The Prisoner's Dilemma, a new formulation

The Prisoner's Dilemma is a Game Theoretic problem wherein two prisoners must choose whether to betray their partner in crime or remain silent. Betrayal is rewarded by going free, and the betrayed gets the heaviest punishment. If both betray the other, both gain a lighter punishment. But if both cooperate, then both gain the lightest punishment of all.

Nevertheless, since neither can know what the other will do, the rational move is always to betray the other in the hope of going free, and both end up with middling punishments instead of the lightest. This is only altered when the game is iterated, so that punishment for betrayal (i.e. future betrayal on the part of the betrayed) becomes a decisive factor.

It is interesting both as a mathematical problem and a philosophical/ethical one. But the really interesting thing is that such a simple choice begets such complexity when presented at the same time to more than one decision maker (or agent, in the terminology). The reciprocal effects drive the potential complexity through the roof - in other words, trying to calculate, or take account of, the actions of the other party, knowing they are doing the same for you and they know that you are trying to predict their actions when deciding what yours will be, and so ad infinitum...but where does that break down when the agents are fallible humans? How much calculation can one human do?
This is what makes player modelling a hard problem - you can't reduce it to a case of agents.

*Although actually, the prisoner's dilemma, a new formulation by moi: wank or work out!
:D