Prisoner’s Dilemma

What Does the Prisoner’s Dilemma Mean?

The prisoner’s dilemma is a game theory concept that explains why two purely rational agents or individual decision-makers acting in their self-interest don’t produce the best outcome. In other words, it involves two parties making decisions without the knowledge of what the other will choose.

Mathematicians Merrill Flood and Melvin Dresher proposed this concept in 1950. It was later formalized and given its name by Albert W. Tucker, a game theorist. 

How Does It Work?

Two criminals (Prisoner A and Prisoner B) are arrested and questioned in separate rooms. However, there are no other witnesses, and the prosecutor only has enough evidence to convict one of them. This only happens if one prisoner agrees to testify against the other.

For this reason, the prosecutor offers each prisoner a bargain: a reduced sentence or freedom for testifying against the other. As such, each prisoner can either remain silent or betray the other prisoner by testifying against them.

This situation can lead to four potential outcomes:

• Prisoner A betrays Prisoner B while the latter stays silent. A goes free while B serves a five-year sentence.
• Prisoner B betrays Prisoner A while the latter remains silent. B is set free while A serves a five-year sentence.
• Both A and B cooperate and remain silent. They both serve a one-year sentence each.
• Both criminals betray each other and serve three years each.

From this scenario, if the prisoners act in their best interest, the outcome is suboptimal, and the best outcome is cooperation. However, game theory suggests that a purely rational agent or actor will opt to betray since the consequence of cooperation is high. This leads to the only potential outcome of both prisoners betraying each other.

The prisoner’s dilemma could otherwise be described as a two-person, non-cooperative, variable-sum game. That is to say, it incentivizes participants to harm each other despite the alternative of cooperating for a greater mutual benefit. In the context of crypto, an example of this would be if an individual miner prioritizes their own needs over the interests of the entire network. For instance, if all Bitcoin miners cooperate by mining honestly, the entire network remains secure and reliable for everyone. However, an individual miner might benefit more by mining maliciously—such as attempting a 51% attack or Finney Attack, to gain extra rewards at the expense of network security.

In practice, crypto mining more closely resembles an iterated prisoner’s dilemma, where the prisoner’s dilemma is repeated over time, and participants can be rewarded or punished based on their behavior. This relates to mining pools, where miners repeatedly interact and develop reputation systems that encourage honest participation for long-term mutual benefits, and discourage short-term incentives to cheat.