answer question with work please

1. Below is a 2player game in matrix form: Player2 L C R Player U 2,6 2,7 4,4 1 D 1,0 9,1 6,1 Consider the innitely repeated extension of the above matrix game, in which players have discounted payoffs with discount factor 6 E (0, 1). Suppose the players play the following strategy prole. They begin the the game in state 1 (Le, the null history is in state 1). In state 1, the players play (U, R). If the players play (U, R) in state 1, they remain in state 1. If they do not play (U, R) in state 1, they move to state 2. In state 2, the players play (D,L). If they play (D, L) in state 2, they return to state 1. If they do not play (D, L) in state 2, they remain in state 2. Determine for what values of 6, if any, this strategy prole is a subgame perfect Nash equilibrium of the game. (20 points)