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

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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]``.
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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