Problem VII: Consider the following dynamic game between two players. Player 1 starts the game by choosing between up and down. After observing Player 1's move, Player 2 follows with his own choice between up and down. The payos are as follows: if player 1 goes up and player 2 goes up as well, both players get $10 each. If 1 goes up and 2 goes down, they each get$2. If 1 goes down and 2 goes down, they each get $1. If 1 goes down and 2 goes up, 1 gets$15 and 2 gets \$5. Find all the Nash equilibria and also the Sub-game Perfect Nash equilibrium of this game.