Player 3 (matrix)
4. Consider two firms producing the same good, competing in prices (Bertrand competition model) instead of quantities. Each firm faces the same market de- mand function q(p) 1000-p. Firm 1 has constant marginal cost of production c1200, while firm 2 has constant marginal cost c2 = 400.
Both firms decide the price for their product simultaneously. If their prices are different, the firm with the lowest price captures all the market. If both firms set the same price then each firm captures half of the demand at that price.
a. Draw the profit function #1 (P1, P2) when p2 = 600 (don't forget to identify all relevant points in the graph).
b. Compute the best response correspondences for each firm.
C. Is there a Nash equilibrium in this game?
d. Consider a modified game in which if both firms set the same price then firm 1 captures all the market. All the other rules remain the same.
Compute the best response correspondences. Is there a Nash equilibrium in this modified model?
Gs has three players: Player 1 chooses rows, Player 2 chooses columns, and Player 3 chooses which matrix will be played.