where the number on the left is the payoff to Player 1 and t

where the number on the left is the payoff to Player 1, and the number on the right is the payoff to Player 2.  

A) Does Player 1 have a dominant strategy, and if so what is it?

B)Does Player 2 have a dominant strategy and if so what is it?
C)For each of the following strategy combinations, write TRUE if it is a Nash Equilibrium, and FALSE if it is not:

i) Top/Left

ii) Top/Right

iii) Bottom/Left

iv) Bottom Right

D) What is Player 1’s maximin strategy?

E) What is Player 2’s maximin strategy?

F) If the game were played with Player 1 moving first and Player 2 moving second, using the backward induction method we went over in class, what strategy will each player choose?

Solution

a) Yes Player 1 has a dominant strategy . When Player 2 selects Left or Right , in both the cases , Player 1 will select Top . Since ( 6 > 4 ) and ( 9 > 5 ) . The dominant strategy for player 1 is Top

b) When Player 1 takes Top , 2 will select : Right .

When 1 takes : bottom , 2 will select : Left . Hence there is no dominant strategy for player 2 .

c) Nash equilibrium : ii) Top/Right : 9        6

d) When Player 1 plays Top , 2\'s payoff minimizing action against 1 is to play Left .

When Player 1 plays Bottom , 2\'s payoff minimizing action against 1 is to play Left .

Playing Left yeilds 1 a lesser payoff in both cases . Hence 1 will play strategy Top which yeilds maximum of these two payoffs ( 6 > 4 )

So Top is the maximin strategy for player 1 .