Game Theory of Oligopolistic Pricing Strategies

In competitive, monopolistically competitive, and monopolistic markets, the profit maximizing strategy is to produce that quantity of product where marginal revenue equals marginal cost. This is also true of oligopolistic markets — the problem is, it is difficult for a firm in an oligopoly to determine its marginal revenue because the quantity of product that can be sold for a given price will depend on the prices charged by the other firms in the oligopoly and the quantity that they produce. Economists have examined this interdependence by using game theory, which analyzes strategies used by individual players that take into account what the other players will do.

Experimental economics studies game theory by designing scientific experiments using real individuals in specific situations to determine actual outcomes that are not dependent on statistical analysis. Nonetheless, even though statistical analysis is needed to analyze real-world scenarios, game theory offers insights into how oligopolistic firms price their product.

A common scenario for applying game theory to decision-making is the prisoners' dilemma. Bennie and Stella were arrested for robbing banks. Each was interrogated in separate rooms, where the interrogators offered them a choice:

There are 4 possibilities, which are represented by the following payoff matrix:

Prisoners' Dilemma Payoff Matrix
Stella confesses: 5 years
Bennie confesses: 5 years
Stella silent: 10 years
Bennie confesses: goes free
Stella confesses: goes free
Bennie silent: 10 years
Stella silent: 2 years
Bennie silent: 2 years

The best possibility for both as a group would be if neither confessed, which would mean that they would only have to spend 2 years in prison. The worst possibility for both of them as a group is if they both confessed — then they would have to spend 5 years in prison. However, as individuals, they may be able to do better or worse, depending on how successfully they anticipate what the other will do. If Stella confesses, the worst she can do is spend 5 years in prison, and the best that she can do is go free; likewise for Bennie. In this case, confessing is what is called in game theory a dominant strategy, which yields the best outcome regardless of what other players do, which is the strategy to take when it is impossible to anticipate their decision. For instance, if Stella does not confess, then she will either spend 10 or 2 years in prison, depending on whether Bennie confesses or not. Stella would probably only choose silence if she was fairly confident that Bennie would not confess and that she cared enough about him to not choose to confess to free herself; on the other hand, if she was not confident about Bennie's decision, then she would select the dominant strategy.

When firms in an oligopoly must decide about quantity and pricing, they must consider what the other firms will do, since quantity and price are inversely related. If all of the firms produce too much, then the price may drop below their average total costs, causing them losses. If they can restrict quantity to that which corresponds to where marginal cost equals marginal revenue for the oligopoly as a whole, then they can maximize their profits. However, they do have one advantage over the prisoner's dilemma scenario — they usually know what the other firms did in the past, so they can decide on quantity and pricing based on the assumption that they will act in the same way in the future. But if the firm is wrong in its anticipation, then they can make corrections in its production schedule.

Where firms have a history of working together, they can choose a dominant strategy based on the choices that the other firms have made, which is called a Nash equilibrium, named after the theoretical economist John Nash, whose life was portrayed in the movie A Beautiful Mind.

Sometimes firms in an oligopoly try to eliminate guesswork by forming a cartel, where they agree on a particular output, so that they can sell their output at a profit maximizing price.

Cartels often fail because one or more firms will be tempted to cheat, since this will allow them to earn outsized profits, especially if they are a smaller firm that contributes only a small share of the total output of the oligopoly. For that would allow the firm to sell a greater quantity at the profit maximizing price without lowering demand, and therefore, the price. It would also improve the firm's economy of scale.

Diagram showing how much profit a cartel earns when they all cooperate, when 1 firm cheats, and when none of the firms cooperate.
  • MR = Marginal Revenue
  • MC = Marginal Cost
  • D = Market Demand, Price

When firms in a cartel cooperate by restricting quantity for higher prices, then each firm gets Po for its product by restricting its quantity to the agreed amount Qo (it is assumed that Qo is equal to each firm's MR = MC output), and each firm earns the revenue above its marginal cost represented by the areas 1 + 3 in the diagram on the left. Hence, the oligopoly earns what a monopoly would earn. (Note that the quantity Qo would probably be different for the different firms, but the graph still represents each firm's revenue, but the quantity axis would be adjusted, depending on the firm's market share, which is usually commensurate with its size.)

When none of the cartel members cooperate, then the quantity increases to Qc and the market price declines to the competitive price Pc, and each firm in the oligopoly earns 3 + 4 above their marginal cost. (Again, the size of the 2 areas will be commensurate with the size of the firms and their corresponding market share.)

If a firm cheats, then it earns: 1 + 2 + 3 + 4 by producing more until MC = Po, which is equal to the quantity, Qcheater. This assumes that the firm produces only a small portion of the output of the oligopoly; otherwise, the firm's increased output would cause the market price to decline, and the market demand curve for the oligopoly as a whole would shift to the left.