certain degree of stability when you have £113 billion of assets. Hands up if you can honestly way you have any idea what £133 billion even is in real terms: I haven't a clue. (If you have your hand up, feel free to comment below with some ideas of large and impressive things one might buy with that much).
It's stable and it's not going anywhere soon, because it's got lots of assets. So the customers are safe. In fact, the only I can think of that might threaten that stability would be a sudden loss of assets. And that isn't going to happen. Unless...
Unless everyone with money in savings tries to get it out. Which of course they are, because once there's even a whisper that your savings institution might go under, trusting them with your money is a Prisoner's Dilemma. It's big and multiplayer, granted, but still relatively simple in principle. If everyone leaves their money in, the institution is likely to be fine: small risk. If you get your money out quick enough, you'll have it all, but you'll be increasing the risk of those who still have an investment. Because of the time aspect, an all-defect scenario is unlikely: there's almost guaranteed to be some poor bugger with his money still in play when the ship sinks.
Although it's the first time I've mentioned the Prisoner's Dilemma by name, it's not my first post about games with the best mutual solution ruled out by individual distrust. During the last bout of fuel 'strikes' I was moaning about panic buying: it was claimed that supplies were fine for normal use, but of course as soon as there's a danger of anyone trying to stockpile, everyone needs to do so so that they aren't the one left without fuel.
With regards panic, Northern Rock may be lucky: their 'resale' nature limits the extent of their assets that panicked investors could take away. Their reliance on financial institutions has made them the first institution to make the news in what could be quite the epidemic of squeezing in the financial sector, but it also gives them less to fear from the selfishness of human nature.
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