# Answer to Question #64269 in Microeconomics for niharika

Question #64269

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.

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.

Expert's answer

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.

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.

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## Comments

Assignment Expert07.06.17, 21:27Dear atul,

please use panel for submitting new questions

atul07.06.17, 21:14What is indirect utility funxtion? How will u derive an indirect utilty function frm direct utilty function ? Explain roy identity?

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