Suppose that two players are playing the following

Suppose that two players are playing the following game. Player 1 can choose either Top or Bottom, and
Player 2 can choose either Left or Right. The payoffs are given in the following table: Player 1 Top
Bottom Left
3
5 Player 2
Right
0
9
4
8 1
3 where the number on the left is the payoff to Player 1, and the number on the right is the payoff to Player
2.
1:Suppose the game is player where Player 1 chooses its strategy first and then Player 2 chooses its
strategy. Using the backward induction method we discussed in class, what will be the outcome of the
game? Find the Nash equilibrium in mixed strategies. Remember that a Nash equilibrium in mixed strategies is
a pair (p,q) where player 1 plays Top with probability p (and therefore plays Bottom with probability 1-p),
and player 2 plays Left with probability q (and therefore plays Right with probability 1-q).