Question: Consider the twice-repeated version of the "battle of the sexes" stage game shown in figure 11.19, where the players maximize the sum of their per-period payoffs.
(a) Show that, although the path where players choose (S,W) in both periods can be supported by subgame-equilibrium, the component where (S, W) is played in both periods does not contain a stable set. (Hint: Use iterated application of NWBR on the game's reduced strategic form.)
(b) Characterize the stable paths that are in pure strategies.
(c) Construct a stable component where both players randomize (½,½) in the first stage. (Van Damme (1989) and Osborne (1987) discuss forward induction in repeated games)
