Other Market Models Oligopoly Understanding a Cartel as a Prisoner’s Dilemma Page 1 of 1

Let’s apply game theory to the case of a cartel. A cartel is an oligopoly where the individual members try to act as a monopolist. Remember, the monopoly always maximizes profits in a given market. So, if we have a number of firms that can get together and act as one, that is, set price and quantity together, they can choose the monopoly price, the monopoly quantity and earn the monopoly profits, which they can then divide among themselves. A cartel arrangement like this always maximizes profits for the members of the oligopoly. However, holding together a cartel may prove difficult, because of the prisoner’s dilemma. After all, if your two rivals are showing restraint, that is, they’re restricting the quantity that they produce so as to help keep the price high, then you’re tempted to try to sell a larger quantity to take advantage of that higher price. It’s individually rational for a single firm to take advantage of its rival’s restraints by increasing the quantity that it sells. However, if all of the firms subject to the same temptations try to increase their outputs simultaneously, then the price falls back towards the competitive levels. The firms compete, output increases, price falls and the cartel, for all practical purposes, doesn’t exist. The firm sells more output than a monopoly would at a lower price and earns a much smaller profit. What we’re going to do, in this lesson, is show how the cartel’s problem is a special case of the prisoner’s dilemma. Let’s look at two countries that are part of a want to be cartel; they are Nigeria and Venezuela. These two countries would like to cooperate in the production and sale of oil so that the price of oil stays high and they are able to act as a monopoly jointly and maximize their profits. Then, Nigeria and Venezuela each have two strategies. The first is to cooperate with the cartel agreement. In which case, you produce your share of the monopoly output. The monopoly output of oil is determined and Venezuela produces its half, Nigeria produces its half and in that case the monopoly profit is produced and shared between the two countries. Alternatively, you can cheat on the agreement. You can let your rival hold the price high by restricting his output and then you can try to sell a lot of output to take advantage of the high price. This would be called cheating on the cartel agreement and what it really means is that Venezuela would be producing a larger quantity of oil than the cartel prescribed for it. So, instead of restricting itself to one-half of the monopoly output, Venezuela might produce three- quarters of the monopoly output or some larger amount of oil. That then has a bad effect on your rivals who have restricted their quantity, because now you’re pushing down the price and you’re leaving them in trouble. So, let’s fill in the table then, with the numbers. Let me make an assumption first of all. The assumption is going to be that if both firms cooperate with the cartel arrangement, if the firms act jointly as a monopoly, that they will make a total of $10,000,000, and that if Venezuela produces half of the output and Nigeria produces half of the output, each of them gets half of that monopoly profit. So, if they both cooperate and the cartel is successful, then each of them will get $5,000,000 worth of profit, 5,000,000 for Nigeria, 5,000,000 for Venezuela. Now, notice here that the numbers in the matrix represent profits from oil sales and since profits are good, each country would like to have as large a number as possible. This contrasts with our previous example where the numbers represented jail terms.