Assuming that the withdrawals of the two companies are known, what is the likely outcome in this case? To achieve this balance, we assume that each company adapts its production to maximize its profits, which correspond to an oligopoly, is a situation in which a small number of companies sell the most or all of the goods in a market. Oligopolists earn their highest gains if they can come together as an agreement and act as a monopoly by reducing production and raising prices. Since each member of the oligopoly can individually benefit from the expansion of production, such an agreement often collapses – especially since explicit agreements are illegal. Because of the complexity of the oligopoly, which is the result of interdependence between companies, there is not a single theory, generally accepted, on the behavior of oligopolies, as we have theories for all other market structures. Instead, economists use game theory, a branch of mathematics that analyzes situations where players have to make decisions and then get payments based on what other players decide to do. Game theory has found widespread applications in the social sciences as well as in commercial, legal and military strategy. Perhaps the simplest approach for collusant oligopolists, as you can imagine, would be to sign a contract together, that they keep production low and keep prices high. If a group of U.S. companies signed such a contract, it would be illegal. Some international organizations, such as the member nations of the Organization of the Petroleum Exporting Countries (OPEC), have signed international agreements to act as a monopoly, maintain production and keep prices high, so that all countries can reap high profits on oil exports. However, such agreements are legally unenforceable because they fall within a shadow of international law.
For example, if Nigeria decides to lower prices and sell more oil, Saudi Arabia will not be able to sue Nigeria and force it to stop. Many real oligopolies, marked by economic changes, legal and political pressures and the egos of their senior managers, are going through episodes of cooperation and competition. If the oligopolies could maintain cooperation between themselves in terms of production and pricing, they could reap profits as if they were a monopoly.