Attempts: Average: /2 3. Solving for dominant strategies and the Nash equilibriu

Question

Attempts: Average: /2 3. Solving for dominant strategies and the Nash equilibrium Suppose Alex and Becky 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 Alex chooses Right and Becky chooses Right, Alex will receive a payoff of 9 and Becky will receive a payoff of 8 the lower-right cell Becky Left Right Left 8,5 8,7 Righ 3,69, 8 Alex Alex Becky The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Alex chooses and Becky chooses

Explanation / Answer

Answer.

If Alex chooses Right, Becky chooses right as 8>6. If Alex chooses left then also Becky chooses right as 7>5. Thus becky as a dominant strategy of choosing Right.

If Becky chooses Right, then Alex chooses Right as 9>8. However if Becky chooses Left then Alex chooses left as 8>3.

Hence for part a. Becky has a dominant strategy of choosing Right.

Part b) Here we know Becky has a dominant strategy of chossing right. Thus we eliminate the option of left for Becky.

Now in the reduced matrix with Becky choosing Right, Alex too will choose Right as 9>8. Thus in the Nash equilibrium both will choose right.

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