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Culture and scope of cooperation. Consider two ladies Amy (A) and Betty (B). Now they face a game with the following payoff matrix: B cooperates B betrays A cooperates (2, 2) (0, 2.5) A betrays (2.5, 0) (1, 1 ) 1. (2) Find out all the Nash equilibria in the game. 2. (2) Do A and B have a cooperation or coordination problem, or do they have any problem? Why? 3. (2) Denote A and B's social distance as d > 0, and a small d would suggest that they are very close to each other, e.g., are siblings, while a great d would suggest they are strangers. Assume that each between A and B enjoys an extra psychological payoff r = e-" from choosing to cooperate, regardless the other lady's choice, a > 0. Here e is the base of the natural logarithm. This specification suggests that the greater the social distance between A and B (d), the lower this psychological payoff r. This is intuitive: for example, we cherish behaving morally more with someone we love compared to with someone we do not know at all. Note that the greater a, the faster this psychological payoff (x) is decreasing in the social distance (d). Now the payoff matrix becomes as follows. Under what conditions in terms of a and d would "A cooperates, B cooperates" be a Nash equilibrium? B cooperates B betrays A cooperates ( 2+e-", 2+e-" ) (e-and, 2.5) A betrays (2.5, e-ad) (1, 1) 4. (2) Your answer to the above question should yield a critical threshold of d, below which "A cooperates, B cooperates" would become a Nash equilibrium. Hereby we find the scope of cooperation in terms of the range of social distance that can sustain cooperation. How would a, the speed of decrease of the positive psychological payoff from cooperation in social distance, affect the scope of cooperation