Solving for dominant strategies and the Nash equilibrium Suppose Edison and Hilary are playing a game in which both must simultaneously choose the action Left or Right

The pay-off matrix of the game is as follows :

Edison is the row player and Hillary is the column player. The first term of each cell represents the pay-off of Edison from a particular strategy while the second term represents Hillary's pay-off.

We indicate the optimal choices by underlinning them.

• When Edison chooses Left , Hillary chooses Right because it gives her a higher pay-pff. (4>3)
• When Edison chooses Right , Hillary also chooses Right. (4>3)
• When Hilalry chooses Left , Edison chooses Left. (8>5)
• When Hillary chooses Right , Edison also chooses Right. (5>4)

Thus , Hillary always chooses Right irrespective of what Edison chooses. The only dominant strategy in this game is for Hillary to choose Right.

The cell containing the 2 underlines gives us the Nash Equilibrium of the game.
Thus , (Right , Right ) is the pure strategy Nash Equilibrium of this game , giving pay-offs of (5,4)

At the unique Nash Equilibrium of the game , Hillary chooses Right and Edison also chooses Right.