Think about a dictator game in which one player divides $20 between himself and someone else. Let's use S to stand for the amount he keeps for himself and F for the absolute value of the difference between the amount he keeps, and the amount he gives the other player. For instance, if he keeps $16, then F = 12 (because he gives $4 to the other player); if he keeps $8, then F = 4 (because he gives $12 to the other player). Suppose the dictator ranks the outcomes according to the value S - AF, where A is a positive number. That is, he cares about both his own dollar payoff and the fairness of the outcome (where greater equality implies greater fairness).What will the dictator do if A< 0.5? What will he do is A> 0.5?