Question

Suppose Brian and Crystal 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 Brian chooses Right and Crystal chooses Right, Brian will receive a payoff of 5 and Crystal will receive a payoff of 6.

Crystal
Left Right
Left 6, 3 6,4
Brian Right 3, 3 7,4
The only dominant strategy in this game is for_____to choose____. The outcome reflecting the unique Nash equilibrium in this game is as follows: Brian chooses____and Crystal chooses____.

Answer 1

The only dominant strategy in this game is for Crystal to choose Right. The outcome reflecting the unique Nash equilibrium in this game is as follows: Brian chooses Right and Crystal chooses Right.

Step-by-step explanation:

Given:

Crystal

Left Right

Brian Left 6, 3 6, 4

Right 3, 3 7, 4

A dominant strategy refers to a strategy that makes a player being better off regardless of the choice his opponent in a game.

It can be seen from the payoff matrix above that when Brian plays Left, Crystal chooses Right because 4 > 3. Also, when Brian plays Right, Crystal chooses Right because 4 > 3. The indication of this is that Crystal will always choose Right no matter what Brian chooses. This means that the dominant strategy for Crystal is Right.

On the other hand, when Crystal Chooses Left, Brian will also choose Left because 6 > 3. And when Crystal chooses Right, Brian will also play Right because 7 > 6. This is an indication that Brian does not have any specific strategy that makes him better off. Therefore, Brian does not have a dominant strategy.

Based on the analysis above, we have:

The only dominant strategy in this game is for Crystal to choose Right. The outcome reflecting the unique Nash equilibrium in this game is as follows: Brian chooses Right and Crystal chooses Right.