7. Solving for dominant strategies and the Nash equilibrium Suppose Eric and Gin

Question

7. Solving for dominant strategies and the Nash equilibrium Suppose Eric and Ginny 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 Eric chooses Right and Ginny chooses Right, Eric wll receive a payoff of 3 and Ginny will receive a payoff of 7. Ginny Left Right Left4,66,8 3, 7 Right 7,5 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Eric choosesand Ginny chooses

Explanation / Answer

Answer:

If Eric chooses left then Ginny gets a pay-off of 6 if she also chooses left and pay-off of 8 if she chooses right.

Since, pay-off is higher in case of right, Ginny will choose right if Eric chooses left.

If Eric chooses right then Ginny gets a pay-off of 5 if she chooses left and pay-off of 7 if she chooses right.

Since, pay-off is higher in case of right, Ginny will choose right if Eric chooses right.

It can be observed that Ginny will choose right whatever be the choice of Eric (left or right).

When a player always chooses a strategy irrespective of strategy choosen by opponent then such strategy is called dominant strategy.

So, Ginny has dominant strategy and that strategy is to choose right.

If Ginny chooses left then Eric gets a pay-off of 4 if he also chooses left and pay-off of 7 if he chooses right.

Since, pay-off is higher in case of right, Eric will choose right if Ginny chooses left.

If Ginny chooses right then Eric gets a pay-off of 6 if he chooses left and pay-off of 3 if he chooses right.

Since, pay-off is higher in case of left, Eric will choose left if Ginny chooses right.

It can be observed that choice of Eric changes as per the change in choice of Ginny.

So, Eric has no dominant strategy.

With Ginny having dominant strategy of right, she will always choose right.

When Ginny chooses right, Eric will choose left.

So, uniques Nash equilibrium would be (left, right)

Thus,

The only dominant strategy in this game is for Ginny to choose Right.

The outcome reflecting the unique Nash equilibrium in this game is as follows: Eric chooses Left and Ginny chooses Right.

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