Oligopoly/Duopoly and Game Theory

Updated12/20/2016 Jacob Reed
An oligopoly is a market structure with only a few firms. Products can be homogeneous or differentiated. Game theory is the main way economists understands the behavior of firms within this market structure. Games consist of 2 players (in a duopoly which is all there is in Advanced Placement Microeconomics) each with two strategies. This creates a pay off matrix with 4 possible outcomes. The trick to solving these problems is that you must put yourself in the mind of one actor while pondering how the actions of the second affect the decisions of the first. Mark the best decisions for each player as you go through the matrix. In the example below, green is used to mark the best decisions given the choice of the other player. 
Take a look at the payoff matrix for the prisoners' dilemma (see figure 1). In this classic game theory example two criminals are caught for stealing a car. The police also think they robbed a bank but they don’t have any evidence against them. The police separate the prisoners and question them individually. If they both confess to the bank robbery they both go to prison for 5 years. If they both deny robbing the bank, they both go to prison for 2 years. If one confesses while the other does not, the one who confesses will only go to prison for 1 year while the other will go to prison for 10 years. This scenario creates 4 possible outcomes illustrated in the 4 quadrants of the payoff matrix below.
Let’s look at prisoner A first. If prisoner A thinks prisoner B will confess, then prisoner A is deciding between confessing as well and getting 5 years in prison or denying and getting 10 years in prison (see figure 2). Confessing is a better option for Prisoner A.
If, on the other hand, prisoner A thinks prisoner B will deny, then prisoner A is deciding between confessing and getting 1 year in prison or denying and getting 2 years in prison (see figure 3). Again, confessing is the better option for prisoner A.
If, on the other hand, prisoner A thinks prisoner B will deny, then prisoner A is deciding between confessing and getting 1 year in prison or denying and getting 2 years in prison (see figure 3). Again, confessing is the better option for prisoner A.
Now let’s look at prisoner B (see figure 4). If prisoner B thinks prisoner A will confess, then prisoner B is deciding between 5 years in prison (confessing also) or 10 years in prison (denying). Confessing is a better option for prisoner B.
If prisoner B thinks prisoner A will deny (see figure 5), then prisoner B is deciding between 1 year in prison (confessing) and two years in prison (denying). Again denying is the better option for prisoner B.
If prisoner B thinks prisoner A will deny (see figure 5), then prisoner B is deciding between 1 year in prison (confessing) and two years in prison (denying). Again denying is the better option for prisoner B.
One thing you must know for these problems is the Nash Equilibrium. This is the most likely outcome if there is no collusion. It is also the quadrant containing two likely choices (upper left quadrant with 2 green triangles in figure 6 ). You should note there is not always a Nash Equilibrium.
Occasionally you get a question asking about a Collusion outcome. This is much easier to figure out. For that you just look at all the quadrants in the pay off matrix and decide where the two entities would chose to end up if they could talk it out and come to some negotiated agreement. In our example that is the lower right quadrant where both prisoners deny and only spend two years in prison.
Occasionally you get a question asking about a Collusion outcome. This is much easier to figure out. For that you just look at all the quadrants in the pay off matrix and decide where the two entities would chose to end up if they could talk it out and come to some negotiated agreement. In our example that is the lower right quadrant where both prisoners deny and only spend two years in prison.
You also need to know what a Dominant Strategy is. This is the choice one of the players will make regardless of the other player's action. In our prisoners' dilemma, both prisoners have a dominant strategy to confess. That is both prisoners should confess regardless of what the other player does. You should note, there is not always a dominant strategy for a particular player. If there is not, it is because the actions of that player are dependent on the actions of the other player.
Up Next:
Review Game: Oligopololy Game Theory
Content Review Page: Monopsony and Perfectly Competitive Factor Markets
Up Next:
Review Game: Oligopololy Game Theory
Content Review Page: Monopsony and Perfectly Competitive Factor Markets
Other recommended resource: Jason Welker