Consider the infinitely repeated game with discount factor infinity , where the strategic form game below is the stage game,

Player 2

L R

Player 1 U-----------(1,1)----------- (-2,5)

D-----------(2,0)----------(0,0)

(a) For what range of values of infinity player-1 will decide to play U in every period, when player-2 plays L at all times?

(b) For what range of values of infinity player-2 will decide to play L in every period, when player-1 plays U at all times?

(c) Using your answer in (b) and (c) explain that for sufficiently patient players, the SPNE (U,L) is played in every period. What is the minimum required discount factor for which (U,L) is achieved as SPNE for all

the time periods?

Problem 7: Consider the infinitely repeated game with discount factor (3, where the strategic form game below is Player 2 --II "-m the stage game, (a) For what range of values of 5 player1 will decide to play U in every period, when player-2 plays L at all times? (3) (b) For what range of values of 5 player-2 will decide to play L in every period, when player1 plays U at all times? (3) (c) Using your answer in (b) and (c) explain that for sufficiently patient players, the SPNE (U,L) is played in every period. What is the minimum required discount factor for which (U,L) is achieved as SPNE for all the time periods? (4)