Question

Consider the pay-off matrix of a game given below:

Player 1

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.

(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.

07 Feb 2018
Answer :
Word Count : 815

The only Nash equilibrium is (N, I ). Player 1 has a dominant strategy, player 2 does not.

Now suppose that Player 1 moves first by choosing either A or N . Player 2 observes player 1’s action and then chooses I or O. For every action combination, the players’ payoffs are the same as in the above payoff matrix. Draw a

tree of this new game. How many strategies does player 1 have and what are they?

How many strategies does player 2 have and what are they? Find all the subgame perfect equilibria of this game.

S1 = {A, N }

S2 = {II, IO, OI, OO}

Image ignouacademy-com--p-2017-19269

Image ignouacademy-com--span-game-57106 Image ignouacademy-com--span-given-20966 Image ignouacademy-com--span-below-83799 Image ignouacademy-com--span-academy-26009 Image ignouacademy-com--span-ignou-32373 Image ignouacademy-com--span-2016-39943 Image ignouacademy-com--span-2017-92587 Image ignouacademy-com--span-consider-53864Subgame perfect equilibrium is (A, OI ) .

 

 

II

IO

OI

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