Introduction to Oligopoly

Measuring Market Concentration

Definition 1

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 1

Calculate the 4-firm CR of the following example:

Calculate the 4-firm CR
Firm	Sales
1	20
2	20
3	20
4	20
.......	.......
5	10
6	10

CR₄ = (S₁ + S₂+ S₃ + S₄) / S_T = 80 / 90 = 0.88

Definition 2

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 2

Calculate the 4-firm CR - Solution

The 4-firm CR - Solution
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

Calculate the 4-firm CR - Solution 2
P	Q
$0	1000
$5	900
$10	800
$15	700
$20	600
$30	500
$40	400
$50	300
$60	200
$70	100

The revenues, costs, and profits are shown below.

RCP
P	Q	Revenue	Cost	Profit
$0	1000	$0	$10,000	−$10,000
$5	900	$4,500	$9,000	−$4,500
$10	800	$8,000	$8,000	0
$15	700	$10,500	$7,000	$3,500
$20	600	$12,000	$6,000	$6,000
$30	500	$15,000	$5,000	$10,000
$40	420	$16,800	$4,200	$12,600
$50	340	$17,000	$3,400	$13,600
$60	200	$12,000	$2,000	$10,000
$70	100	$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 1

Exercise-1 on Collusion vs. self-interest

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

Exercise 2

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 3: 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 3

Exercise on Fare Wars Game

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

For more details, please contact me here.