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Solving for dominant strategies and the Nash equilibrium Suppose Lorenzo and Neha are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Lorenzo chooses Right and Neha chooses Right, Lorenzo will receive a payoff of 6 and Neha will receive a payoff of 5
Neha
Left Right
Lorenzo Left 8,4 4,5
Right 5,4 6,5
1. The only dominant strategy in this game is for (Neha/Lorenzo) to choose (Right/Left)
2. The outcome reflecting the unique Nash equilibrium in this game is as follows: Lorenzo chooses (Right/Left) and Neha chooses (Right/Left) .

Sagot :

Answer:

1. The only dominant strategy in this game is for Neha to choose Right.

2. The outcome reflecting the unique Nash equilibrium in this game is as follows: Lorenzo chooses Right and Neha chooses Right.

Explanation:

A dominant strategy is a strategy that results in a player being better off no matter the choice his or her opponent in a game.

For this game, when Lorenzo plays Left, Neha will choose Right because 5 > 4. Also, when Lorenzo plays Right, Neha will still choose Right because 5 > 4. This shows that Neha will always play Right no matter what Lorenzo plays. This implies the dominant strategy for Neha is Right.

On the other hand, when Neha plays Left, Lorenzo will also play Left because 8 > 5. But when Neha plays Right, Lorenzo will choose will also play Right because 6 > 4. This shows that Lorenzo does not have any particular strategy that make him better off. Therefore, Lorenzo does not have a dominant strategy.

Therefore, we have:

1. The only dominant strategy in this game is for (Neha/Lorenzo) to choose (Right/Left)

Based on the analysis above, the only dominant strategy in this game is for Neha to choose Right.

This is because the dominant strategy for Neha is Right, but Lorenzo does not have a dominant strategy.

2. The outcome reflecting the unique Nash equilibrium in this game is as follows: Lorenzo chooses (Right/Left) and Neha chooses (Right/Left) .

Based on the analysis above, the outcome reflecting the unique Nash equilibrium in this game is as follows: Lorenzo chooses Right and Neha chooses Right.

The reason is that Neha will always play Right and Lorenzo will be better of by also playing Right because 6 > 4.

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