Abstract
In the ultimatum game, two people need to agree on the division of a sum of money. People usually divide money equally for the sake of fairness, and prefer to suffer financial losses rather than accept unfair divisions, contradicting the predictions of orthodox game theory. Models aimed at accounting for the evolution of such irrational preferences have put forward a great variety of explanations: biological, cultural, learning-based, human-specific (or not), etc. This diversity reflects the current absence of consensus in the scientific community, and possibly even an absence of debate. Here, we review 36 theoretical models of the evolution of human fairness published in the last 30 years, and identify six families into which they can all be broadly classified. We point out connections between the different families, and instantiate five of the mainstream models in the form of agent-based simulations for purposes of comparison. We identify a variety of theoretical, terminological, and conceptual problems that currently undermine progress in the field. Finally, we suggest directions for future research, and in particular the modeling of the evolution of fairness in a wider and more realistic range of situations.