Question

Suppose Kevin and Maria 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 Kevin chooses Right and Maria chooses Right, Kevin will receive a payoff of 7 and Maria will receive a payoff of 6.

Maria
Left Right
Kevin Left 4, 3 6, 4
Right 6, 7 7, 6

The only dominant strategy in this game is for ___________ to choose ______________ The outcome reflecting the unique Nash equilibrium in this game is as follows: Kevin chooses _______________ and Maria chooses _____________

Answer 1

The only dominant strategy in this game is for Kelvin to choose right. The outcome reflecting the unique Nash equilibrium in this game is as follows: Kevin chooses right and Maria chooses left.

Step-by-step explanation:

A dominant strategy can described as a strategy that makes a player better off no matter his or her opponent in a game chooses.

In the game in the question, when Kelvin plays left, it best for Maria to play right because 4 > 3. But when Kelvin plays right, Maria will play left because 7 > 6. Therefore, there is no particular strategy that will make Maria better off. This implies Maria has no dominant strategy.

On the other hand, when Maria plays left, Kelvin will play right because 6 > 4. And when Maria plays right, Kelvin will still also play right because 7 > 6. This implies that no matter what Maria plays, Kelvin will always be better off by playing right. Therefore, the dominant strategy for Kelvin is right.

The implication of the above analysis in that the only dominant strategy in this game is for Kelvin to choose Right.

The only dominant strategy in this game is for Kelvin to choose right. The outcome reflecting the unique Nash equilibrium in this game is as follows: Kevin chooses right and Maria chooses left.