Question

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 payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Antonio chooses Right and Caroline chooses Right, Antonio will receive a payoff of 3 and Caroline will receive a payoff of 7.

Caroline
Left Right
Antonio Left 4, 6 6, 8
Right 7, 5 3, 7

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_________ .

Answer 1

Answer:

Caroline to choose right

Antonio chooses left and Caroline chooses right.

Explanation:

Interpreting the payoff matrix:

Both choose right:

Antonio receives 3, Caroline receives 7

Both choose left:

Antonio receives 4, Carolina receives 6

Caroline chooses left, Antonio chooses right:

Antonio receives 7, Caroline receives 5

Caroline chooses right, Antonio chooses left:

Antonio receives 6, Caroline receives 8

As we can see, Antonio only has a better payoff then Caroline if she chooses left and he chooses right. Therefore, the dominant strategy is for Caroline to choose right, this way she will always have the greater payoff.

If Antonio chooses right, the outcome may alter depending on the outcome, therefore it is not a Nash Equilibrium. However, if Antonio chooses left, no matter what Caroline chooses, she will have the greater payoff. At the same time, if Caroline chooses right, Antonio cannot change the outcome by changing his strategy. Therefore, the outcome reflecting the unique Nash equilibrium in this game is as follows: Antonio chooses left and Caroline chooses right.