# Cournot Nash Equilibrium Between Two Firms [migrated]

Suppose we have two firms with specialized, but similar products. Suppose market demand for the two products is: $$p_1(q_1,q_2)=a-bq_1-dq_2$$ $$p_2(q_1,q_2)=a-bq_2-dq_1$$ where $d \in (-b,b)$. Suppose that both firms have cost $c(q)=q$

What does $d$ mean intuitively? Is the Cournot Nash Equilibrium for this $$q_1=\frac{2ba - ad + dc'(q_2)-c'(q_1)2b} {1 - d^2}$$ $$q_2=\frac{2ba - ad + dc'(q_1)-c'(q_2)2b} {1 - d^2}$$ Thanks a ton.

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## migrated to math.stackexchange.com by Jason B♦May 1 '12 at 19:55

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