# 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 = 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 depends on the prices charged by the other firms in the oligopoly and and on their production. Economists have examined this interdependence by using **game theory**, which analyzes strategies used by individual players that account for what the other players will do. What distinguishes game theory from other types of economic decisions is that decisions in game theory are based on what other people in the game will do or would be expected to do. Most other economic decisions are not based on the reaction or expected reactions of others but are based on details of the thing being decided.

**Experimental economics** studies game theory by designing scientific experiments using real individuals in specific situations to determine actual outcomes that do not depend 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:

- if they both confessed, they would both get 5 years in prison;
- if one confessed, the confessor would go free while the other one would get 10 years;
- if neither confessed, then they would each get 2 years.

There are 4 possibilities, represented by the following **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 must spend 5 years in prison. However, as individuals, they can 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 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 = marginal revenue for the oligopoly as a whole, then they can maximize their profits. However, they do have 1 advantage over the prisoner's dilemma scenario — they know what the other firms did in the past, so they can decide on quantity and pricing based on the assumption the others will act similarly in the future. But if the firm anticipates wrongly, they can modify their production schedule accordingly.

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.