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Cournot’s model of oligopoly - page 3 / 38

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Nash equilibrium

Payoff functions

Firm 1’s profit is

π1(q1, q2) = q1(P (q1 + q2) c)

=

cq1 q1(α c q 2

q1)

if q1 α q2 if q1 > α q2

Best response functions

Firm 1’s profit as a function of q1:

profit of firm 1

q 2 = 0

q 2 > 0

0

a - ca a - c- q 2

q

1

Up to α q2 this function is a quadratic that is zero when q1 = 0 and when q1 = α c q2.

3

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