A population of agents repeatedly plays the ultimatum game, each holding an evolving "offer" strategy (as proposer) and a "minimum acceptable offer" threshold (as responder). Watch strategies evolve generation after generation as the offer distribution drifts toward a fair 40-50% split.
Classical game theory predicts a rational proposer should offer close to nothing and a rational responder should accept any positive amount. Real humans — and, as shown here, evolving agent populations — instead converge toward offers near 40-50%, because overly stingy offers get rejected and lose payoff for both players.
Watch the left grid of agents change color as their offer strategies evolve, and the right-hand histogram of offers reshape itself generation by generation. Adjust population size and mutation rate to see how quickly and how stably the population converges. Toggle the rational baseline marker to compare against the game-theoretic prediction of near-zero offers.
The ultimatum game was introduced by economists Werner Güth, Rolf Schmittberger, and Bernd Schwarze in 1982. Since then it has been run in dozens of countries and cultures — modal human offers cluster around 40-50%, and offers below about 20% are rejected roughly half the time, even though rejecting is costly to the responder too.
This simulation models a repeated, evolutionary version of the ultimatum game, one of the most studied experiments in behavioral economics. In each round two agents are paired; one proposes a split of a fixed pie and the other decides whether to accept it. If accepted, both players receive their share; if rejected, both receive nothing. Every agent in the population carries two evolving numbers — the offer it makes as proposer, and the minimum offer it will accept as responder. After each generation of pairings, poorly-performing agents tend to copy the strategies of better-performing ones, with a small amount of random mutation, mimicking cultural or reproductive selection pressure.
Classical game-theoretic analysis, using backward induction, predicts that a purely rational proposer should offer the smallest possible positive amount and a purely rational responder should accept it, since something is better than nothing. Yet this simulation — like real experiments run since Güth, Schmittberger, and Schwarze's original 1982 study — instead shows the population converging toward offers around 40-50%. Overly stingy proposers get rejected often enough that generosity becomes the more successful, and therefore more heavily copied, strategy, illustrating how norms of fairness can emerge from self-interested evolutionary dynamics rather than requiring pure altruism.
The ultimatum game is a two-player economic experiment in which one player (the proposer) suggests how to split a fixed sum of money, and the other player (the responder) either accepts the split, in which case both players receive their agreed shares, or rejects it, in which case both players receive nothing. It is a one-shot test of fairness versus pure self-interest, and it remains one of the most replicated experiments in behavioral economics.
A population of agents appears as a colored grid on the left, where color reflects each agent's current offer strategy, and a histogram on the right shows the full distribution of offers across the population. Every fraction of a second the population plays one generation of pairings and then evolves; watch the histogram gradually shift and cluster near 40-50%. Use the population and mutation-rate sliders to change how many agents interact and how quickly strategies drift, and toggle the rational baseline marker to compare against the game-theoretic 0% prediction.
Pure backward-induction logic assumes responders will accept any positive offer, since something beats nothing. But real responders — and the evolving population in this simulation — often reject offers perceived as unfair, sacrificing their own payoff to punish stinginess. Because rejected offers cost the proposer their share too, strategies that offer too little get outcompeted over many generations by strategies offering a more generous, less rejection-prone amount, pulling the population average up toward roughly 40-50%.
The ultimatum game was introduced in 1982 by German economists Werner Güth, Rolf Schmittberger, and Bernd Schwarze in their paper "An Experimental Analysis of Ultimatum Bargaining," published in the Journal of Economic Behavior & Organization. Their original experiments already showed that human proposers offered far more than the game-theoretic minimum and that responders frequently rejected low offers, launching decades of follow-up research into fairness, reciprocity, and bounded rationality in economic decision-making.
Yes, somewhat. Large cross-cultural studies, most notably by Joseph Henrich and colleagues surveying societies from industrialized nations to small-scale hunter-gatherer and horticultural groups, found that modal offers and rejection thresholds vary by culture, ranging from roughly 25% to over 50%, correlated with factors like market integration and the payoffs to cooperation in daily life. However, an offer of exactly 0% is essentially never observed anywhere, and fairness-influenced behavior appears to be a broad human universal even as its exact calibration varies.
In the dictator game, a simplified relative of the ultimatum game, the proposer simply decides how to split the pie and the responder has no power to reject it — they must accept whatever is offered. Comparing the two reveals how much of generous behavior in the ultimatum game is driven by strategic fear of rejection versus genuine other-regarding preferences: dictator-game offers are typically lower than ultimatum-game offers, though still usually above zero, suggesting both strategic and genuinely altruistic motives are at play.
Each generation, agents are randomly paired and play the game (with roles swapped so both act as proposer once), accumulating payoffs. Then every agent compares its payoff to that of one randomly chosen other agent; if the other agent scored higher, the focal agent copies its offer and minimum-acceptable-offer values, subject to small Gaussian mutation controlled by the mutation-rate slider. This is a simplified imitation-based evolutionary dynamic, related to the replicator dynamics studied formally in evolutionary game theory, where strategies that yield higher payoffs spread through the population over successive generations.
Active research uses variants of the ultimatum game to study the neuroscience of fairness perception via brain imaging, the role of emotions such as anger and disgust in rejection decisions, multiplayer and network-structured versions where reputation and repeated interaction change outcomes, and evolutionary agent-based models — similar to this one — that explore which population structures (spatial grids, social networks, varying group sizes) most reliably produce fairness norms rather than purely selfish equilibria.