Suppose Sam and Teresa are playing a game in which both must simultaneously choose the action Let 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 Sam chooses Right and Teresa chooses Right, Sam will receive a payoff of S and Teresa will receive a payoff of 1. Teresa
Left Right
Sam Left 8, 4 4, 5
Right 5, 4 6, 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: Sam chooses and Teresa chooses .

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

Explanation:

Given:

                        Teresa

                     Left       Right

Sam Left     8, 4         4, 5

       Right   5, 4         6, 5

A dominant strategy is one that makes a player in a game better off regardless of the choice of strategy of his opponent.

An examination of the payoff matrix above shows that when Sam plays Left, Teresa will play Right because 5 > 4. When Sam plays Right, Teresa will still play Right because 5 > 4. This is an indication that Teresa will always play Right no matter what Sam plays. Therefore, the dominant strategy for Teresa is Right.

On the other hand, when Teresa plays Left, Sam will also play Left because 8 > 5. And when Teresa plays Right, Sam will also play Right because 6 > 4. This implies that Sam does not have any unique strategy that make him better off. Therefore, Sam does NOT have a dominant strategy.

Therefore, we have:

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

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