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 is played

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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