### Economic Game Theory Analysis#### Game SetupTwo firms, X and Y, are in competition. Firm X can produce one of three products: X1, X2, or X3. Similarly, firm Y can produce one of three products: Y1, Y2, or Y3. Each firm's profit depends on its own and its competitor’s decisions regarding which product to produce. The table below shows the profits for each scenario, where the first number indicates Firm X's profit and the second number denotes Firm Y's profit. The firms make their product choice decisions simultaneously and independently of each other.#### Payoff Table| | Y1 | Y2 | Y3 ||----|--------|---------|---------|| X1 | 12, 8 | 18, 9 | 0, 0 || X2 | 16, 16 | 20, 15 | 8, 12 || X3 | 15, 20 | 18, 18 | 9, 18 |**Example Interpretation**:- If Firm X chooses to produce X3 and Firm Y chooses to produce Y1, Firm X earns $15, and Firm Y earns $20.#### Analysis Questions1. **Question 11**: Does this game have any equilibrium in dominant strategies? If yes, find all of them.2. **Question 12**: Besides any equilibrium in dominant strategies identified in the previous question, does this game have any other equilibria? If yes, identify all of them.3. **Question 13**: Assume that Firm X finds out one of its employees is leaking information to Firm Y, allowing Firm Y to know which product Firm X will produce. Firm Y then bases its decision on this information. If Firm X cannot determine or stop the information leak, which products will Firms X and Y eventually produce?#### Steps for Analysis:1. **Identify Dominant Strategies**: - A dominant strategy is one that yields a better outcome for a player regardless of what the other player does. 2. **Check for Nash Equilibria**: - A Nash equilibrium occurs where neither player has anything to gain by changing only their own strategy. 3. **Analyze Scenario with Information Leak**: - Determine the best responses for both firms under the condition that Firm Y can anticipate Firm X’s choice due to inside information

The payoff matrix for both the firms is given below :- Y1 Y2 Y3 X1 12, 8 18, 9 0, 0 X2 16,…

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lepends on its own and its competitor's decision about which product to produce. These profits

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

### Economic Game Theory Analysis

#### Game Setup

Two firms, X and Y, are in competition. Firm X can produce one of three products: X1, X2, or X3. Similarly, firm Y can produce one of three products: Y1, Y2, or Y3. Each firm's profit depends on its own and its competitor’s decisions regarding which product to produce. The table below shows the profits for each scenario, where the first number indicates Firm X's profit and the second number denotes Firm Y's profit. The firms make their product choice decisions simultaneously and independently of each other.

#### Payoff Table

| | Y1 | Y2 | Y3 |
|----|--------|---------|---------|
| X1 | 12, 8 | 18, 9 | 0, 0 |
| X2 | 16, 16 | 20, 15 | 8, 12 |
| X3 | 15, 20 | 18, 18 | 9, 18 |

**Example Interpretation**:
- If Firm X chooses to produce X3 and Firm Y chooses to produce Y1, Firm X earns $15, and Firm Y earns $20.

#### Analysis Questions

1. **Question 11**: Does this game have any equilibrium in dominant strategies? If yes, find all of them.
2. **Question 12**: Besides any equilibrium in dominant strategies identified in the previous question, does this game have any other equilibria? If yes, identify all of them.
3. **Question 13**: Assume that Firm X finds out one of its employees is leaking information to Firm Y, allowing Firm Y to know which product Firm X will produce. Firm Y then bases its decision on this information. If Firm X cannot determine or stop the information leak, which products will Firms X and Y eventually produce?

#### Steps for Analysis:

1. **Identify Dominant Strategies**:
- A dominant strategy is one that yields a better outcome for a player regardless of what the other player does.

2. **Check for Nash Equilibria**:
- A Nash equilibrium occurs where neither player has anything to gain by changing only their own strategy.

3. **Analyze Scenario with Information Leak**:
- Determine the best responses for both firms under the condition that Firm Y can anticipate Firm X’s choice due to inside information

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