1. Suppose the following finitely repeated game G(T, δ) where the stage game is:
1/2 X Y Z
X 6, 6 2, 7 2, 5
Y 9, 3 5, 6 2, 3
Z 5, 2 4, 2 3, 3
and where we assume that δ = 1.
(a) Specify the pure-strategy Nash equilibria of the stage game.
(b) Let T = 2. Is there a subgame perfect equilibrium that allows {X, X} to be played in any period? Carefully specify such a strategy, if it exists.
(c) Supposed instead that T = 3. Can {X, X} be part of a subgame perfect equilibrium in this case? Carefully specify such a strategy, if it exists.