Question

Consider the following stage game to be played twice; assume no discount between the periods. X...

Consider the following stage game to be played twice; assume no discount between the periods.

X

Y

W

Z

A

11,11

6, 12

1, 3

0,0

B

12, 6

7, 7

2,2

0,0

C

3, 1

2,2

5,5

0,3

D

0, 0

0,0

3, 0

3, 3

(i) Identify the PSNE of the game.

(ii) Can there be a subgame perfect equilibrium where (A, X) is played in stage 1? Prove your answer, whatever that might be. You will need an appropriate game matrix to support your contention.


Homework Answers

Answer #2

Q1)

X Y Z W
A (11,11) (6,12•) (1,3) (0,0)
B (12*,6) (7*,7•) (2,2) (0,0)
C (3,1) (2,2) (5*,5•) (0,3)
D (0,0) (0,0) (3,0) (3*,3•)

Pure strategy NE:

(B,Y) (C,Z) (D,W)

2) twice repeated game

then, sustain (A,X) in first stage

so, if both Cooperate , then play pareto superior NE :(B,Y) in second period, bcoz NE acts as Credible threat

then total Cooperation payoff

Vc = 11+7 = 18

If one cheats , it gets 12 in the cheating period, & then play pareto inferior NE : (D,W)

deviation total payoff

then Vd = 12+3= 15

so as Vc > Vd

so this strategy sustains (A,X) in first period

answered by: anonymous
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