# Oligopoly

## Measuring Market Concentration

### Definition

• Concentration ratio (CR)is a ratio that indicates the size of firms in relation to their industry as a whole.
• It is the ratio of the combined market shares of a given number of firms to the whole market size.
• Usually, it is defined as the percentage of the market's total output supplied by its four largest firms.

### Example

Calculate the 4-firm CR of the following example:
Firm Sales
1 20
2 20
3 20
4 20
....... .......
5 10
6 10
CR4 = (S1 + S2+ S3 + S4) / ST = 80 / 90 = 0.88

### Definition

Oligopoly is a market form wherein a small number of large sellers dominate a market or industry.
In this market form, a firm's decisions regarding the price or quantity can affect other firms and cause them to react.
Hence, the firm needs to consider these reactions when making such decisions about P and Q.

### Example

 Assume a relatively small city has 1000 residents Currently, there are firms providing cellular products (duopoly): Vodafone and O2 Each firm's costs: FC = \$0, MC = \$10 per unit
P Q
\$01000
\$5900
\$10800
\$15700
\$20600
\$30500
\$40400
\$50300
\$60200
\$70100

The revenues, costs, and profits are shown below.
P Q Revenue Cost Profit
\$0 1000 \$0 \$10,000 −\$10,000
\$5 900 \$4,500 \$9,000 −\$4,500
\$10800 \$8,000 \$8,000 0
\$15700 \$10,500 \$7,000 \$3,500
\$20600 \$12,000 \$6,000 \$6,000
\$30500 \$15,000 \$5,000 \$10,000
\$40420 \$16,800 \$4,200 \$12,600
\$50340 \$17,000 \$3,400 \$13,600
\$60200 \$12,000 \$2,000 \$10,000
\$70100 \$7,000 \$1,000 \$6,000

Note that Competitive outcome happens when P = MC = \$10, Q = 800, Profit = \$0, and
Monopoly outcome occurs when P = \$50, Q = 340, Profit = \$13,600

In this situation, one possible outcome from this scenario is collusion, where an agreement among the two firms about Q or P.
For example, both would agree to each produce half of the monopoly output.
So, for each firm: Q = 170, P = \$50, Profits = \$6,800

### Exercise

Exercise-1 on Collusion vs. self-interest

Check your answers here: Solution-1 to the Exercise on Collusion vs. self-interest

### Exercise

Exercise-2 on Collusion vs. self-interest

Check your answers here: Solution-2 to the Exercise on Collusion vs. self-interest

Note that in the above example, both firms choose their best strategy given the strategies that all the others have chosen (Nash equilibrium)
Our duopoly example has a Nash equilibrium in which each firm produces Q = 340.
• Oligopoly Q is greater than monopoly Q but smaller than competitive Q.
• Oligopoly P is greater than competitive P but less than monopoly P.

### The Size of the Oligopoly

As the number of firms in the market increases,
• the price effect becomes less
• the oligopoly starts behaving like a competitive market
• P gets closer to MC
• the market quantity draws near the socially efficient quantity

## Game Theory

• Game theory is the study of mathematical models, which helps to understand oligopoly and other situations
where "players" and rational decision-makers interact and behave strategically.
• Dominant strategy: a strategy that is best for a decision-maker (player) in a game
regardless of the strategies chosen by the other decision-makers (players)
• Prisoners' dilemma: a "game" between two captured criminals that
illustrates why cooperation is difficult even when it is mutually beneficial

### Example: Prisoners' Dilemma

• Police officers have caught Joe and Mike, two suspected hackers, but only have enough evidence to imprison each for 6 months
• After a thorough investigation, an offer is made to each one the following deal:
• If you confess and implicate your partner, you go free.
• But if you do not confess but your partner implicates you, you get 12 years in jail.
• If you both confess, each gets 5 years in prison.
Note that confessing is the dominant strategy for both players and Nash equilibrium is that both confess.

Outocme
• Both would have been better off if both remained silent.
• If both Joe and Mike confess, each gets 5 years in jail.
• But even if Joe and Mike had agreed before being caught to remain silent, the logic of self-interest takes over and leads them to confess.

### Oligopoly as a Prisoners' Dilemma

• In a situation of oligopoly where cartel members hope to reach a monopoly outcome,
they endup playing the prisoners' dilemma example
• In the previous example: Vodafone and O2 qre duopolists in a city.
• The cartel outcome maximizes profits: Each firm agrees to serve Q = 340 customers.
Here is the "payoff matrix" for this example:

### Exercise

Exercise on Fare Wars Game

Check your answers here: Solution to the Exercise on Fare Wars Game