Suppose Paolo and Sharon 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 Paolo chooses Right and Sharon chooses Right, Paolo will receive a payoff of 9 and Sharon will receive a payoff of 5.

Sharon
Paolo Left Right
Left 6,6 8,5
Right 3,6 9,5

The only dominant strategy in this game is forto choose.
The outcome reflecting the unique Nash equilibrium in this game is as follows: Paolo chooses and Sharon chooses.

Paolo Left

Left Left

Explanation:

All of the possible outcomes for this game are listed below by interpreting the payoff matrix:

if Paolo chooses Left and Sharon chooses Right, Paolo will receive a payoff of 8 and Sharon will receive a payoff of 5.

if Paolo chooses Left and Sharon chooses Left, Paolo will receive a payoff of 6 and Sharon will receive a payoff of 6.

If Paolo chooses Right and Sharon chooses Right, Paolo will receive a payoff of 9 and Sharon will receive a payoff of 5.

if Paolo chooses Right and Sharon chooses Left, Paolo will receive a payoff of 3 and Sharon will receive a payoff of 6.

If Paolo chooses left, he will never earn less than Sharon (either more or the same) therefore, the only dominant strategy in this game is for Paolo to choose left.

Nash equilibrium occurs when the payoff is the same for both parties. Thus, Nash equilibrium in this game is as follows: Paolo chooses Left and Sharon chooses Left.

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