Puzzle 1: A greedy person was walking down the road, and tried to pass an envious person, who tripped him. The two began to fight, and one picked up a rock only to discover a golden lamp beneath it, inscribed "A wish for you". Both grabbed it at the same time, and felt it shake and rumble. Then a genie appeared, and said, "Normally, I am only called forth by a single person. Since there are two of you, and I need to be amused, I will grant you both a wish. But one of you must wish first, and the other will simply get twice of what the first wishes."
Who spoke first, and what was wished for?
Puzzle 2: The mathematical field of "game theory" tries to explain the actions of independent people with differing goals who must obey a set of rules while seeking rewards and avoiding penalties. These situations are imagined as games, in which players alternate moves. In the simplest game, player A makes a choice, then player B makes a choice, and the rewards are determined for each player based on these choices. For mathematical analysis, it is assumed that the players are "rational", and that the only criterion they use to choose a move is whether it will increase their own final reward.
A particular example of such a game works as follows. A prize of $100 is to be divided between players A and B. A moves first, and the move is simply to propose the division of the prize between player A and B. Player B moves next. Player B may either accept the division, or reject it. The game is now over. If Player B accepted the division, the prize is divided in the way Player A proposed. Otherwise, both players get nothing.
From a mathematical standpoint, what will happen in this game? If you play this game in real life, what actually happens?
I give up, show me the solution.