Consider the following two-stage experiment. In the first stage the subjects played a dictator game where they were asked to split 10 tokens (convertible to dollars at the rate of 1 token = 1$) between themselves and an anonymous other person in the room. Assume that each subjects had a Fehr-Schmidt utility function, UA = xA A max(xB xA, 0) A max(xA xB, 0). After all subjects made their choices they were randomly divided into two equally sized groups called Senders and Receivers and randomly matched in pairs. If a subject was chosen to be a Sender his payoff was equal to what he decided to keep for himself of the 10 tokens. If he was chosen to be a Receiver, his payoff was equal to the amount given to him by the Sender whom he was matched with. Subjects were not told their payoff from the first stage until after both stages of the experiment were completed.

After the first stage was completed subjects moved on to the second stage, where they were randomly matched with another subject in the lab. After they were matched, they were offered, as a Receiver, the amount that the subject whom they were matched with sent as a Sender in the first stage. In other words, if a subject was matched with a person who gave 3 tokens in the first stage, he was offered 3 tokens in the second stage as his payoff while the other subject got 7. Subjects did not have the option of rejecting proposals, but they could, if they wished, punish their pair member by reducing his payoff by 1 token at no cost to themselves. To elicit their response, we used the strategy method in that rather than having the subjects punish directly, we asked them to set a cutoff before seeing the offer. If the offer was equal to or less than the cutoff, 1 token would be removed from the other subject's payoff.

For example, say that a subject chose a cutoff of 4. If the subject was matched with a subject who offered 3 tokens in the first stage, and hence kept 7 for himself, then the computer would reduce the pair member's payoff by 1 token from7 to 6. If the Sender gave 5 tokens and kept 5 tokens, his tokens would not be reduced and will stay at 5.

The second stage payoff was determined as follow. After subjects made their choices in the second stage, the computer randomly determined whether they are a Sender or a Receiver. If a subject was designated to be a Receiver the subject whom he was matched with was designated to be a Sender and vice versa. A Sender's payoff was equal to what he decided to keep for himself in the first stage minus any 1-token reduction by his pair member if there was a punishment.

The task of any subject in this experiment was to make an offer in the first stage and set a cutoff in the second stage.

a) As A increases for any subjects what happens to the offer he or she makes in the first stage?

b) What is the maximum offer that a subject would make in the first stage.

c) Does a subjects A coefficient affect the offer they make in stage 1.

d) What will the cutoff be for a subjects in stage 2?

e) Given what the equilibrium offer in stage 1 from any subject does the A coefficient of the subject affect his behavior in the second stage.