Cournot game in Game Theory

(7 Points) 111 the Cournot game. the market demand function is P= a-Q. (340}, where P is the market price and Q is the total output of two rms. Assume that the marginal cost of a rm be C, and there is no xed cost. Assuming that the game is repeated an innite number of times. at each stage of the game, each rm can observe the output level of its opponent. Firrns all adopt the "Trigger Strategy". If one firm adopts noncooperative behavior in order to maximize shortterm prots, it will trigger the competitor to never cooperate and adopt the Coumot production level forever. [1] Please calculate the conditions for the discount factor 5, which makes the Trigger Strategyr to form the subgame perfect Nash equilibrium. (2) Suppose there are n rms, what is the value range of 3 under this condition? Explain the relationship between S and n