## XVI.5.2 The game Prisoner’s dilemma describes a situation when betraying the cooperating opponent brings the greatest profit, mutual cooperation a bit lower profit, mutual betrayal an even lower profit and one-sided betrayal on the part of the betrayed causes the greatest loss

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.

An analogy of the prisoner’s dilemma game is used in situations when an individual who follows its own goal against a large group of players, e.g. against a whole society. In this case, the behavior of all the participants will end up in a situation called the “Tragedy of Commons” (Hardin 1968). The course and result of this game were very graphically described using the example of the fate of English country commons, the pastures open to all. If a village’s commons were not regulated as to how intensively they could be pastured, they were completely destroyed by immoderate pasturing and the cattle of villagers, which were dependent on the commons, died of hunger. If the commons were divided among villagers, each could only have as many animals as his pasture would be able to feed. In the commons case, the most advantageous strategy for each individual was to get as many animals as possible as soon as possible; before someone else’s animals would destroy the pasture and without – moreover - losing out against other herdsman until complete devastation of the commons occurred.

A similar game, the so called wolf’s dilemma, belonging into a broader category of “common welfare” games, can be modeled in the laboratory using the methodology of experimental games. Compared to the prisoner’s dilemma game, the reward for mutual cooperation is even higher than the reward for one-sided betrayal, although the risk of betrayal is higher because of the greater number of participants. We seat twenty experimental subjects in separate cabins before the keyboards of a computer terminal and acquaint them with the following rules: the first to press a key gets – completely anonymously, without the other players knowing – \$ 4. If no one presses a key during 10 minutes, each participant gets \$ 20. It is highly probable the game will be short and we will only have to pay a \$ 4 reward. Betraying and receiving a small reward immediately after starting the game, before someone else finds the right solution, is regrettably the most rational solution. (In any case this is not guaranteed; don’t ask me for compensation if you run into a cooperative group and will have to pay out \$ 400 in rewards.)