Question

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.

Answer 1

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