Image there is two companies in an oligopoly competing with homogeneous goods. In this case, lets use Shell and Exon mobile gas companies. Lets imaging that these are the only two gas companies in America and that they are a cartel. The two companies have full control of the market and are working with each other. The game theory comes into this example because what is best for the gas industry as a whole is not best for the individual firms. If both firms have a contract to produce the same output at the same price, each firm’s total profit would be less than if they cheated in the contract and produced more output. The dominate strategy nash equilibrium in this case would be a profit of $2000 for each firm. Each firm has an incentive to cheat because if Firm 1 cheated and produced more output, then their total profit would be $3000 and Firm 2 total profit would be $500. So why wouldn’t firm 1 produce more if they would get more profit? Because the profit they would get if Firm 1 cheated is not worth the repercussions of what Firm 2 would do to retaliate. An example is called the trigger strategy. If Firm 1 did not cooperate in the past, this triggers a more competitive response from Firm 2 today and forever after. So each firm actually has an incentive to keep their agreed output at the dominate strategy nash equilibrium because the total profit all-together is greater for each firm in the long-run.
