I am learning basic Oligopoly models.
I know that :
- In Cournot model firms set output - output is the strategic variable.
- In Bertrand model firms set prices - price is the strategic variable.
Simple problems I see are usually given demand/cost fucntion for a differentiated duopoly and let us determine the Bertrand or Cournot equilibrium.
Here however is a mixed market:
Assume the following duopoly (firms are denoted by 1 and 2) with the following demand functions:
$$P_1=100-0.5Q_1-0.4Q_2 \\ P_2=100-0.5Q_2-0.4Q_1$$
Firm 1 plays Cournot while firm 2 plays Bertrand. Assuming that there are no costs, find the optimal Nash quantity-price solution.
How can I solve for the equilibrium?