Question

Suppose that player 1 moves first by choosing either A or N. Players 2 observe
player 1’s action and then choose I or, O. For every action combination, the
4
player’s pay-offs are the same as in the above pay-off matrix. Draw a tree of this
new game. How many strategies does player 1 have and what are they? Find all the
sub-game perfect equilibria of this game.

Answer 1

Suppose that player 1 moves first by choosing either A or N. Players 2 observe
player 1’s action and then choose I or, O.
A tree of this new game is:
A -> Player 2 chooses I
Player 1 /
\ N -> Player 2 chooses O
Player 2 has 2 strategies either to choose I or to choose O, and his choice depends on the choice of player 1.