Game Theory Pt.2
Prisoner's dilemma model
Prisoner's Dilemma: this model can be used to understand how interdependent decision making can explain a firm's actions/strategies.
The diagram below shows a basic viewpoint of the prisoner's dilemma. I have purposely made this diagram very simple to show you how this works. There are more difficult examples out there which you may or may not have come across, but this gets the point of the prisoner's dilemma across to you.
The above diagram is called a payoff matrix. We use it to calculate what is the best available strategy for the firm to employ. We have two prisoners, Prisoner A and Prisoner B. They both have been brought in for questioning. They are not allowed to communicate with each other. We also assume that the two prisoners have no strong trust or bond with one another. This is very important in this experiment.
The detective starts by questioning Prisoner A and moves on to question Prisoner B. The detective offers both of them some options. From the options above, it might like denying is the best option at first glance. This is because if you deny and your partner in crime doesn't confess, you will both get away with the crime and serve 0 years.
However, you don't know if your partner in crime will confess, because you have no communication with that person. So you anticipate that your partner in crime might rat you out and serve less time. If you partner in crime does this, you have to serve 20 years!
So in the example above, it is too risky to deny your crime. The best option is to confess. This is because the worst case scenario is serving 3 years in prison and the best case scenario is serving 0 years.
This is also known as the Nash Equilibrium. Each firm has picked the choice, taking into account the choice of the other party.
How is this appropriate to oligopolies?
Scenario A: This example can be used in many applciations. For example, when firms decide how much to spend on advertising. If your competitors are spending a lot on advertising, then it might be a good idea to do the same because if you don't, then your competitor's advertising campaign will probably be more successful and they will steal all of your customers.
Scenario B: What about when a regulator is investigating a number of oligopoly firms for collusion. The best thing for the firm to do is to confess to their crime and assist the regulator as much as possible and pay a lower penalty.
What have we learned?
Definition of prisoner's dilemma
A simple payoff matrix diagram
Nash equilibrium
Why is this relatable to oligopolies
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