(a) Consider the same game as in question above, but suppose T is not known.
Instead, we know that the game continues with probability d and ends with probability 1- d after each round with each player getting zero if the game ends (or, if you prefer, d is the discount factor). Is it possible to play (B, b) in each period if d = 0.8? What if d = 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
probability d, is 1 + d + d2 + d3 + .....
Is (D, D) forever a SPNE outcome for d = 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.