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# Payoff Matrix and Prisoners Dilemma

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Firm B
(Problem 1) ___________
Low Price High Price
__________________________________________________________________
Low Price (1,1) (3, -1)
Firm A
High Price (-1,3) (2,2)
___________________________________________________________________

(a) From above (Problem 1), explain why the payoff matrix indicates that firms A and B face the prisoners' dilemma?
Firm B
(Problem 2) ___________
Low Price High Price
__________________________________________________________________
Low Price (1,1) (3, -1)
Firm A
High Price (-1,3) (4,2)
___________________________________________________________________

(b)Do firms (in Problem 2) A and B face the prisoners' dilemma? Why?

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#### Solution Preview

(a)
To figure out the prisoners' dilemma, we need to find out the dominant strategy for each firm,
For Firm A, if Firm B uses Low Price, Firm A will look at two outcomes: (1, 1) or (-1, 3). Since 1 > -1, Firm A will select Low Price to obtain the (1, 1) state. Similarly, if Firm B uses High Price, Firm A will decide between two states: (3, -1) and (2, 2). Since 3 > 2, Firm A will again take Low Price as its strategy. As a result, the dominant strategy for Firm A is Low Price.

Now let's consider Firm B, if Firm A takes Low Price, Firm B will ...

#### Solution Summary

The solution determines the payoff matrix and the prisoners dilemma.

\$2.19

## Solution contains explanation of Nash Equilibrium in pure strategy, Prisoner's Dilemma and interrelation between both of them through an example.

Below is a payoff matrix for Intel and AMD. In each cell, the first number refers to AMD's profit, while the second is Intel's.
a. Is there a Nash Equilibrium(s)? Why or why not?
b. Is this an example of the Prisoner's Dilemma? Why or why not?

Intel
AMD Lower Price Same Price Higher Price
Lower Price -2, -6 6, -2 12,-15
Same Price 6,14 9, 8 15, 4
Higher Price -13,7 3, 9 16,20

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