Cournot Duopoly

Published by Mario Oettler on

The Cournot Duopoly is another example of how selfish (uncoordinated) behavior can lead to a worse outcome than unselfish behavior.

Suppose we have to sellers A and B that face a price-demand-function:

p: price

p = 1000 – (qA + qB)

Whereas qA is the quantity offered by A and qB is the quantity offered by B.

For simplicity, we neglect cost. Each seller wants to maximize his profit (=turnover).

The profit is calculated as:

GA: profit for A

GA = p * qA= [1000 – (qA + qB)] * qA

To find the maximum, we calculate the first derivation and set it zero:

dGA/dqA = 1000 – 2qA – qB = 0

This yields:

qA = (1000 – qB)/2

For B, we do the same and get:

qB = (1000 – qA)/2

In the end, we get the quantities:

qA = 333.33


qB = 333.33

The profit for each seller is:

GA = [1000 – (333.33 + 333.33)] * 333,33 = 111,111.1112

GB = [1000 – (333.33 + 333.33)] * 333,33 = 111,111.1112

The total profit is 222,222.222.

If we replace the 1000 in our price demand function by a parameter a, we get as quantities

qA = 1/3*a

qB = 1/3*a

Is this the best result we can expect? If we assume that both sellers coordinate their quantities (like acting as one company), we get the following situation:

GC = p * Q

GC: profit in the coordination case

Q: total quantity

GC = (1000 – Q)*Q

dGC/dQ = 1000 – 2Q = 0

Q = 500

We can see that the optimal quantity here is 500 (compared to 333.33 + 333.33 in the selfish case).

The total profit is 250,000.

This is more than in the selfish case.

Cournot Duopoly Calculator

With this tool, you can calculate prices, qantities and profits for a simple Cournot Duopoly price demand function:

p = a - q
  • p: price
  • q: quantity
  • a: reservation quantity


Selfish (uncoordinated) Behavior

quantity A:
quantity b:
quantity price:
profit A:
profit B:
Total profit:

Coordinated Behavior

quantity A:
quantity b:
quantity price:
profit A:
profit B:
Total profit: