Question

There are two players, i = 1,2. There are also two time periods, te {1,2}. In each period, the following symmetric stage game


A B C А в с 1,1 0,0 5,0 0,0 3,3 0,0 0,5 0,0 4,4 That is, the players first play this stage game once. Then, after having obse
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Answer #1

Payoff matrix

A B C
A (1*,1•) (0,0) (5*,0)
B (0,0) (3*,3•) (0,0)
C (0,5•) (0,0) (4,4)

Pure strategy NE of game :

(A,A) & (B,B)

both play A & both play B

b) now two period game :

If both Cooperate in first period, that is both play (C,C)

Then in next period ,Pareto superior NE : (B,B) is played

• if any player deviates in first period to play A, then in next period pareto inferior NE : (A,A) is played

let d : discount factor

Then Cooperation payoff Vc = 4+3d

Deviation payoff = 5+1d =

Now sustain cooperation

If Vc > Vd

4+3d > 5 +d

2d > 1

d > .5

so if d > .5 , cooperation could be sustained as SPNE

​​​​

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