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.
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
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