## Prisoner’s dilemma

In a particular setting of the pay-off matrix, specifically in cases when betraying the cooperating opponent brings the greatest profit, mutual cooperation brings a lower profit, mutual betrayal an even lower profit and betrayal on the part of the betrayed brings the greatest loss and, at the same time, the total reward sum for one-sided betrayal for both participants is smaller than double the reward for mutual cooperation, the players get into situation called the prisoner’s dilemma. The prisoner’s dilemma game comes in several variants; one of them may be described as follows: Two prisoners got caught after they committed a serious crime together. There is no direct evidence against them, so if they will cooperate, meaning that they will deny the accusation, nobody will be able to prove they are guilty of committing a major crime. They will only be accused of committing a minor crime, e.g. having possession of a stolen object, and given a relatively mild sentence, like three years in prison. Each prisoner is now in his cell and gets the following offer. If he will own up first and accuse his accomplice of being the major culprit of the crime, he will get an even milder sentence, e.g. one year in prison. If he continues to deny his guilt, while the other prisoner, who got the same offer, pleads guilty first, he will get many years’ imprisonment. If both prisoners betray their accomplice, each gets five years in prison. Most works analyze the game where the reward for mutual cooperation is 3 points, for mutual betrayal 1 point and for one-sided betrayal the traitor gets 5 points and the betrayed 0 points. Mathematical analysis of this situation shows that, under the given conditions, it is most advantageous for any prisoner to betray his accomplice to avoid risk of being the second to come up with this solution. The course of a majority of actual processes shows that, to find the only right strategy, most prisoners do not need to know the mathematical apparatus of game theory.
Of course, a situation more or less analogous to the prisoner’s dilemma is also encountered in nature. An individual sometimes gets into a situation when it has to decide among betrayal that can bring either great profit or minor loss, cooperation that can bring average profit if the partner will also cooperate, and great loss if the partner betrays it. In a situation when the partners are not going to meet in the future or the organisms are not able to recognize or remember their ex-opponents, they are most likely to choose the strategy to always betray.