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Suppose Kevin and Maria are playing a game in which both must simultaneously choose the action...

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 2.

Maria
Left Right
Kevin Left 6, 5 4, 4
Right 5, 3 7, 2

The only dominant strategy in this game is for (KEVIN/MARIA) to choose (LEFT/RIGHT) .

The outcome reflecting the unique Nash equilibrium in this game is as follows: Kevin chooses (LEFT/RIGHT) and Maria chooses (LEFT/RIGHT   .

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We can see from above table that If Kevin chooses Left then Maria will also choose Left(5 > 4) and If Kevin chooses Right then Maria will also choose Left(3 > 2). Hence whatever Kevin chooses Maria will always choose left and hence Left is a dominant strategy for Maria.

We can see from above table that If Maria chooses Left then Kevin will also choose Left(6 > 5) and If Maria chooses Right then Kevin will also choose Right(7 > 4). Hence decision of Kevin is depending on Maria and hence Kevin does not have any Dominant strategy.

As Left is a dominant strategy for Maria. Hence Maria will always choose left. As discussed above If Maria chooses Left then Kevin will also choose Left. Hence, Nash equilibrium strategy is Both choosing Left.

The only dominant strategy in this game is for MARIA to choose LEFT .

The outcome reflecting the unique Nash equilibrium in this game is as follows: Kevin chooses LEFT and Maria chooses LEFT .

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