The Prisoner’s Dilemma and its application to pricing

The Prisoner’s dilemma is one of my favourite concepts in Game Theory which is a branch of behavioural economics. Under a Prisoner’s Dilemma situation there are 2 parties. The best outcome arises when both actors co-operate. However because they make their moves concurrently without knowledge of the other’s move, they are incentivised to look after their own personal interest at the expense of the other.

Suppose there are 2 prisoners who have committed a robbery together. The police suspect that the prisoners are guilty however they don’t have hard evidence. They want one of the prisoners to testify against the other. The police separate them into 2 rooms. If neither testifies they will both be charged with a minor offence and each will serve one year in prison (2 years total). If one testifies against the other, then the one who testifies will get off, and the other will get 10 years in prison (10 years total). If they both testify then they will each get 7 years in prison (14 years total).

The best collective outcome is that they both remain silent. However, let’s look at this from the perspective of prisoner A. Suppose B chooses to remain silent. A can testify and will get no prison time, or can remain silent and will get one year in prison. A would be better off testifying. Now suppose B chooses to testify against A. If A testifies then they both go to prison for 7 years. If A remains silent then he will go to prison for 10 years. Once again, A would be better off testifying.

In summary, regardless of what B does, A should testify. However the best collective outcome is if they both remain silent.

There are lots of applications of this concept in the real world including war and negotiation. Of particular interest is pricing. When there are a small number of competitors in a market (we call this an oligopoly), the best outcome for each competitor is if everyone keeps their price high. However even if there is an agreement or understanding (which is of course illegal) between the competitors to keep their prices high, the incentive is there for one competitor to break the agreement and reduce their prices. However as soon as one competitor does this, others may follow suit which will result in a worse outcome for everyone.

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