In an oligopoly, there are even fewer firms compared to monopolistic competition, and there are higher barriers to entry. The players need to keep an eye on each other’s strategy. If one firm changes its prices, you can expect the same move from other firms as well. The firms are interdependent and one firm’s actions will have an impact on the other firm’s demand curve as well. The oligopolies can be described using the following models:

1. Kinked Demand Curve Model
2. Cournot Duopoly Model
3. Nash Equilibrium Model
4. Stackelberg Dominant Firm Model

Kinked Demand Curve Model

According to this model, each firm in the oligopoly believes that if it raises its price, its competitors will not follow, but if it lowers its price all of its competitors will follow. The following graph shows the kinked demand curve model. According to each firm, the demand for its product has a kink at the current price (P) and quantity (Q).

If prices are greater than P, then increasing the price by a small amount leads to a large decrease in quantity sold. If price is less than P, large price cuts lead to low increases in the quantity sold. If competitors also lower prices, then there is no advantage to cutting prices.

Demand is relatively elastic above the kink. This is because the prices of all other firms remain unchanged.

Demand is relatively inelastic below the kink because if the firm shown in the figure changes its prices, all other firms’ prices will also change.

Firms produce at the point where MR = MC. This model states that price and quantity are not very sensitive to small cost changes.

The kink in the demand curve means that the MR curve is discontinuous at the current quantity. This is shown by gap in the figure below.

The main drawback of this model is the assumption that the other firms will not raise prices when one firm does and other firms will cut prices if one firm does. This assumption may not be correct and what determines the market price at which the kink occurs is not explained by the model.

Cournot Duopoly Model

Cournot duopoly model is another model used to describe the prices and outputs of firms in an oligopoly. The model assumes that there are only two firms in the oligopoly (it’s a duopoly). 

The key assumption of the Cournot model is that each firm assumes the other firm’s output is given and fixed, and maximizes its own profit based on that assumption. When firm 1 chooses its output y1 to maximize its profit, it takes firm 2’s output y2 as given and fixed; and, similarly, when firm 2 chooses its output y2 to maximize its profit, it takes firm 1’s output y1 as given and fixed.

When each firm chooses to produce the same quantity, they cannot make additional profits by changing quantities and we have equilibrium. The market price as a result of this will be less than the profit maximizing price as would be charged by a monopolist; however, it will be higher than the marginal cost, i.e., the price that would be charged by a firm in perfect competition.

Further, as new firms enter the oligopoly, the equilibrium market price will fall till price equals marginal cost.

Nash Equilibrium (Prisoner’s Dilemma)

Game theory is the study of strategic behavior that takes into account how others are expected to behave, and the mutual recognition of interdependence. Game theory can be used to study oligopolies. 

The prisoners’ dilemma game has the following four characteristics: 

• Rules 
• Strategies
• Outcomes
• Payoffs

A good Web version of the game can be found on a site operated by a group called Serendip at Bryn Mawr College in Pennsylvania. The URL (also on your Economics Place Web site) is http://serendip.brynmawr.edu/playground/pd.html

Rules

The rules describe the setting of the game, the actions the players may take, and the consequences of those actions. 

In the prisoners’ dilemma game, two prisoners (A and B) have been caught committing a petty crime. Each is held in a separate cell and cannot communicate with each other.

Each is told that both are suspected of committing a more serious crime.

If one of them confesses, he will get a 1-year sentence for cooperating while his accomplice get a 10-year sentence for both crimes.

If both confess to the more serious crime, each receives 3 years in jail for both crimes.

If neither confesses, each receives a 2-year sentence for the minor crime only.

Strategies

Strategies are all the possible actions of each player. 

A and B each have two possible actions:

1. Confess to the larger crime.

2. Deny having committed the larger crime.

With two players and two actions for each player, there are four possible outcomes:

1. Both confess.

2. Both deny. 

3. A confesses and B denies.

4. B confesses and A denies.

Payoffs

Each prisoner can work out what happens to him—can work out his payoff—in each of the four possible outcomes.

Outcome

Nash equilibrium (developed by John Nash) happens when player one makes the best decision, given player two’s actions and vice versa. For example, if A confesses, then it is in the best interest of B to also confess to avoid the very long prison sentence. The same is true for A if B confesses. In this case, it is in the best interest of both prisoners to confess. But this is not the best outcome for both prisoners. It would be better if neither of them confessed, then neither would be convicted of the serious crime. There is no way to avoid the bad outcome from confessing because the prisoners cannot communicate with each other.

Game Theory in Oligopolies

Firms in an oligopoly can decide to collude with each other or not. For an oligopolistic firm, the key factor in determining the demand is the pricing strategy of other firms in the oligopoly. So, it’s important for the firm to predict how other firms will react if they adjust their own prices. While we may not be able to determine the exact price and output, we can analyze two extreme cases. In reality, however, firms operate somewhere in between these two extremes.

Collusion

Under collusion, firms agree to avoid various competitive practices, specifically price reductions. A collusive agreement is an agreement between two (or more) firms to restrict output, raise the price, and increase profits. The oligopolistic firms restrict their output to the monopoly level, i.e., to the point where MR = MC. The market price of the products is set at the monopoly price, and all firms earn monopoly profits. An example of a collusive agreement is a cartel. Sellers coordinate supply decisions so that the joint profits of members will be maximized.

No Collusion

Under no collusion or non-cooperation, all oligopolistic firms set their price independently. In this case, the market price is driven to the competitive price since all firms will lower their price as much as possible in order to attract customers. Any firm with a price above the competitive level will have zero demand. The zero profit rule applies when oligopolists do not collude.

There is an incentive to cheat among oligopolists. If there is an undetected price cut, the firm cutting prices will attract more customers, both those who would not purchase the good at the higher price, and customers of competing firms. The demand curve for an individual firm in the oligopoly will be more elastic than the overall market demand curve. The price that maximizes prices for the whole industry is higher than the price that is best for an individual firm which charges a lower price than the remaining firms in the oligopoly. Like the prisoners’ dilemma, each firm in the oligopoly faces a conflict: cooperate with competitors to maximize joint profits or secretly cheat on the agreement to maximize its share of the joint profits. A firm does not benefit from cooperating if the other firms cheat.

In this case, there may be a Nash equilibrium in which the best outcome (all firms cooperating) is not in the best self interest of each individual firm. An equilibrium in which the best strategy is to cheat, no matter what the strategy of the other firms, is called dominant strategy equilibrium. If such an equilibrium doesn’t exist, the firms may be playing a game of chicken, where the first player to flinch loses. If one firm improves its products, it knows its research will be copied, and it will lose the benefits from innovating. It hopes its rival firm will innovate instead, so it can copy that research. If neither firm innovates, then no firm gains. Equilibrium only exists if one firm innovates and the other copies.

Many games are repeated. Cooperative equilibrium exists when firms make and share monopoly profits. This occurs if cheating is punished. In a “tit for tat” strategy, the firms take turns cheating, and therefore share monopoly profits. In a “trigger strategy,” if one firm cheats, the others also cheat, reducing economic profits to zero in the long run. This can result in price wars among oligopolistic firms.

Dominant Firm Model

This model states that the dominant firm has a large cost advantage over competing firms in the oligopoly. The dominant firm sets prices for the remaining firms. The dominant firm behaves as a monopoly and the remaining firms are price takers, behaving like firms in perfect competition.

The dominant firm sets the price where MR = MC. The smaller firms accept the price set by the dominant firm.