Consider 2 player game that repeats the following stage game T times: Player 1 Player 2 L R U 3; 3 0; 5 D 5; 1 2; 2A) What is the unique sub-game perfect Nash equilibrium of this nitely repeated game? Now let's slightly relax the assumption of mutual rationality and see what happens. Say that player 1 believes that player 2 will play according to the strategy you found for them in a) with probability 9 10 , but that with probability 1, 10 player 2 will follow a `grim strategy'. Player 1 is considering two options. The rst is to play her own grim strategy until the last period and then play D in the last period. The second is to play according to the SPNE strategy. B) Find the smallest T such that player 1 prefers the rst option rather than the second. Explain the intuition for why the length of the game matters. C) If the payo in the case (U;L) had been (4; 4), how would you expect your answer to b) to change and why?