The Prisoner's Dilemma

The prisoner's dilemma is a game theory thought experiment involving two rational agents, each of whom can either cooperate for mutual benefit or betray their partner ("defect") for individual gain. The dilemma arises from the fact that while defecting is rational for each agent, cooperation yields a higher payoff for each.

The prisoner's dilemma models many real-world situations involving strategic behavior. In casual usage, the label "prisoner's dilemma" is applied to any situation in which two entities can gain important benefits by cooperating or suffer by failing to do so, but find it difficult or expensive to coordinate their choices.

The story goes: Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with the other. The police admit they don't have enough evidence to convict the pair on the principal charge. They plan to sentence both to a year in prison on a lesser charge. Simultaneously, the police offer each prisoner a Faustian bargain. If he testifies against his partner, he will go free while the partner will get three years in prison on the main charge. If both prisoners testify against each other, both will be sentenced to two years in jail.

Prisoner B

Prisoner A

Prisoner B stays silent (cooperates)

Prisoner B testifies (defects)

Prisoner A stays silent (cooperates)

Each serves 1 year

Prisoner A: 3 years Prisoner B: goes free

Prisoner A testifies (defects)

Prisoner A: goes free Prisoner B: 3 years

Each serves 2 years

This leads to three different possible outcomes for prisoners A and B:

  1. If A and B both remain silent, they will each serve one year in prison.

  2. If one testifies against the other but the other doesn’t, the one testifying will be set free while the other serves three years in prison.

  3. If A and B testify against each other, they will each serve two years.

Assumptions and Conclusion

- We assume that both prisoners prefer to minimize their jail time.

- We assume both prisoners are selfish (i.e., they do not care about the fate of the other).

- We assume there is only one interaction.

- We assume the prisoners cannot interact and plan their responses in advance.

These assumptions lead to a suboptimal outcome in the game: (defects, defects), which results in each serve 2 years. We can see that if both prisoners remain cooperate, they would receive less jail time. However, this is an unstable equilibrium because if both believe the other will stay silent, they are tempted to testify against the other.

Therefore, (defects, defects) is the only Nash Equilibrium. A Nash Equilibrium is a state in a game where, given what the other prisoners are doing, no prisoner wants to deviate from their strategy.

However, if both prisoners could cooperate, they would achieve a better outcome. This is an important conclusion because it shows that two individuals may choose not to cooperate, even though it appears to be the best strategy for both.

Overcoming the Prisoner's Dilemma has significant implications for society at large and for ORIZON. We are often told that in a capitalist economy, individuals only care about their own interests, so selfish and competitive behavior is the norm, whereas cooperation is actually the best way to succeed. This insight is key for both society and the ORIZON ecosystem.

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