The Ultimatum Game: Why Evolution Keeps Rediscovering Fairness

A one-shot split, with a veto

The ultimatum game, introduced by Werner Güth, Rolf Schmittberger and Bernd Schwarze in 1982, could not be simpler to state. Two players are offered a fixed sum of money. The proposer suggests how to split it; the responder either accepts, in which case both players get exactly the proposed split, or rejects, in which case both players get nothing. There is no negotiation and no second round — it is a single take-it-or-leave-it offer.

The rational prediction, and why nobody follows it

Solved by backward induction under the standard assumption that both players only care about their own money, the result is stark: a responder who cares only about maximising their payoff should accept any offer above zero, since even one cent is strictly better than nothing, and a proposer who anticipates this should therefore offer the smallest positive amount possible and keep nearly everything. This is the unique subgame-perfect Nash equilibrium. It is also, empirically, almost never what happens: across dozens of experiments run in many different countries and cultures, typical offers cluster around 40 to 50 percent of the total, and offers below roughly 20 percent are rejected surprisingly often, even though rejecting always leaves the responder strictly worse off in that single interaction.

strategy space:
  proposer offers a share p of the pot to the responder
  responder has a minimum acceptable offer q
  if p ≥ q → both keep the split (proposer keeps 1−p, responder gets p)
  if p < q → both get 0

rational (self-interest only) prediction: p → 0, q → 0
observed in humans, and in evolution WITH reputation: p, q → ~0.4-0.5

Evolving strategies: reputation is the missing ingredient

The simulation on this page follows a well-studied evolutionary approach, closely related to the model published by Martin Nowak, Karen Page and Karl Sigmund in 2000, in which a population of agents is characterised by two evolving numbers: the share p they offer as proposer, and the minimum share q they will accept as responder. Agents with higher average payoffs reproduce more, passing their (p, q) pair, with small mutations, into the next generation. Run this in a fully anonymous world — every pairing is a one-off, with no memory of past behaviour — and evolution slides both p and q down toward the rational-but-unfair prediction, exactly as backward induction says it should.

Add just one ingredient — reputation, meaning a responder can see something about how a proposer has treated others before deciding whether to accept — and the outcome flips. Proposers who make low offers get identified and rejected by informed responders, which lowers their payoff, so evolution instead favours proposers who offer close to half and responders who hold out for close to half. Fairness, in this model, is not a moral instinct bolted on from outside; it is what natural selection converges to once the game stops being fully anonymous and starts letting reputation carry information across interactions.

What this tells us about human behaviour

Human societies are essentially never the fully anonymous, one-shot world where the naive rational prediction holds — reputations, repeated interactions, and social observation are the norm rather than the exception, which is one leading explanation for why real ultimatum-game behaviour looks so much like the reputation-driven evolutionary outcome rather than the backward-induction one. Behavioural economists such as Ernst Fehr and Klaus Schmidt have also proposed direct inequity-aversion preferences — people dislike unequal outcomes even when they personally lose from rejecting one — as a psychologically grounded complement to the evolutionary reputation story, and both explanations point the same direction: the "fair" behaviour observed at the poker table, in the lab, and in the simulation on this page is not an anomaly to be explained away, but the expected outcome once the game is embedded in a social context richer than a single anonymous transaction.

Frequently asked questions

Try it live

Everything above runs in your browser — open Ultimatum Game and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.