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PS3_212Fal10

# PS3_212Fal10 - ECON 212 Game Theory Prof Andrew Postlewaite...

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Unformatted text preview: ECON 212 Game Theory Prof. Andrew Postlewaite Fall 2010 University of Pennsylvania Suggested Solution for Problem Set 3 1. Osborne 163.2 The extensive game can be modeled as the following. Players: i ∈ { 1 , 2 } Strategies: s 1 ∈ { X,Y,Z } s 2 = ( s 2 ( X ) ,s 2 ( Y ) ,s 2 ( Z )) , where s 2 ( X ) ∈ { Y,Z } ,s 2 ( Y ) ∈ { X,Z } ,s 2 ( Z ) ∈ { X,Y } X X X X X Y Y Y Y Y Z Z Z Z Player 1 Player 2 Z Figure 1: Osborne 163.2: Extensive Game Let the payo from the best to worst policy be 3,2, and 1 for each person. YXX YXY YZX YZY ZXX ZXY ZZX ZZY X (1,3) (1,3) (1,3) (1,3) (2,2) (2,2) (2,2) (2,2) Y (1,3) (1,3) (3,1) (3,1) (1,3) (1,3) (3,1) (3,1) Z (2,2) (3,1) (2,2) (3,1) (2,2) (3,1) (2,2) (3,1) 1 We can see that there are two Nash equilibria, ( Z,Y XX ) and ( Z,ZXX ) . 2. Osborne 173.3 The SPE is ( Z,Y XX ) . Thus, ( Z,ZXX ) is Nash, but not SPE. Nash equilibrium outcomes are the same as that of the SPE. If person 2's preference is Y X Z , then the Nash equilibrium outcome is X when person 1 moves rst, but...
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