Suppose the following stage game is repeated infinitely many times. Let (0, 1) denote the discount factor for both players.

5. (15 points) Suppose the following stage game is repeated infinitely many times. Let 6 E (0, 1) denote the discount factor for both players. Prisoner 2 Confess Not Confess I Prisoner 1 Confess 1, 1 5, 0 Not Confess 0, 5 4, 4 Consider a two-period punishment trigger strategy s: . Play "Not confess" in the first stage. . In stage t 2 2, if some player deviated to "Confess" in the last period when he is supposed to play "Not Confess", then play "Confess for 2 periods and then restart the game. In other words, after playing " Confess" for two stages, play "Not Confess" in the next stage as if it is the first stage of the game. Otherwise, play " Not Confess". Find the necessary and sufficient condition on o for (s, s) to be an SPE. (Hint: Solutions to equation ax2 + bx + c =0 are =6+vb--4ac and =b-vb2-4ac ) 2a 2a