Question: A common economic experiment is called the "ultimatum game." Subject A receives a small amount of cash, say $10. She can give some whole dollar amount to subject B, a stranger whom she cannot see and who cannot see her. If subject B approves of the amount he receives, both keep their portions of the $10. If subject B disapproves, they both get nothing.

a. Can you show that if subject A is interested only in herself, her rational strategy is to give subject B $1 (Why not nothing?), and subject B's rational response is to accept that amount?

b. How might you explain the fact that in actual experiments the average amount offered by subject A (who is chosen at random) is an average of $3, and subject B (also chosen at random) usually accepts it?

c. What do you think happens to the average amount transferred by subject A and the probability that subject B will accept it if the setup is changed so that subject A wins her place as the giver by outscoring B on a short test of general knowledge? Explain.

d. What do you think happens to the average amount transferred and the probability of acceptance if subjects A and B are told they might be matched with each other to play the game again at some date in the future but do not know in advance who will be the donor and who the recipient?

e. If, instead of $10, subject A gets $200 to give away, what do you expect will happen to the amount she offers subject B? Why?