Answer:
Given that:
Now consider that two players with discount factor 0 < < 1 play the stage game in each of an infinate number of periods.
Payoff matrix
W | X | Y | Z | |
A | 8,9 | 14,9 | 5,0 | 1,4 |
B | 8,0 | 19,13 | 7,18 | 9,16 |
C | 9,80 | 33,33 | 5,13 | 0,84 |
NE : (B,Y)
e)
The possible cooperative eqm should be (C,X)
Where both get 33, Both are better off as compared to (B,Y)
f)
punishment threat, NE : (B,Y) will be played each period .
Both will be worse off, as compared to Cooperation payoff
since it's the NE, so it's credible
g)
P1 will not deviate, bcoz he is getting Maximum payoff of 33
using Grim trigger strategy;
p2 has incentive to deviate, so if P1 plays C , p2 has incentive to play Z , as it gets 84
next period onwards, punishment starts,
so NE is played
so, if discount factor is d
then present discount value PDV of Cooperation payoff
Vc = 33+33d + 33d2+33d3+ ...
= 33/(1-d)
Vd = 84+ 18d +18d2 + 18d3 +....
= 84 + 18d/(1-d)
Cooperate if, Vc > Vd
33/(1-d) > 84+ 18d/(1-d)
33 > 84-84d + 18d
66d > 51
d > 51/66 = .772
So discount factor should be between .772 & 1, for no
defection
answer parts e f g pls 4. Consider the following game presented in the strategic form:...
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