I know the answer to (a), the SPNE is when player 1 picks N and player 2 also pi

Question

I know the answer to (a), the SPNE is when player 1 picks N and player 2 also picks N. But what about (b)? I've included the entire question for reference. Thanks!

1. (15 points) On a given week, two selfish children (S) ur not (N). The payoff matrix is the following parents simultaneously choose between spending time with ther Player 2 (a) Assuime that the parents repeat this game fur 52 weeks, What are the Subgame Porfet Naih Equilibriu stralogies? What is the SPNE outcome? b) Now assume the parents repeat this game infinitely Consider the following smatnegs "Start by Playing S and continue playing S as long as (S.S) was played on every previons weck. Otherwise, play N forever players to play the strategy above? Why or why noe?

Explanation / Answer

The total payoff to the strategy(s,s) infinitly will be

= 5 + 5 + 5^2 . . . . . . . .. + 5^t . . . . . .. = 5/1-

So, the given strateegy will be better, provided

5/1- > 6 (here 6 is the payoff to the alternate strategy(i.e if player deviates, So if payoff from the given strategy is more than the alternate strategy then players will not deviate and it will be a SPNE)

or   > 1/6

So , In over given case   for player 2 is 1/8 ,

Thus for player 2

The payoff to the strategy = 5/1-1/8

The payoff if he deviates = 6

And 5/1-1/8 < 6 or 5.71<6

Hence Player 2 has an incentive to deviate .

Thus the given strategy is not a SPNE

If you don't understand anything then comment , I will revert back on the same.

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