4

When t = 2n for n = 0,1,2,...

Both players will choose to play (C,D) therefore payoff for each player in even period will be 0 for player 1 and 10 for player 2.

Similarly,

Both players will choose to play (D,C) therefore payoff for each player in odd period will be 10 for player 1 and 0 for player 2.

Now we have SPNE if both players collude is (C,C) = (5,5) hence in this case both players will choose to play (C,C) infinitely.

We need to show that if Present value of payoff from strategy given in the question is greater than present value of SPNE with (C,C).

Present value of payoff from the strategy given in the question for player 1 & d is the discount rate where 0<d<1; we use to find present value of future payoffs.

0+10d+0+10d^3+0+10d^5+... = 10d(1+d^2+d^4+d^6+...) = 10d/(1-d^2)

Present value of payoff from the strategy (C,C) for player 1.

5+5d+5d^2+5d^3+.... = 5/(1-d)

thern if we can find any value "d" which is valid one then we can firmly say that strategy given in the question is an SPNE.

Therefore, we should have

10d/(1-d^2) >= 5/(1-d)

10d/(1+d) >= 5

10d >= 5+5d

5d >= 5

d >= 1

therefore this can be SPNE iff d= 1. This means that when both players are patient enough about the future payoffs then this can be SPNE else for any feasible value of 0<d<1 we don't have this strategy as SPNE.