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5. (5 marks) Consider the following version of the innitely repeated Cournot duopoly problem. In the stage game, the market inverse demand function is _ aq ifq c. Both rms discount future payoffs using the discount factor 3/4. The stage game has a unique Nash equilibrium in which each rm produces qc = (a. c) / 3. A monopolist would produce qm = (a c) / 2 in the stage game. Let 3,03,) be the strategy in which rm i chooses (i) (a c)/4 in the rst play of the game, (ii) (a c) / 4 after every history in which both rms have played (a c) / 4 in every previous period, and (iii) 3:,- if in any previous period either rm has chosen an output different from (a c)/4. We know that (51(qc), 52(qc)) is a subgame perfect equilibrium for this innitely repeated Cournot game. Are there any other values for :31 and .182 such that (51(m1),52(m2)) is a subgame perfect equilibrium of this innitely repeated game? If not, explain why. If yes, what are they