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On a given week, two selfish parents simultaneously choose between spending time with their children (S) or not (N). The payoff matrix is the following. Player 1 Player 2 S N S 5,5 -1,6 N 6,-1 0,0 (a) Assume that the parents repeat this game for 52 weeks. What are the Subgame Perfect Nash Equilibrium strategies? What is the SPNE outcome? (b) Now assume the parents repeat this game infinitely. Consider the following strategy: "Start by Playing S and continue playing S as long as (S,S) was played on every previous week. Otherwise, play N forever." Assume Payer 1's discount factor is δ1 = ¼ and Player 2's is δ2 = 1/8. Is it a SPNE for both players to play the strategy above? Why or why not?
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