The prisoner's dilemma is a standard example of a game analyzed in game theory that shows why two completely "rational" individuals might not cooperate, even if it appears that it is in their best interests to do so.
This is an incredibly important concept to understand, as it has real world implications. Variations of this were used in the cold war between the Soviet Union and the USA, and was partly responsible for avoiding nuclear winter and the destruction of the human species.
The general problem is typically presented like this:
Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge. They hope to get both sentenced to a year in prison on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to: betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The offer is:
- If A and B each betray the other, each of them serves 2 years in prison
- If A betrays B but B remains silent, A will be set free and B will serve 3 years in prison (and vice versa)
- If A and B both remain silent, both of them will only serve 1 year in prison (on the lesser charge)
As it turns out, the best strategy is to betray (defect). However, when you have many iteration, the situation changes quite a lot.
The iterated prisoner's dilemma is just like the regular game except you play it multiple times with an opponent and add up the scores. But it can change the strategy and has more real world applications as it resembles a relationship.