Behavioral Game Theory

The ultimatum game is one of the most well known and well studied games. Yet there still seems much confusion and misunderstanding over the basic theory behind the game. This is worrying because it means one of the key lessons we can learn from the ultimatum game goes unrecognised.        In the ultimatum game a proposer and responder need to decide how to split, say, $10. The proposer moves first by making a take-it-or-leave-it-offer. The responder then either accepts the offer or rejects it. If he accepts it the deal is done. If he rejects both get nothing. For example, the proposer could offer $3. If the offer is accepted the proposer gets $7 and the receiver $3. If it is rejected both get $0.        What is going to happen? In the experimental lab the almost universal outcome is that the proposer offers $5 and this is accepted. We also know, although the evidence for this is less unequivocal, that offers of less than $5 can be rejected.          What does theory say should h