Brain Teasers · One Offer, No Discussion
Ultimatum Game Puzzle - The Rational Offer
The ultimatum game as a story: one split of 100 pounds, one accept-or-reject, no negotiation.
What is the ultimatum game?
The ultimatum game is a two-player bargaining game with a simple structure: one player, the proposer, suggests how to split a fixed sum of money; the other, the responder, either accepts the split, in which case both get what was proposed, or rejects it, in which case both get nothing. There is no counter-offer and no negotiation - it is a single take-it-or-leave-it move. The game was introduced experimentally by Werner Guth, Rolf Schmittberger, and Bernd Schwarze in a 1982 paper that became one of the most replicated experiments in behavioural economics.
Solved by backward induction, the game has a stark prediction: a responder who cares only about money should accept any offer above zero, because something is better than nothing. Knowing that, a proposer who also cares only about money should offer the smallest possible positive amount and keep almost everything. That outcome is the subgame perfect equilibrium of the game as formally specified.
Real people playing the game do not behave this way, and that gap is the entire reason the ultimatum game became famous. Offers below roughly 20 to 30 percent of the pot are rejected at high rates across cultures and experimental settings, even though rejecting is a strictly worse outcome in dollar terms for the responder. Proposers, anticipating this, typically offer close to an even split rather than the theoretical minimum.
The standard interpretation is that responders are willing to pay a cost to punish an offer they perceive as unfair or disrespectful, and proposers factor that willingness into their offer. The ultimatum game is now a core tool for demonstrating that pure self-interest fails as a model of real bargaining behaviour, and cross-cultural studies have found the rejection threshold varies meaningfully with social norms around fairness and reciprocity.
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.
Play One Offer, No Discussion on Outcry
One Offer, No Discussion is free to play on Outcry, in the Brain Teasers section, and every run is timed and scored. Read the guide once, then play One Offer, No Discussion and check your score against the strategy above. The guide book has a written guide for every other game, and the practice hub and mock assessments put the same skills under a real screen's clock.