7. Solving for dominant strategies and the Nash equilibrium Suppose Antonio and Trinity are playing a game that requires both to simultaneously choose an action: Up or Down. The payoff matrix that follows shows the earnings of each person as a function of both of their choices. For example, the upper-right cell shows that if Antonio chooses Up and Trinity chooses Down, Antonio will receive a payoff of 4 and Trinity will receive a payoff of 4. Antonio Up Down Up 8,3 5,3 Trinity Down 4,4 5,4 Down Up
7. Solving for dominant strategies and the Nash equilibrium Suppose Antonio and Trinity are playing a game that requires both to simultaneously choose an action: Up or Down. The payoff matrix that follows shows the earnings of each person as a function of both of their choices. For example, the upper-right cell shows that if Antonio chooses Up and Trinity chooses Down, Antonio will receive a payoff of 4 and Trinity will receive a payoff of 4. Antonio Up Down Up 8,3 5,3 Trinity Down 4,4 5,4 Down Up
Chapter1: Making Economics Decisions
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![### 7. Solving for Dominant Strategies and the Nash Equilibrium
Suppose Antonio and Trinity are playing a game that requires both to simultaneously choose an action: Up or Down. The payoff matrix that follows shows the earnings of each person as a function of both of their choices. For example, the upper-right cell shows that if Antonio chooses Up and Trinity chooses Down, Antonio will receive a payoff of 4 and Trinity will receive a payoff of 4.
#### Payoff Matrix
| | Trinity: Up | Trinity: Down |
|:------------------:|:-----------:|:-------------:|
| **Antonio: Up** | 8, 3 | 4, 4 |
| **Antonio: Down** | 5, 3 | 5, 4 |
In this game, the only dominant strategy is for
``[Antonio]`` to choose ``[Up]``.
The outcome reflecting the unique Nash equilibrium in this game is as follows: Antonio chooses ``[Up]`` and Trinity chooses ``[Down]``.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F72a6c93d-fdfd-4269-a1ad-44ac8a950dd4%2Fb0557f59-2053-471d-b1f0-9f1df8175e20%2Fbcsqz3_processed.png&w=3840&q=75)
Transcribed Image Text:### 7. Solving for Dominant Strategies and the Nash Equilibrium
Suppose Antonio and Trinity are playing a game that requires both to simultaneously choose an action: Up or Down. The payoff matrix that follows shows the earnings of each person as a function of both of their choices. For example, the upper-right cell shows that if Antonio chooses Up and Trinity chooses Down, Antonio will receive a payoff of 4 and Trinity will receive a payoff of 4.
#### Payoff Matrix
| | Trinity: Up | Trinity: Down |
|:------------------:|:-----------:|:-------------:|
| **Antonio: Up** | 8, 3 | 4, 4 |
| **Antonio: Down** | 5, 3 | 5, 4 |
In this game, the only dominant strategy is for
``[Antonio]`` to choose ``[Up]``.
The outcome reflecting the unique Nash equilibrium in this game is as follows: Antonio chooses ``[Up]`` and Trinity chooses ``[Down]``.
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