Q3 Consider the following inverse demand function, p(Q) = 5 762, Q = q1 + Q2, where {11: denotes rm 71's output, 2' = 1, 2. Assume that the total cost of rm '5' is 0931/ 2, with c > 0. Firms choose quantities simultaneously and non cooperatively. The game described above is innitely repeated. Firms use grim trigger strategies (innite Nash reversion). Firms discount future prots at a rate 'r > 0. a) Compute the cartel prots. b) Derive the critical discount factor above which full cartelization (joint prot maximization) is sustainable as a Subgame Perfect Nash Equilibrium (SPNE) of the innitely repeated game. Consider now the following prisoner's dilemma game: 0 N 0' 9,9 0,12 N 12,0 3,3 The above game is repeated a random number of times. After each stage is played, the game ends with probability p. Players discount future payoffs at a rate 'r > 0. c) Compute the threshold of 33 below which (0, C) is a SPNE of the repeated game that ends after a random number of repetitions (hint: think how the discount factor is affected by p). Comment. d) In repeated games, if players discount future payoffs at a different rate, is it possible for cooperation to be sustainable? Explain