Game Theory · GT-15
Rational-choice theory predicts you should accept any non-zero offer — real humans reliably punish stingy ones, even at a cost to themselves.
One player proposes a split of a fixed sum; the other can accept (both get the proposed split) or reject (both get nothing). Subgame-perfect logic says any positive offer should be accepted — but decades of experiments show people routinely reject low offers, sacrificing their own payoff to punish perceived unfairness.
Introduced by Werner Güth, Rolf Schmittberger, and Bernd Schwarze in a 1982 experimental economics paper; became one of the most replicated experiments in behavioral economics.
The Mechanism
Predicted equilibrium vs. observed human behavior
The gap between theory and observed behavior is the actual finding — proposers, anticipating rejection, don't even try to exploit the theoretical prediction; they converge toward near-fair splits well before experiments even test the responder's threshold.
01 · SUBGAME PERFECTION SAYS ACCEPT ANYTHING
The backward-induction prediction
Solving the game by backward induction: the responder should accept any offer greater than zero (something beats nothing), so the proposer should rationally offer the smallest positive amount possible. This is the textbook subgame-perfect equilibrium — and it is reliably, dramatically wrong as a behavioral prediction.
02 · REJECTIONS ARE COSTLY PUNISHMENT, NOT IRRATIONALITY
Fairness has a real, measurable price people will pay
Across hundreds of replications in dozens of countries (surveyed extensively by Camerer, 2003, and Henrich et al.'s 2001 cross-cultural study), responders reject offers below roughly 20-30% often enough to matter, willingly forgoing free money to punish an offer perceived as unfair — a finding robust across vastly different cultures, though the specific rejection threshold varies with local norms.
03 · IT REVEALS THAT 'RATIONAL' NEEDS A BROADER DEFINITION
Utility isn't just the dollar amount
The experiment's real contribution to economics wasn't proving humans are irrational — it's evidence that people's utility functions include fairness and reciprocity as real arguments, not just personal payoff. Once you add 'inequity aversion' terms to the model (as Fehr and Schmidt did formally in 1999), the observed rejections become perfectly rational again, just under a richer objective function.
Where It Fails / Inversion
Where it fails / inversion
Assuming counterparties will behave as pure payoff-maximizers in any negotiation with a rejection option is a reliable way to trigger costly punishment — real people (and real customers, employees, and partners) will walk away from objectively positive deals they perceive as unfair, even when walking away costs them something too. Ignoring this is one of the most common and costly modeling mistakes in negotiation design.
How To Use It
Worked example · designing a compensation or settlement offer
A company structuring a severance or settlement offer that is legally and 'rationally' sufficient but perceived as insultingly low risks the equivalent of an ultimatum-game rejection — the counterpart may reject, litigate, or publicize the dispute at real cost to themselves, purely to punish the perceived unfairness, exactly as ultimatum-game responders do. Anticipating this, well-run negotiations price in a fairness premium above the bare legal minimum, because the alternative (a technically rational lowball) systematically triggers rejection in practice.
How to use it
When making a take-it-or-leave-it offer, don't calculate only the recipient's rational floor — calculate their fairness threshold, which is usually higher and less predictable. Decades of ultimatum-game data suggest that offers perceived as unfair get rejected at real cost to both sides far more often than pure rational-choice models predict.
See Also