Did not under previous explation. I need clear explanation ### Two Firms' Profit Matrix and Nash Equilibrium Analysis#### 2. Profit Matrix Analysis of Two Competing Firms:Below is the profit matrix for two competing firms facing strategic decisions regarding pricing:| | | **Firm 1** | | ||----------------|------------------|-----------------------|------------------------|------------------------|| | | **Low Price** | **High Price** || **Firm 2** | **Low Price** | 0, 2 | 2, 1 || | **High Price** | 7, 0 | 6, 6 |**a. Dominant Strategy and Nash Equilibrium:**- **Dominant Strategy:** - A dominant strategy is one that results in the highest payoff for a player regardless of the other player's decision. - **Firm 1:** - If Firm 2 chooses a low price, Firm 1 would get 0 with low price and 2 with high price. Hence, Firm 1 prefers high price. - If Firm 2 chooses a high price, Firm 1 would get 7 with low price and 6 with high price. Hence, Firm 1 prefers low price. - **Firm 2:** - If Firm 1 chooses a low price, Firm 2 would get 2 with low price and 1 with high price. Hence, Firm 2 prefers low price. - If Firm 1 chooses a high price, Firm 2 would get 0 with low price and 6 with high price. Hence, Firm 2 prefers high price. - Neither firm has a dominant strategy. - **Nash Equilibrium:** - **Pure-Strategy Nash Equilibrium:** - The game has two pure-strategy Nash equilibria where both firms are choosing best responses: - Firm 1 chooses high price; Firm 2 chooses low price (Payoffs: 2 for Firm 1 and 1 for Firm 2). - Firm 1 chooses low price; Firm 2 chooses high price (Payoffs: 7 for Firm 1 and 0 for Firm 2). - **Mixed-Strategy Nash Equilibrium:** - Both firms randomize over their strategies such that each firm is indifferent to the strategies chosen by the other.**b. Analysis with

Nash equilibrium is the point of a game corresponding to which each participant optimizes his…

Answered: a. Does either firm have a dominant…

a. Does either firm have a dominant strategy? Does this game have a unique, pure-strategy Nash equilibrium? Identify all pure and mixed-strategy Nash equilibria.

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ISBN:9780190931919

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Chapter1: Making Economics Decisions

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Question

Did not under previous explation. I need clear explanation

### Two Firms' Profit Matrix and Nash Equilibrium Analysis

#### 2. Profit Matrix Analysis of Two Competing Firms:

Below is the profit matrix for two competing firms facing strategic decisions regarding pricing:

| | | **Firm 1** | | |
|----------------|------------------|-----------------------|------------------------|------------------------|
| | | **Low Price** | **High Price** |
| **Firm 2** | **Low Price** | 0, 2 | 2, 1 |
| | **High Price** | 7, 0 | 6, 6 |

**a. Dominant Strategy and Nash Equilibrium:**
- **Dominant Strategy:**
- A dominant strategy is one that results in the highest payoff for a player regardless of the other player's decision.
- **Firm 1:**
- If Firm 2 chooses a low price, Firm 1 would get 0 with low price and 2 with high price. Hence, Firm 1 prefers high price.
- If Firm 2 chooses a high price, Firm 1 would get 7 with low price and 6 with high price. Hence, Firm 1 prefers low price.
- **Firm 2:**
- If Firm 1 chooses a low price, Firm 2 would get 2 with low price and 1 with high price. Hence, Firm 2 prefers low price.
- If Firm 1 chooses a high price, Firm 2 would get 0 with low price and 6 with high price. Hence, Firm 2 prefers high price.
- Neither firm has a dominant strategy.

- **Nash Equilibrium:**
- **Pure-Strategy Nash Equilibrium:**
- The game has two pure-strategy Nash equilibria where both firms are choosing best responses:
- Firm 1 chooses high price; Firm 2 chooses low price (Payoffs: 2 for Firm 1 and 1 for Firm 2).
- Firm 1 chooses low price; Firm 2 chooses high price (Payoffs: 7 for Firm 1 and 0 for Firm 2).
- **Mixed-Strategy Nash Equilibrium:**
- Both firms randomize over their strategies such that each firm is indifferent to the strategies chosen by the other.

**b. Analysis with

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Step 3: Part a pure strategy:

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Step 4: Part a mixed strategy:

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Step 5: Part b Dominant strategy:

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Step 6: Part b pure strategy:

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