a Find a subgame perfect equilibrium of this game What is pl

(a) Find a subgame perfect equilibrium of this game. What is player 1’s equilibrium payoff in this subgame perfect equilibrium?

(b) Find a pure strategy Nash equilibrium of this game in which player 1’s payoff is strictly higher than her payoff in the subgame perfect equilibrium you have found in part (a).

I know how to deal with question a, is just application of backward induction. However, i am confused about question b. Can you please tell me how to find a pure nash equilibrium in this game tree with steps? I just know how to find a pure nash in a normal form.

Solution

We know both the players are parallel in moves then if player 1 plays strategy T then player 2 would definitely play R because if he had played L he would be left with either 1 or 2 but now he knows subgame nash equilibrium of this game is (4.3) becuase player 1 will aslo play d to maximize his payoff

Now player 1 knows if he plays B then Subgame Nash Equilibrium is (B,Y)=(5,1) which is anytime higher than previous subgame Nash equilibrium

hence Pure Nash Equilibrium in this game is (B,Y)=(5,1)