Take it or leave it
Ultimatum Game
You and a stranger will split a pile of money. One of you proposes the split. The other can accept it — or reject it, in which case both of you get nothing. There is no haggling. One offer. One answer.
The Ultimatum Game is how experimental economists study fairness with almost no story attached. One person divides a pie. The other can only accept or burn it. If both were perfectly selfish, the proposer would keep almost everything and the responder would take the crumbs.
That is not what happens. Across cultures, modal offers cluster near an even split, and stingy offers are often rejected. Responders give up money to punish unfairness. Proposers anticipate that — or share because they think it is right.
Compare it with the Dictator Game, where the recipient has no veto. The gap between the two is a measure of how much strategic fear of rejection, rather than pure generosity, drives sharing.
What theory predicts
A perfectly selfish responder should accept any positive amount. Knowing that, a selfish proposer should offer the smallest possible slice. That is the subgame-perfect Nash equilibrium.
What people actually do
People are not that cold. Offers around 40–50% are common. Offers below about 20–30% are often rejected — responders punish unfairness even when it costs them.