9. In class we said that NE often gives sharper predictions than the iterative process of...

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9. In class we said that NE often gives sharper predictions than the iterative process of elimination of strictly dominated strategies. In this problem, you will see that that's true only if some Nash equilibrium exists. Hence, there are games where eliminating strictly dominated strategies gives a smaller set of outcomes than those prescribed by the notion of Nash equilibrium. To see this, let's revisit the following game we saw in class: b1 b2 b3 b4 2, 3 0,4 аg | 4,4 | 2,5 | 1,2 | 0,4 3,1 4, 2 2,3 1,4 а1 3, 2| 4, 1 1 a3 1,3 3,1 5, 1 3,1 a. Show that there is no Nash equilibrium in this game; b. Apply the iterative process of strictly dominated strategies and write down the set of outcomes that survive; c. What is the set of rationalizable outcomes? 9. In class we said that NE often gives sharper predictions than the iterative process of elimination of strictly dominated strategies. In this problem, you will see that that's true only if some Nash equilibrium exists. Hence, there are games where eliminating strictly dominated strategies gives a smaller set of outcomes than those prescribed by the notion of Nash equilibrium. To see this, let's revisit the following game we saw in class: b1 b2 b3 b4 2, 3 0,4 аg | 4,4 | 2,5 | 1,2 | 0,4 3,1 4, 2 2,3 1,4 а1 3, 2| 4, 1 1 a3 1,3 3,1 5, 1 3,1 a. Show that there is no Nash equilibrium in this game; b. Apply the iterative process of strictly dominated strategies and write down the set of outcomes that survive; c. What is the set of rationalizable outcomes?

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