Ouestion 6 Consider the following Cournot game with three fi

Ouestion 6 Consider the following Cournot game with three firms i-1,2 and 3. The demand function is PCO) 100 - Q, with Q-41+q2 +43- The production costs are: C() 10 23 l- Find the Nash equilibrium of this game

Solution

Profit for firm 1

=(100-q1-q2-q3-10-2q1)q1

=100q1-q1^2-q1*q2-q3*q1-10q1-2q1^2

Finding FOC we get

100-2q1-q2-q3-10-4q1=0

90-6q1-q3-q2=0

Similarly for different firms

90-6q2-q1-q3=0

90-6q3-q1-q2=0

90-6q3-q1=90-6q1-q3

q1=q3=q2

We have 3 unknowns and 3 equations

90-6q1-q2-q3=0

90-8q1=0

q1=q2=q3=11.25=11(approx.) and Price 100-33.75=66.25