What would you do in the prisoner’s dilemma?

The prisoner’s dilemma is a fundamental problem in game theory. It shows that people can choose not to cooperate, even if that decision goes against their interests. With this game, we analyze the decisions made by two prisoners imprisoned for a minor crime, when they are offered the possibility of reporting their partner to the police.

If a prisoner collaborates with the police, he or she will obtain prison benefits. These benefits will be greater or lesser depending on the decision that the other prisoner makes. In this game it is assumed that each prisoner is imprisoned separately. In this way they cannot communicate with each other, nor know the other’s decision.

Therefore, The prisoners cannot agree on their decisions or know what the other prisoner is going to do.. Thus, getting the decision that the other prisoner will make right will be essential when it comes to anticipating the consequences of one’s own decision.

Possible decisions regarding the prisoner’s dilemma

The possibilities that both prisoners have are two: to betray their partner or not to betray him.. It is the base and starting point of the game. Therefore, taking into account the two decisions that each of the prisoners can make, A total of four possibilities are defined that can occur depending on the decisions of both prisoners.

Neither of the two prisoners betrays their partner. In this case, each prisoner would receive only two years in prison (-2, -2).Only one of the prisoners betrays his partner. In this case, the prisoner who betrays his partner would be sentenced to only one year in prison, while the prisoner who does not betray his partner would be sentenced to ten (-10, -1 or -1, -10).The two prisoners betray their partner. In this case, the prison sentence for each of them would be six years (-6, -6).

Impact of decisions in the prisoner’s dilemma

There is a condition that we have to take into account if we play this game, and that is that each prisoner will want the best for himself, without caring what happens to his partner. At first glance, if we enter the skin of one of the two prisoners. Therefore, The best decision would be to betray the other prisoner.since in all cases the sentences would be lower.

Following this type of logic, it is assumed that the other prisoner thinks the same and ends up giving us away.. In this case, since we have both betrayed each other, the prison sentence would be six years for each of us. If, on the other hand, we had both decided to cooperate and not betray each other, the sentences would have been shorter, only two years.

The Nash equilibrium

The situation that arises with this game is called a “Nash equilibrium.” The name is given by the mathematician John Forbes Nash.known among the general public for the film that gives its name to this blog, “A Beautiful Mind.”

In this “Nash equilibrium” situation, each individual player gains nothing if he changes his strategy while the other players do not change theirs. Therefore, changing the individual decision implies worsening conditions. So, Each player executes the best move he can given the moves of the other players..

By not being able to coordinate decisions with the other players, the best decision that can be made will be the one that allows the most benefits individually. However, this decision will not be the best for all players.

Variants of the prisoner’s dilemma game

The prisoner’s dilemma also has different variants in which more players can participate. Some of these are the following:

1. Rock, paper, scissors

This game is perhaps best known for its popular use in making preference decisions. Although this game is not a variant of the prisoner’s dilemma, it does present a “Nash equilibrium.” since each option chosen has a third chance and whether it is a winner or loser will depend on what the other does.

2. Trust game

It is a sequential game in which one player first decides his level of trust in the second player. The greater the trust, the greater the payment generated for the second player. Next, you must decide whether to reciprocate the trust with a decision that is mutually beneficial for both of you.

3. Friend or enemy

In this game three pairs of people compete. When each pair is eliminated, they play a prisoner’s dilemma game to determine how their winnings are divided. If both cooperate (“friend”), they share their benefits 50/50. When one cooperates and the other deserts (“enemy”), the deserter takes all the profits and the cooperator none. And if both desert, neither takes anything.

The application of the prisoner’s dilemma

The prisoner’s dilemma is a simple game that has allowed researchers to better understand how we make decisions. Although we think that logical decisions, such as in this case ratting out the other prisoner, that will bring us more benefits are the correct ones and those that people usually opt for, other decisions that are not so logical, such as not ratting him out, can give us more benefits. , taking into account that other people do not opt ​​for logical decisions either.

In conclusion, the decisions we make are not so simple and depend on many factors. Thus, the decisions we usually make do not usually seem logical at first glance. To find its logic, we must delve deeper into that series of factors and cognitions that lead us to opt for those decisions to the detriment of other more logical ones.

Finally, we leave you with a quote by John Forbes Nash:

You might be interested…