Question: Cournot:

1. Solve for the Cournot Nash equilibrium quantities, prices and profits for the two firms. Call these \(q*,p*,\pi *\).
2. What if these two firms formed a cartel and maximized joint profits? Solve for the resulting quantities, prices and profits. Call them \({{p}^{j}},{{q}^{j}},{{\pi }^{j}}\)
3. What if firm 2 cheats when firm 1 sets \({{q}_{1}}={{q}^{j}}\) ? What are the resulting quantities, prices and profits?
   (Hence, firm 1 gets the profits reduced)
   For firm 2:
   \[\pi _{2}^{*}=\left( p-c \right){{q}_{2}}*=\left( \frac{3a+5c}{8}-c \right)\frac{3\left( a-c \right)}{8b}=\frac{\left( 3a-3c \right)3\left( a-c \right)}{64b}=\frac{9{{\left( a-c \right)}^{2}}}{64b}\]
   (which implies that firm 2 gets the profits increased)
4. What does this have to do with the prisoner’s dilemma?

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