Suppose Antonio and Caroline are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoffs each person will earn as a function of both of their choices. Forexample, the lower-right cell shows that if Antonio chooses Right Caroline chooses Right, Antonio will receive a payoff of 5 and Caroline will receive a payoff of 5.

The only dominant strategy in this game is for to choose

The outcome reflecting the unique Nash equilibrium in this game is as follows : Antonio chooses and Caroline chooses

See explanation column for answer

Explanation:

                                Caroline

                           left           Right

Anthonio   left   6,6             6,3

                  Right  4,3            5,5

The first digits in both left and right  is Anthonio's best response payoff given what Caroline chooses. Also, the second digit on both left and right is Caroline's best response payoff  based on what Anthonio chooses.

When Antonio chooses left, Caroline should choose left so as to get a payoff of 6, also when Antonio chooses right, Caroline chooses right to get a payoff of 5. therefore, there is no dominant strategy for Caroline.

The dominant strategy for Antonio occurs  

When Caroline chooses left, Antonio will have to choose left to get a payoff of 6, also when  Caroline chooses right, Antonio should choose left to get a payoff of 6. So, the dominant strategy for Antonio is to choose left.

The only dominant strategy in this game is for Antonio, to choose left.

b).  For Nash Equilibrum, Antonio will have to choose his dominant strategy, that is to choose left, which will make  Caroline is to choose left so as to get a payoff of 6. So, the Nash equilibrium is for Antonio to choose left and caroline chooses left too