where the number on the left is the payoff to Player 1, and the number on the ri
ID: 1159376 • Letter: W
Question
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?
Explanation / Answer
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 .
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