Midterm-2010

Midterm-2010 - 6.254 Game Theory with Engr App Midterm...

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Unformatted text preview: 6.254 Game Theory with Engr App Midterm Thursday, April 8, 2010 Problem 1 (35 points) For each one of the statements below, state whether it is true or false. If the answer is true, explain why. If the answer is false, give a counterexample. Explanations and counterexamples are required for full credit. (7 points each) (1) In the following game, a strategy is strictly dominated if and only if it is a never-best response. A B C 4, 2 0, 3 D 3, 1 1, 0 E 0, 0 2, 2 (2) In the following game, the set of correlated equilibria is the same as the set of Nash equilibria. H T H 1,- 1- 1, 1 T- 1, 1 1,- 1 (3) Suppose that function f satisfies strictly increasing differences. That is, suppose that for all x > x and θ > θ , we have f ( x , θ )- f ( x , θ ) > f ( x , θ )- f ( x , θ ) . Let X * ( θ ) = argmax x ∈ R { f ( x , θ ) + g ( x ) } be nonempty for each θ . For θ > θ if z ∈ X * ( θ ) and y ∈ X * ( θ ) then y ≥ z ....
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Midterm-2010 - 6.254 Game Theory with Engr App Midterm...

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