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Homework answers / question archive / 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
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 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 Edison chooses Right and Hilary chooses Right, Edison will receive a payoff of 5 and Hilary will receive a payoff of 4. Hilary Left Right Left 8,3 4,4 Edison Right 5,3 5,4 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Edison chooses and Hilary chooses
The pay-off matrix of the game is as follows :
| Left | Right | |
| Left | 8 , 3 | 4 ,4 |
| Right | 5 , 3 | 5 , 4 |
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.
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.
