Question #44104

Consider the following payoff matrix:
Player B Strategy
1
2
$1,000
-$2,000
1
$2,000
-$1,000
Player A Strategy
-$1,000
$2,000
2
-$2,000
$1,000
a. Does Player A have a dominant strategy? Explain why or why not.
[3 marks]
b. Does Player B have a dominant strategy? Explain why or why not.

Expert's answer

a. Player A has a dominant strategy, he will preffer the strategy 1 to minimize possible losses and maximize possible gains. This strategy is more preferable for him, because the possible gains are higher ($2000>$1000) and possible losses are lower (-$1000>-$2000) than according to the atrategy 2. In our case both Player A and Player B will chose strategy 1, so Player A will get $2000 and Player B will get $1000.b. Player B has a dominant strategy too, he will preffer the strategy 1 to minimize possible losses. He may think, that the player A will choose the strategy 2, so it is more preferable for him to choose lower possible losses and lower possible gains. That's why, in our case both Player A and Player B will chose strategy 1, so Player A will get $2000 and Player B will get $1000.

## Comments

Assignment Expert25.09.14, 17:36Dear Najla.

We can say the same in other words. Top (1) is better strategy for A than Bottom (2) no matter what B is doing. Left (1) is better strategy for B than Right (2) no matter what A is doing. We consider entries a11=(-1000,1000), a12=(2000,-2000), a21=(-2000,2000), a22=(1000,-1000).

Najla10.09.14, 07:18is the answer for a & b ?

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