We’re going to look at two important concepts in this video.
The prisoner’s dilemma and the payoff matrix.
I’ll explain what the prisoner’s dilemma is and how its related to the idea of a payoff
matrix.
Then we’ll use a payoff matrix to see how a firm may make a business decision while
keeping its competitor in mind.
I’ll start with a story.
There are two individuals who have decided to rob a house, Richard and Nathan.
While they’re in the process of getting away, they are caught by a police officer,
whom we will call Officer Smith.
Enter the prisoner’s dilemma.
Officer Heath separates the two prisoners into separate rooms.
He interviews them both separately and offers them a deal.
If they are willing to betray their counterpart, they will be set free but the other person
will be sentenced to 2 years in prison.
If they both remain silent, they each serve 1 year in prison.
There are four possible outcomes here.
I’ll present each one.
First, upon hearing the deal, Richard decides to tell.
The detective presents the same deal to Nathan, and he decides to tell.
In this instance, they are both sentenced to 3 years in prison each.
Second, Richard hears the deal and thinks there’s no way Nathan would tell so he cannot
bring himself to rat on his friend.
However, he’s wrong about Nathan and Nathan rats on Richard – resulting in a 2 year
prison sentence for Richard.
Third, Richard decides to tell on Nathan but Nathan refuses to tell on Richard.
This results in a 2 year sentence for Nathan.
Richard is set free.
Finally, both Richard and Nathan refuse to tell and end up with 1 year in prison each.
The prisoner’s dilemma is simply this…what should they do?
If they both act in self-interest, there’s a much worse outcome that is possible.
If this is a one-shot game, how will it play out?
What you’ve just seen here is a payoff matrix which shows possible outcomes of individual
decisions.
This is tied to the economic concept, game theory, which examines firm behavior when
taking into consideration the possible reactions of competitors.
In the next case, we’ll consider a payoff matrix for two firms that are in direct competition
with each other.
If you watched my earlier videos on collusion, you’ll have seen this example already.
I’m going to setup a payoff matrix which is simply a table that shows the possible
outcomes of two firms’ decisions.
I’ll simplify the oligopoly structure to a duopoly, which is an oligopoly in which
two firms dominate the market – such as Coke and Pepsi.
In this example, I’ll consider two competing firms, Firm X and Firm Y and the influences
on their decisions to increase the level of promotion for their products.
First is Firm X which has the choice to either continue with limited promotion or increase
their level of promotion.
Firm Y has the same choices.
If both firms limit their promotion campaigns, both firms will earn a profit of $40.
However, if only Firm X increases its promotion while Firm Y limits theirs, Firm X can earn
$65 profit – substantially more than the previous strategy.
Firm Y will be left with only $5 profit.
However, Firm X needs to keep in mind what Firm Y would do.
If Firm Y increases promotion while Firm X continues with limited promotion, then Firm
X will earn very little profit while Firm Y earns $65 in profit.
If both firms are unsure of what the other will do, then they may just both increase
their promotion which leads to a profit of $20 each.
In a one-shot game, anything could happen.
However, firms like Coke and Pepsi are in constant back and forth competition.
The result will likely be that both firms decide to limit promotion and continue to
earn $40 profit over the longer term.
You’ll need to understand this payoff matrix and how it relates to game theory.
Game theory looks at the actions of competitors in order to determine an optimal strategy.
At this point, you should be comfortable explaining what the prisoner’s dilemma is and how it
is related to the concept of a payoff matrix.
Understanding how the payoff matrix can inform business decisions will be helpful when you
conduct your analysis of oligopoly markets.
If you have any questions or comments, leave them below or email me at enhancetuition@gmail.com.