Econ398win08hw4sol - pure strategy Nash equilibria(Uy;lua and(Dy;rua are the subgame perfect Nash equilibria 2 Find all equilibria of the following

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ECON 398 HOMEWORK 4 SOLUTIONS Professor Ozdenoren 1. For each of the following sequential games, write the equivalent strategic form and solve for all pure strategy Nash equilibria. Indicate which one is the subgame perfect Nash equilibrium (i.e. the one you find through backward induction). a) The equivalent strategic form game is: L R U -10,-2 6,2 D 3,6 3,6 (D;L) and (U;R) are pure strategy Nash equilibria and only the second one is a subgame perfect Nash equilibrium. b) The equivalent strategic form game is: lua lub lda ldb rua rub rda rdb Dx 4,4 4,4 4,4 4,4 2,10 2,10 2,10 2,10 Dy 4,4 4,4 4,4 4,4 8,4 8,4 6,2 6,2 Ux 5,6 1,2 5,6 1,2 5,6 1,2 5,6 1,2 Uy 5,6 1,2 5,6 1,2 5,6 1,2 5,6 1,2 (Ux;lua), (Uy;lua), (Dy;lub), (Ux;lda), (Uy;lda), (Dy;ldb), (Dy;rua), (Dy;rub) are
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Unformatted text preview: pure strategy Nash equilibria. (Uy;lua) and (Dy;rua) are the subgame perfect Nash equilibria. 2. Find all equilibria of the following game first and then find the sub-game perfect equilibria? (DU; L) and (DU; R) are the two pure strategy Nash equilibria of this game and both are subgame perfect. 3. a) The strategic form of the game is: aa ab ba bb LU 1,3 1,3 -1,2 -1,2 LD 1,3 1,3 -1,2 -1,2 MU 3,0 2,-2 3,0 2,-2 MD 3,0 2,-2 3,0 2,-2 RU 4,1 0,0 4,1 0,0 RD 4,1 2,-1 1,1 2,-1 The equilibria are (RU; aa), (RD; aa), (RD;ba), (RU; ba). b) There are three subgames. c) (RD; aa) is the only subgame perfect Nash equilibrium....
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This note was uploaded on 04/02/2008 for the course ECON 398 taught by Professor Emre during the Winter '07 term at University of Michigan.

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Econ398win08hw4sol - pure strategy Nash equilibria(Uy;lua and(Dy;rua are the subgame perfect Nash equilibria 2 Find all equilibria of the following

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