Puzzle 1: The greedy person says nothing, thinking "If I wait for the other to choose, then I shall get twice as much, and that is better!". The envious person says "I wish to have one eye removed."
(This story is based on an old folk tradition. Or so I was told by Myra Brenner.)
Puzzle 2: The mathematical analysis of this game is simple. Let's first analyze the game from B's perspective. A has made a proposed division of the prize. As long as this division offers a positive amount to B, (no matter how small!), it is in B's rational interest to take it, because it improves his situation. Now, since this is what B will do, A realizes that it is in his best interest to offer B something, but the least possible something. Therefore, A offers to divide the prize as follows: $99.99 for A, and $0.01 for B. B accepts, and that's it.
However, when a version of this game was played with real people, it didn't work out the way a "rational" analysis suggested. Player A usually was much more generous than mathematically necessary, and Player B would often refuse a division of the award if Player A was to receive more than 80 percent of the total.
One way to understand these results is to assert that it simply shows that people are not rational; they can't actually see what is in their best interest. Or perhaps mathematicians are foolish to believe that rationality rules the world. Or perhaps mathematicians are guilty (in this case) of believing in greed when it's really envy that makes the world go round!