In the mixed-strategy equilibrium, what is the probability of Firm 1 setting a low price? Please help me with both the questions ## Profit Matrix AnalysisThe following table represents the profit matrix for two firms, Firm 1 and Firm 2, which face different pricing strategies that affect their respective profits.### Profit Matrix| **Firm 2** | **Low price** | **High price** ||------------|---------------|----------------|| **Low price** | 2, 2 | 4, 7 || **High price** | 7, 4 | 3, 3 |### Description:- **Rows**: Each row represents the pricing strategy chosen by Firm 2 (either "Low price" or "High price").- **Columns**: Each column represents the pricing strategy chosen by Firm 1 (either "Low price" or "High price").- **Cells**: Each cell shows the profits earned by Firm 1 and Firm 2 under the corresponding combination of strategies. The first number in each cell is the profit for Firm 1, and the second number is the profit for Firm 2.### Key Points:1. **Both Firms Choose Low Price**: When both Firm 1 and Firm 2 choose a low price, they each earn a profit of 2 (top-left cell).2. **Firm 1 Chooses High Price, Firm 2 Chooses Low Price**: When Firm 1 chooses a high price and Firm 2 chooses a low price, Firm 1 earns a profit of 4, and Firm 2 earns a profit of 7 (top-right cell).3. **Firm 1 Chooses Low Price, Firm 2 Chooses High Price**: When Firm 1 chooses a low price and Firm 2 chooses a high price, Firm 1 earns a profit of 7, and Firm 2 earns a profit of 4 (bottom-left cell).4. **Both Firms Choose High Price**: When both Firm 1 and Firm 2 choose a high price, they each earn a profit of 3 (bottom-right cell).### Conclusion:This profit matrix illustrates the interdependence of pricing strategies between the two firms and the resulting profits. It is a classic example of game theory in economics, showing how the choices of one firm affect the outcomes for both. **Understanding Nash Equilibrium in Game Theory****Which of the following is a pure Nash equilibrium for this game? Select all that apply.**- [ ] Firm 1 high price; Firm 2 high price- [ ] Firm 1 low price; Firm 2 high price- [ ] Firm 1 low price; Firm 2 low price- [ ] Firm 1 high price; Firm 2 low priceA Nash equilibrium is a concept within game theory where the optimal outcome of a game is one where no participant can gain by a unilateral change of strategy if the strategies of the others remain unchanged. In other words, in a Nash equilibrium, each player's strategy is optimal when considering the decisions of other players. To identify which of the given choices represents a pure Nash equilibrium, we need to evaluate each scenario to determine if both firms are making the best decisions they can, given the other firm's choice. ---Feel free to explore other educational resources to deepen your understanding of Nash equilibria and strategic decision-making in competitive settings.

Nash equilibrium is the point where best response of both players intersect

Answered: the mixed-strategy equilibrium, what is…

the mixed-strategy equilibrium, what is the probability of Firm 1 setting a low price? Please help me with both the questions

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

In the mixed-strategy equilibrium, what is the probability of Firm 1 setting a low price?

Please help me with both the questions

## Profit Matrix Analysis

The following table represents the profit matrix for two firms, Firm 1 and Firm 2, which face different pricing strategies that affect their respective profits.

### Profit Matrix

| **Firm 2** | **Low price** | **High price** |
|------------|---------------|----------------|
| **Low price** | 2, 2 | 4, 7 |
| **High price** | 7, 4 | 3, 3 |

### Description:
- **Rows**: Each row represents the pricing strategy chosen by Firm 2 (either "Low price" or "High price").
- **Columns**: Each column represents the pricing strategy chosen by Firm 1 (either "Low price" or "High price").
- **Cells**: Each cell shows the profits earned by Firm 1 and Firm 2 under the corresponding combination of strategies. The first number in each cell is the profit for Firm 1, and the second number is the profit for Firm 2.

### Key Points:
1. **Both Firms Choose Low Price**: When both Firm 1 and Firm 2 choose a low price, they each earn a profit of 2 (top-left cell).
2. **Firm 1 Chooses High Price, Firm 2 Chooses Low Price**: When Firm 1 chooses a high price and Firm 2 chooses a low price, Firm 1 earns a profit of 4, and Firm 2 earns a profit of 7 (top-right cell).
3. **Firm 1 Chooses Low Price, Firm 2 Chooses High Price**: When Firm 1 chooses a low price and Firm 2 chooses a high price, Firm 1 earns a profit of 7, and Firm 2 earns a profit of 4 (bottom-left cell).
4. **Both Firms Choose High Price**: When both Firm 1 and Firm 2 choose a high price, they each earn a profit of 3 (bottom-right cell).

### Conclusion:
This profit matrix illustrates the interdependence of pricing strategies between the two firms and the resulting profits. It is a classic example of game theory in economics, showing how the choices of one firm affect the outcomes for both.

**Understanding Nash Equilibrium in Game Theory**

**Which of the following is a pure Nash equilibrium for this game? Select all that apply.**

- [ ] Firm 1 high price; Firm 2 high price
- [ ] Firm 1 low price; Firm 2 high price
- [ ] Firm 1 low price; Firm 2 low price
- [ ] Firm 1 high price; Firm 2 low price

A Nash equilibrium is a concept within game theory where the optimal outcome of a game is one where no participant can gain by a unilateral change of strategy if the strategies of the others remain unchanged. In other words, in a Nash equilibrium, each player's strategy is optimal when considering the decisions of other players.

To identify which of the given choices represents a pure Nash equilibrium, we need to evaluate each scenario to determine if both firms are making the best decisions they can, given the other firm's choice.

---

Feel free to explore other educational resources to deepen your understanding of Nash equilibria and strategic decision-making in competitive settings.

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