# ps5sol - 14.12 Game Theory Muhamet Yildiz Fall 2005...

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14.12 Game Theory Muhamet Yildiz Fall 2005 Solution to Homework 5 1. Answer to Problem 1 (a) The game can be written formally as follows: Actions space: A 1 = { X, Y, Z } , A 2 = { L, R } Types space: T 1 = { t 1 } , T 2 = { θ = 1 , θ = 1 } Beliefs: p ( θ = 1 | t 1 ) = p ( θ = 1 | t 1 ) = 1 / 2 and p ( t 1 | θ 1 ) = p ( t 1 | θ 2 ) = 1 Finally, the payoffs for the two players are given by: u 1 ( X, L ; θ = 1 , t 1 ) = 3 and u 2 ( X, L ; θ = 1 , t 1 ) = 1 u 1 ( Y, L ; θ = 1 , t 1 ) = 2 and u 2 ( Y, L ; θ = 1 , t 1 ) = 2 u 1 ( Z, L ; θ = 1 , t 1 ) = 0 and u 2 ( Z, L ; θ = 1 , t 1 ) = 0 u 1 ( X, R ; θ = 1 , t 1 ) = 0 and u 2 ( X, R ; θ = 1 , t 1 ) = 0 u 1 ( Y, R ; θ = 1 , t 1 ) = 2 and u 2 ( Y, R ; θ = 1 , t 1 ) = 1 u 1 ( Z, R ; θ = 1 , t 1 ) = 3 and u 2 ( Z, R ; θ = 1 , t 1 ) = 1 u 1 ( X, L ; θ = 1 , t 1 ) = 3 and u 2 ( X, L ; θ = 1 , t 1 ) = 1 u 1 ( Y, L ; θ = 1 , t 1 ) = 2 and u 2 ( Y, L ; θ = 1 , t 1 ) = 2 u 1 ( Z, L ; θ = 1 , t 1 ) = 0 and u 2 ( Z, L ; θ = 1 , t 1 ) = 0 u 1 ( X, R ; θ = 1 , t 1 ) = 0 and u 2 ( X, R ; θ = 1 , t 1 ) = 0 u 1 ( Y, R ; θ = 1 , t 1 ) = 2 and u 2 ( Y, R ; θ = 1 , t 1 ) = 1 u 1 ( Z, R ; θ = 1 , t 1 ) = 3 and u 2 ( Z, R ; θ = 1 , t 1 ) = 1 (b) Starting with player 2, for type θ = 1 R strictly dominates L and thus s 2 ( θ = 1) = R . For type θ = 1 ,

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