P2, firm 1 still gets a positivedemand for its product. Regulation does not allow either firm to charge a price higherthan 20. Both firms have a constant marginal cost c=4.(a) Construct the best...

Extracted text: (1) Two firms produce goods that are imperfect substitutes. If firm 1 charges price pi and firm 2 charges price p2, then their respective demands are q1 = 12 – 2p1 + p2 and q2 = 12 + p1 – 2p2. So this is like Bertrand competition, except that when p1 > P2, firm 1 still gets a positive demand for its product. Regulation does not allow either firm to charge a price higher than 20. Both firms have a constant marginal cost c=4. (a) Construct the best reply function BR1 (p2) for firm 1. That is, pi = the optimal price for firm 1 if it is known that firm 2 charges a price p2. Construct a Nash equilibrium in pure strategies for this game. Are there any Nash equilibria in mixed strategies? If yes, construct one; if no provide a justification. BR1 (P2) is (b) Notice that for any given price p1, firm 1's demand increases with p2, so firm 1 is better off when firm 2 charges a high price p2. What is the best reply to p2 best reply to p2 = 0? 20? What is the (c) What prices for firm 1 are not strictly dominated? What prices would survive two rounds of strict dominance? Provide a reason for each strategy that you eliminate. (d) Challenge question: If you continue the iterative elimination of strictly dominated strategies, what strategies will survive?