Solving for dominant strategies and the Nash equilibrium Suppose Carlos and Deborah 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 Carlos chooses Right and Deborah chooses Right, Carlos will receive a payoff of 3 and Deborah will receive a payoff of 7.
Deborah Left Right Carlos 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: Carlos chooses and Deborah chooses .

The dominant strategy is for Deborah to choose left.

Carlos chooses right while Deborah chooses left.

Explanation:

Nash equilibrium is a state where both the participants gain from the payoff matrix by choosing a strategy which is beneficial for both of them. The Deborah is in a state that she will gain when she chooses left. Carlos is indifferent as she can choose right also but to be in Nash equilibrium Carlos should choose right and Deborah should go with left.

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