Show the spne strategies - if the game was played twice

Question

(a) Consider the same game as in question 2 above, but supposeTis not known.

Instead, we know that the game continues with probabilitydand ends with probability1-dafter each round with each player getting zero if the game ends (or, if you prefer,dis thediscount factor). Is it possible to play(B, b)in each period ifd= 0.8?What ifd= 0.2?

(b) Consider the infinitely repeated version of the following game.

H D

H 1,1 3,0

D 0,3 2,2

The payoff of player 1, if (H, H) is played infinitely with discount factor or continuation probabilityd,is1 +d+d²+d³+.....

Is (D, D) forever a SPNE outcome ford= 2/3?If it is, show the SPNE strategies. If it is not explained why.

If the game was played twice, would playing(D, D)in the first period be a subgame perfect equilibrium first-period outcome? Explain why or why not.