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Pluralism in Economics: inequalities, innovation, environment
Pluralism in Economics: inequalities, innovation, environment

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13 Collusion

Imagine a market in which, when firms compete with one another, they end up producing a quantity that gives them a certain profit lower than in a monopoly. If firms competing in this market start cooperating, and agree to restrict the quantity produced to the same quantity that a monopolist would produce, they will increase their profits. This type of cooperation between firms to increase profits is called a cartel.  

The UK Competition and Markets Authority (CMA) defines a cartel as an agreement between businesses to not engage in competition. Cartel members might agree to a determined level of production, but they can also do the same with prices, discounts, credit terms, customers, geographies or bids in auctions. In the case of cartels, there are verbal agreements, contracts or other strategies to maintain firms working through the same conditions, because a firm can gain extra profit by defecting whilst the other participants in the cartel maintain their agreed behaviour. For example, if oligopolists decide to restrict output to increase prices and gain extra profit, the colluding firms will have an incentive to increase their output beyond the agreed quota to earn even more profit. 

There is another type of agreement that is not necessarily coordinated and explicit, called tacit collusion. Tacit collusion refers to coordination that competitors reach without contracts or verbal agreements. Firms send signals to competitors around the quantity, product or price they will set and expect competitors to follow their direction. An example of this is price leadership, where a firm with market power sets a price level that other firms follow. Other firms have used tacit collusion in different ways, for example using an intermediary to set pricing, or to share price intentions with others. 

Activity 4: A cartel game

Timing: 5 minutes

This activity models cartel behaviour using a technique from mainstream economics called game theory.

Two firms, A and B, are involved in a cartel where they arrange to restrict the amount of quantity to produce so they can get monopoly profits. Firms have two decisions to make: cooperate or defect. This situation can be modelled using a game whose structure is used in many situations and is called ‘prisoner’s dilemma’ because of its first application. The game is described by the payoff matrix, in which the payoffs represent the profits of the firms. In the example below, firms A and B have made a cartel agreement to restrict their output (Q) so as to raise industry prices and profits. Each can choose to cooperate with the agreement (setting a low output) or defect from the agreement (keeping output high). Firm A’s possible choices are represented in the rows whilst Firm B’s choice are in the columns. Each cell in the payoff matrix shows Firm A’s profits first and Firm B’s profits after the comma. So, for example: if Firm A defects (top row), and set high Q, whilst Firm B cooperates (right column) the payoff (150, 30) shows a profit of 150 for A and 30 for B.

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This table is a square matrix diagram used to illustrate a game theory scenario involving two players, Firm A and Firm B. Each player has two choices:

  • Defect (high Q)
  • Cooperate (low Q)

The matrix is divided into four cells, each representing a combination of choices made by the two. Each cell contains a pair of numbers separated by a comma. These are the payoffs for the Firm A and Firm B, respectively. 

Firm A is the row player such that its choices are shown in two rows: Defect (high Q) in the top row, and Cooperate (low Q) in the bottom row. Firm B is the column player such that its choices are shown in two column: Defect (high Q) in the left column, and Cooperate (low Q) in the right column.

The payoffs of Firm A, the row player, are always written first, so they are the left payoff in each cell of this matrix, and the payoffs of Firm B, the column player, are always written second after a comma, so they are the right payoff in each cell. Each cell shows the following: 

  • Top-left cell: When both play Defect (high Q). The payoffs are 50, 50 
  • Top-right cell: When Firm A plays Defect (high Q) but Firm B plays Cooperate (low Q). The payoffs are (150, 30). 
  • Bottom-left cell: When Firm A plays Cooperate (low Q) but Firm B plays Defect (high Q). The payoffs are (30, 150). 
  • Bottom-right cell: When they both play Cooperate (low Q). The payoffs are (100, 100).
The payoff matrix of the cartel game
Firm A  Firm B
 

Defect 

(high Q) 

Cooperate (low Q) 

Defect 

(high Q) 

50,50  150,30 

Cooperate 

(low Q) 

30, 150  100,100 

Using the payoff matrix and assuming both firms are only motivated by their own payoffs, answer the following questions:

  1. The game can be solved finding its ‘Nash equilibrium’, which is the pair of choices where both players choose their best response given the other player’s choice. What is the Nash equilibrium of the game? (HINT: In order to find it, you have to identify each player’s best choices for each possible choice of the other player.)
  2. What would be the best outcome for the two firms?
  3. What is the result of the game if it is repeated a indefinite number of rounds over time?

Comment

The Nash equilibrium of the game is when the two firms play their best responses, which are represented by the corresponding payoffs that are underlined as shown in the table below.

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This table repeats the previous one but has underlined four payoffs, to highlight the best response which gives the player the underlined payoff.

So in the top left cell, both 50 are underlined;

In the top right cell, 150 is underlined;

In the bottom left cell, 150 is underlined

The payoff matrix of the cartel game with the best response payoffs underlined
Firm A  Firm B 
 

Defect 

(high Q) 

Cooperate (low Q) 

Defect 

(high Q) 

50,50  150,30 

Cooperate 

(low Q) 

30, 150  100,100 
  1. The Nash Equilibrium of the game is when both firms defect. For Firm A, Defect is better than cooperate (50 is greater than 30 and 150 is greater than 100). Then same applies to Firm B.
  2. Both firms, however, would be better off cooperating because they would earn 100 each instead of 50.
  3.  If the game is repeated an indefinite number of rounds, its outcome is unclear since each player could punish the other when they defect, for example by defecting in the following round. So, it is possible that both players would end cooperating although this is not certain.