In a famous example of Game Theory, two prisoner’s are sat in separate interrogation rooms, about to be grilled by the police. The two are faced with an onerous choice – to avoid a lengthy jail term they can either implicate the other guy or profess total innocence. Assuming that the two act rationally (which may be dubious, given that human beings are often demonstrably irrational) Game Theory tells us that they will both implicate the other one.
Why is that? Well let’s say that if they both keep quiet they will walk away from the jail as free men, the police have no evidence to charge them. However if one of them rats on the other, the one who rats will walk free while the one implicated will get ten years in jail. If they both rat on each other, they end up getting five years a piece (the judge is a little lenient since they both helped the case come to a swift conclusion). Given that they both know this, to stay quiet means that the prisoner will either walk away free or get ten years in jail; whereas to rat means either walking away free or getting five years in jail. So they both rat.
The point is that the rational action is not the one that leads to the best outcome, which would be if they both professed their innocence and walked away scot free. Neither can profess innocence though, rationally, as this takes the chance that the other one rats while they say nothing. Whether police actually use this idea is another question entirely.
Where the prisoner’s dilemma did come into my mind today was when I was thinking about the implication of a £50 bet I made with my wife as to whether we could both lose a certain percentage of our weight in a month (trying to get in shape for Christmas, you see). The bet is that if the other person reaches the goal they get £50. So if we both do it we end up breaking even, so too if neither of us manage, but, like the dilemma for the prisoners, if one of us makes it while the other doesn’t, the loser is £50 worse off (not to mention the gloating that may follow such a win).
Clearly we have the chance to influence each other in this. Last night I said I fancied a pizza, and my wife agreed it was a good idea. Casting aside the health implications (we are not overweight, after all). One course of action would be for us both just to agree to eat unhealthily and screw the bet. We could eat pizza after pizza and get off free. Or else we could both diet away and still end up no better off. However just like in the prisoner’s dilemma, if one of us pigs out while the other diets, they may end up losing £50. And that risk is what is forcing us back on the treadmill. We only eat evening meals together, so in theory, using cunning subterfuge, could diet all day while the other thinks we are stuffing our faces.
So the prisoner’s dilemma points to us both making the effort to diet (stir-fry for dinner tonight), because to pile on the pounds risks the chance of losing money, whereas if we diet we can only gain, which is a good thing, I guess. So there we have it – Game Theory in action, use it to your advantage.
