game theory

Problem Set 5 (Solutions)

ECO 444

Konrad Grabiszewski

Exercise 1

tree NE SPNE

Tree 1 (T,L), (B,R) (T,L)

Tree 2 (T,L), (B,R) (T,L), (B,R)

Tree 3 all profiles all profiles

Tree 4 (B,LX), (B,RX) (B,LX)

Tree 5 (B,LX), (B,LY ), (B,RX), (B,RY ) (B,LX), (B,LY ), (B,RX), (B,RY )

Tree 6 (T,LX), (T,LY ), (B,LY ), (B,RY ) (T,LY ), (B,LY )

Tree 7 all profiles all profiles

Tree 8 (BY,L), (BY,R), (TX,L), (TY,L) (BY,L), (TY,L)

Tree 9 (BX,L), (TX,R), (TY,R), (BX,R) (TX,R), (BX,R)

Tree 10 (M,LY ) (M,LY )

Tree 11 (M,LY ) (M,LY )

Tree 12 none none

Tree 13 none none

Tree 14 (B,βθλ), (C,βθλ) (B,βθλ), (C,βθλ)

Tree 15 none none

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Exercise 2

tree SPNE

Tree 1 (AC,α)

Tree 2 (D,βδθµ)

Tree 3 (B,αγηλ), (B,αγθλ), (B,αδηλ), (B,αδθλ), (C,αγηλ), (C,αγθλ), (C,αδηλ), (C,αδθλ)

Tree 4 (D,αδθλ)

Tree 5 (BCE,β)

Tree 6 (ACE,β)

Tree 7 (T,L,Y W)

Tree 8 (T,R,Y )

Tree 9 (B,RH,Y )

Tree 10 (B,R,G,Y )

Tree 11 (B,G,Y,R)

Tree 12 (TY P,RG)

Tree 13 (B,RG,XP)

Tree 14 (CS,CC)

Tree 15 (CC,CS)

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