Ultimatum Game Explained - The Rational Offer and Why Humans Reject It

The setup

A Proposer splits 100 pounds any way she likes; the Responder either accepts the split or rejects, in which case both get nothing. One offer, no negotiation. What does theory say - and what do people do?

Short answer: Backward induction says offer the smallest positive amount and the Responder accepts - but humans routinely reject low offers, so real proposers offer far more.

The backward-induction answer

Solve from the Responder's decision. Faced with any positive amount, accepting beats rejecting - something beats nothing. Knowing that, the Proposer keeps almost everything and offers the minimum, say 1 pound. That is the subgame-perfect equilibrium: offer 1, accept.

Why the theory answer fails in the lab

People reject. Offers around a fifth of the pot or less get turned down often, because the Responder is not only buying money - they are paying one pound to punish an insult, and many people find that a bargain.

Proposers anticipate this, which is why typical real offers land near 40 to 50 percent. The equilibrium is not wrong; it is the equilibrium of a game with purely monetary payoffs, and the game humans actually play has fairness in the payoff function.

Why interviews ask it

The strong answer gives BOTH halves: the clean subgame-perfect argument, then the observation that rejections are real and what that implies about modelling payoffs. Giving only one half reads as either untrained or cynical.