(Table 12.6) Payoffs represent profits in thousands. Fruit of the Loom T-Shirt Price $8 $6 Hanes T- $8 20, 20 15, 22 Shirt Price $6 22,15 17, 17 $4 19, 10 15, 16 What is the Nash equilibrium? O (14, 14) O (19, 10) or (10, 19) O (17,17) O (20,20) $4 10, 19 16, 15 14, 14 D

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Chapter17: Oligopoly
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### Pricing Strategy for T-Shirts: A Game Theory Perspective

**Table 12.6: Payoffs Represent Profits in Thousands**

#### Payoff Matrix

| Hanes T-Shirt Price | Fruit of the Loom $8 | Fruit of the Loom $6 | Fruit of the Loom $4 |
|---------------------|----------------------|----------------------|----------------------|
| **$8**              | 20, 20               | 15, 22               | 10, 19               |
| **$6**              | 22, 15               | 17, 17               | 16, 15               |
| **$4**              | 19, 10               | 15, 16               | 14, 14               |

Each cell in the table represents the profits in thousands of dollars for Hanes (left value) and Fruit of the Loom (right value) given different pricing combinations for T-Shirts.

### Key Question: What is the Nash Equilibrium?

The Nash equilibrium represents the pricing strategy where neither company can increase their profit by unilaterally changing their price, provided the price of the competitor remains unchanged.

#### Options:
- (14, 14)
- (19, 10) or (10, 19)
- (17, 17)
- (20, 20)

### Analysis:

Selecting a Nash equilibrium involves identifying a strategy combination where neither firm can improve its payoff given the strategy of the other. Let's analyze the given payoffs:

- **(20, 20):** If Hanes chooses $8 and Fruit of the Loom chooses $8, both stay at 20, 20. However, if either changes their price, their profit could be improved in some scenarios.
- **(19, 10) or (10, 19):** This pair does not stabilize as both companies find benefits in switching strategies.
- **(17, 17):** This represents a stable state where neither company benefits from changing their price unilaterally.
- **(14, 14):** Similarly stable, but lower profit compared to (17, 17).

### Conclusion:

Given the analysis, the Nash equilibrium for this scenario is most likely to be the one that provides stability while offering reasonably high profits for both companies.

**Correct Choice:** (17, 17)

Be sure to consider the strategic interdependence where both companies find it optimal not to deviate from the
Transcribed Image Text:### Pricing Strategy for T-Shirts: A Game Theory Perspective **Table 12.6: Payoffs Represent Profits in Thousands** #### Payoff Matrix | Hanes T-Shirt Price | Fruit of the Loom $8 | Fruit of the Loom $6 | Fruit of the Loom $4 | |---------------------|----------------------|----------------------|----------------------| | **$8** | 20, 20 | 15, 22 | 10, 19 | | **$6** | 22, 15 | 17, 17 | 16, 15 | | **$4** | 19, 10 | 15, 16 | 14, 14 | Each cell in the table represents the profits in thousands of dollars for Hanes (left value) and Fruit of the Loom (right value) given different pricing combinations for T-Shirts. ### Key Question: What is the Nash Equilibrium? The Nash equilibrium represents the pricing strategy where neither company can increase their profit by unilaterally changing their price, provided the price of the competitor remains unchanged. #### Options: - (14, 14) - (19, 10) or (10, 19) - (17, 17) - (20, 20) ### Analysis: Selecting a Nash equilibrium involves identifying a strategy combination where neither firm can improve its payoff given the strategy of the other. Let's analyze the given payoffs: - **(20, 20):** If Hanes chooses $8 and Fruit of the Loom chooses $8, both stay at 20, 20. However, if either changes their price, their profit could be improved in some scenarios. - **(19, 10) or (10, 19):** This pair does not stabilize as both companies find benefits in switching strategies. - **(17, 17):** This represents a stable state where neither company benefits from changing their price unilaterally. - **(14, 14):** Similarly stable, but lower profit compared to (17, 17). ### Conclusion: Given the analysis, the Nash equilibrium for this scenario is most likely to be the one that provides stability while offering reasonably high profits for both companies. **Correct Choice:** (17, 17) Be sure to consider the strategic interdependence where both companies find it optimal not to deviate from the
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