Please help with this question. (Game theory)

4. Infinitely Repeated Differentiated-Bertrand Game There are two and only two firms in the industry, selling differentiated products; let's call them Firm A and Firm B. The system of demands is given by 9A = 30 - 2PA + PB 9B = 30- 2PB + PA Both firms have a constant marginal cost of production of 6. The CEO of each firm decides the price for its products. (a) What is the common price that maximizes the industry profit, i.e., the total profit of the two firms? Denote this price by p*. (b) Suppose the game is static (i.e., one-shot). What is the (common) price in the Nash equilib rium? Show your derivation. Denote this price by p. (c) Suppose the game is infinitely-repeated, and both firms share a common discount factor 6 E (0, 1). Consider the following trigger strategy. Charge p* if no firms have deviated from price p* in the past, and charge p otherwise. What is the smallest discount factor such that the trigger strategy above constitutes a SPNE? Explain