Game Theory: Prisoner’s Dilemma

Game theory is the study of how independent economic agents (i.e. people) interact based on their individual preferences/strategies and the overall payoffs. It is generally used to explain why an individual will act the way they do based on the limited information they have.

Prisoner’s Dilemma is a famous example that illustrates key game theory concepts and has been used in classrooms and lectures around the world. It highlights how gains from cooperating tend to be significantly larger than gains from pursuing with self-interest.

Let’s say there are two prisoners who have committed a crime together: Prisoner A and Prisoner B. Each prisoner is taken to an interrogation room and asked whether they want to confess and testify against the other prisoner (both of them don’t know what option the other chose).

1. If Prisoner A confesses and Prisoner B remains silent, Prisoner A will be set free (due to cooperation with the police) while Prisoner B will be given a jail sentence of 10 years and vice versa
2. If Prisoner A confesses and Prisoner B also confesses, both Prisoner A and Prisoner B will be given a jail sentence of 5 years due to the blame getting split between them
3. If Prisoner A and Prisoner B remain silent, they will both be given a jail sentence of 2 years as the police have no concrete evidence and therefore can only press ‘light’ charges

Let’s say we’re Prisoner A. From our perspective, if Prisoner B remains silent, our optimal move would be to confess so we’re immediately set free. On the other hand, if Prisoner B confesses, our optimal move would still be to confess because we would prefer a jail sentence of 5 years instead of 10.

We can see that in both scenarios, regardless of what the other person does, our optimal strategy is to confess. From Prisoner B’s, it also seems like a sensible idea to confess regardless of what Prisoner A does.

Therefore, you end up in a Nash equilibrium state of (5,5) where neither agent sees any added benefit in unilaterally changing their strategy and believes they are making the optimal decision that benefits them individually but not as a group.

Weird isn’t it?