4. Innitely repeated games: practice at the theory. Consider the following game. c d c 1,4 d 3,3 mu Assume that this game is repeated an innite number of times, and that both the row and column player discount the future with the same discount factor 6. (a) Suppose that both players follow the following grimtrigger strategy: \"play :2 as long as noone has ever played 0!; otherwise play d\". Find the minimum value of 5 such that this is a subgameperfect equilibrium. (b) Suppose that row and column are playing some SPE equilibrium of the innitely repeated game. They may or may not have played according to the equilibrium strategies so far. Let VT and VC denote the present discounted values of continuing to play from here on according to the equilibrium strategies. What are the lowest values that V'" and VC could have? [Hintz there are no calculations involved here] (c) [OptionaL] Now suppose that the players follow a strategy in which they both start in \"phase C\" (described below) and then switch \"phases\" as the instructions dictate: 0 phase C: play c provided that, in each period since the (re)start of the phase, either both players chose (2 or both players chose d. Stay in phase C until one player chooses (1 while the other chooses c. In this event, if it is row who chose d go to phase PT; if it is column who chose d go to phase PC. a phase PT: play d for T," periods (regardless of what happens during those periods) then revert to phase C. 0 phase PC: play d for TC periods (regardless of what happens during those periods) then revert to phase 0. Write down expressions in terms of 6 for the smallest TT and TC such that this is an SPE. [These expressions might be quite ugly so do not attempt to simplify them much) For any given 6, which of TT and TC is larger? What is the intuition