Question:

Two players play the following stage-game twice in a row (T = 2), and observe each other's rst-stage action before choosing actions in the second stage. Both players discount second-stage payoffs using a discount factor 6 E [0, 1]. (a) How many pure strategies does each player have in the two-stage game? (b) Can the action prole (U, L) be played in the rst stage of a pure-strategy subgame perfect equilibrium for 5 = 1? If yes, construct such an equilibrium; if not, explain Why not. ((3) Compute the smallest 5 for which the prole (U, L) can be played in the rst stage of a purestrategy subgame perfect equilibrium. (d) Can the action prole (D, L) be played in the rst stage of a purestrategy subgame perfect equilibrium for 5 = 1? If yes, construct such an equilibrium; if not, explain Why not