One Offer, No Discussion

How it works

A Proposer names any split of 100 pounds; the Responder accepts it or rejects, in which case both get nothing. One offer, no counter-offers, no conversation, strangers who play once. The story asks what the Proposer should offer and what the Responder does. You lock in a guess, then step through the answer and breakdown.

How scoring works

No grading - your guess is displayed back beside the answer. The story teasers share one lifetime unlock for free users.

The key insight

Solve from the last mover backward. A money-only Responder accepts any positive amount, so the Proposer offers the minimum - 1 pound - and keeps 99. That is the subgame-perfect equilibrium, and it fails empirically: real people pay to punish insulting offers, so low offers get rejected and real proposers offer far more. The strong answer gives both halves and names the assumption that broke - the payoff function priced the money and not the insult.

The full step-by-step solution lives at /brain-teasers/ultimatum/solution.

A worked example

Responder faces X versus 0: any positive X wins, so he accepts everything. Feed that back: the Proposer offers 1 pound and keeps 99. Then the empirical half: humans reject small offers routinely, so proposers who know that offer close to half.

Common mistakes

• Answering only '50/50 because it is fair' - that skips the induction entirely.

• Answering only '99/1' with no acknowledgment that it fails with real people.

• Solving from the Proposer's move forward instead of from the Responder's decision backward.

Why interviews test this

This tests backward induction plus model humility: derive the equilibrium cleanly, then say why observed play differs. The written solution at /brain-teasers/ultimatum/solution lays out both halves.