h2ansgamef07

h2ansgamef07 - Department of Economics The Ohio State...

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Department of Economics The Ohio State University Econ 817—Advanced Game Theory Fall 2007 Prof. James Peck Homework #2 Answers 1. O-R, exercise 56.4. Answer: By the symmetry of the game, the set of rationalizable pure actions is the same for both players. Call it Z .C o n s i d e r m inf( Z ) and M sup( Z ) . Any best response of player i to a belief about player j (whose support is a subset of Z ) maximizes E ( a i (1 a i a j )) , or equivalently, it maximizes a i (1 a i E ( a j )) .T h u s ,p l a y e r i ’s best response to a belief about player j depends only on E ( a j ) ,wh ichcanbew r i t tena s B i ( E ( a j )) = (1 E ( a j )) / 2 .B e c a u s e m E ( a j ) M must hold, a i B i ( E ( a j )) implies a i [(1 M ) / 2 , (1 m ) / 2] . By the best response property of the rationalizable set, we have m [(1 M ) / 2 , (1 m ) / 2] and M [(1 M ) / 2
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h2ansgamef07 - Department of Economics The Ohio State...

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