Please help me with part(b)

[16 points] Two players, 1 and 2, play the following game repeatedly. The values in the table are the monetary rewards to the players for every possible combination of their actions. At any point in time, the actions taken by both players in the past (i.e. the history of play) are commonly known by both players. C D Player 2 C (2, 2) (0,3) D (3,0) (1, 1) Player 1 Here the first component is Player 1's reward and the second component is Player 2's reward. Both players want to maximize the discounted present value of their per-period rewards, with the same discount factor 5 = 0.9. In other words, if Player 1 receives a stream of monetary rewards (Xo,X1, X2, Xt, ...) over time, his lifetime payoff is U= X0+X1 5 + x; 5 2 + + xt 5 t+w Player 2 evaluates her lifetime payoff similarly. (b) Suppose the game is repeated indefinitely without end. Consider the following pair of strategies. For Player 1: \"Play according to the sequence D, C, D, D, C, D, (repeatedly) as long as both players have followed their prescribed patterns of play. But if any player deviates, then play D forever aerwards.\" For Player 2: \"Play according to the sequence C, D, D, C, D, D, (repeatedly) as long as both players have followed their prescribed patterns of play. But if any player deviates, then play D forever afterwards.\" Represent this strategy prole recursively by a nite-State automaton. Draw the appropriate diagram and specify (i) the states; (ii) the actions prescribed for each player in each state; and (iii) the transitions between states for all possible pairs of current actions