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11) In the following game, list any dominant or dominated strategies. Then, solve the game Player 2 Left Center Right Player 1 Up 1,2 4,6 5,5 Down 6,3 2,4 3,1

11) In the following game, list any dominant or dominated strategies. Then, solve the game Player 2 Left Center Right Player 1 Up 1,2 4,6 5,5 Down 6,3 2,4 3,1

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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**Game Theory Analysis Example** In the following game, list any dominant or dominated strategies. Then, solve the game. **Player Strategies and Payoff Matrix** | | **Player 2** | | | |----------|--------------|----------|----------| | | **Left** | **Center** | **Right** | | **Player 1** | **Up** | 1,2 | 4,6 | 5,5 | | | **Down** | 6,3 | 2,4 | 3,1 | **Explanation:** This is a strategic game represented by a payoff matrix featuring two players, Player 1 and Player 2. Each cell of the matrix shows the payoffs for Player 1 and Player 2, with Player 1's payoff listed first and Player 2's payoff second. - Strategies for Player 1: Up, Down - Strategies for Player 2: Left, Center, Right **Payoff Analysis:** - If Player 1 chooses Up and Player 2 chooses Left, the payoffs are \(1\) for Player 1 and \(2\) for Player 2. - If Player 1 chooses Up and Player 2 chooses Center, the payoffs are \(4\) for Player 1 and \(6\) for Player 2. - If Player 1 chooses Up and Player 2 chooses Right, the payoffs are \(5\) for Player 1 and \(5\) for Player 2. - If Player 1 chooses Down and Player 2 chooses Left, the payoffs are \(6\) for Player 1 and \(3\) for Player 2. - If Player 1 chooses Down and Player 2 chooses Center, the payoffs are \(2\) for Player 1 and \(4\) for Player 2. - If Player 1 chooses Down and Player 2 chooses Right, the payoffs are \(3\) for Player 1 and \(1\) for Player 2. The task is to identify any dominant or dominated strategies and subsequently solve the game based on these insights.
Transcribed Image Text:**Game Theory Analysis Example** In the following game, list any dominant or dominated strategies. Then, solve the game. **Player Strategies and Payoff Matrix** | | **Player 2** | | | |----------|--------------|----------|----------| | | **Left** | **Center** | **Right** | | **Player 1** | **Up** | 1,2 | 4,6 | 5,5 | | | **Down** | 6,3 | 2,4 | 3,1 | **Explanation:** This is a strategic game represented by a payoff matrix featuring two players, Player 1 and Player 2. Each cell of the matrix shows the payoffs for Player 1 and Player 2, with Player 1's payoff listed first and Player 2's payoff second. - Strategies for Player 1: Up, Down - Strategies for Player 2: Left, Center, Right **Payoff Analysis:** - If Player 1 chooses Up and Player 2 chooses Left, the payoffs are \(1\) for Player 1 and \(2\) for Player 2. - If Player 1 chooses Up and Player 2 chooses Center, the payoffs are \(4\) for Player 1 and \(6\) for Player 2. - If Player 1 chooses Up and Player 2 chooses Right, the payoffs are \(5\) for Player 1 and \(5\) for Player 2. - If Player 1 chooses Down and Player 2 chooses Left, the payoffs are \(6\) for Player 1 and \(3\) for Player 2. - If Player 1 chooses Down and Player 2 chooses Center, the payoffs are \(2\) for Player 1 and \(4\) for Player 2. - If Player 1 chooses Down and Player 2 chooses Right, the payoffs are \(3\) for Player 1 and \(1\) for Player 2. The task is to identify any dominant or dominated strategies and subsequently solve the game based on these insights.
Expert Solution
Step 1

Strategies of Player 1:

Up and Down

Strategies of Player 2:

Left, Center, and Right

 

A dominant strategy is the one that player plays irrespective of what other player plays in Nash Equilibrium.

 

Player 1

When Player 2 plays Left, the best response of Player 1 is to play Down.(6>1)

When Player 2 plays Center, the best response of Player 1 is to play Up.(4>2)

When Player 2 plays Right, the best response of Player 1 is to play Up.(5>3)

There is no dominant strategy for player 1

 

 

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