Answer to Question #64269 in Microeconomics for niharika

Question

Consider the pay-off matrix of a game given below:
Player1
Player 2
I O
A 1,1 3,3
N 2,4 4,2
(a) Find all the Nash equilibrium of this game. Which player(s), if any, would have a
dominant strategy?
(b) 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 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

Player 1 Player 2
I O
A 1,1 3,3
N 2,4 4,2
(a) the Nash equilibrium of this game is 4,2 (or N-O). Nobody would have a dominant strategy.
(b) If player 1 moves first by choosing either A or N and players 2 observe
player 1’s action and then choose I or, O, then the pay-offs will be the same as in the above pay-off matrix. The player 1 will choose strategy N and the sub-game perfect equilibria of this game is 4,2 or N-O.