A short comment on two excellent and widely-read papers by Fehr and his collaborators: “Egalitarianism in young children” and “The development of egalitarianism, altruism, spite and parochialism in childhood and adolescence.”
Putting together these two papers, we can obtain an outline about how children respond to the typical allocation tasks that Fehr has used in his research with several samples of children and adults.
Oversimplifying, such an outline would look as follows:

• Children give generous responses to the tasks between 3 and 6 years of age.
• Starting from an age of six to eight years, children show already a tendency to sacrifice their own resources in order to be fair, increasing the likelihood of egalitarian allocations
• Children give the most egalitarian, or “inequality-adverse” responses between 8 and 11 years of age (“egalitarianism peaks around the age of 8-11 years”).
• Starting at 10 years of age, children start giving more altruistic responses, that are also “efficient” in the sense that they maximize the sum of payoffs (“the biggest possible cake”).
• While previous studies have found that egalitarianism increases sharply in 3- to 8-year-old children, this motive loses its dominance in adolescence when the altruistic type becomes prevalent.
• The proportion of such altruistic responses continues to increase up to 18 years of age. At that point, children’s responses are similar to those of adults.
• Children are more altruistic with the ingroup, and less altruistic (and more spiteful) with the outgroup. This effect is higher in males, and increases with age (starting at around 10 years of age).
• girls are significantly more likely to have egalitarian preferences than boys.
• The ingroup-outgroup effect is bigger in boys than girls.
  I believe this research confirms the prevalence of an associative culture of peer exchange in preschool children versus a culture of economic, “strict” reciprocity between children starting with primary school.

Fehr, E., Bernhard, H., & Rockenbach, B. (2008). Egalitarianism in young children. Nature, 454(7208), 1079–1083. https://doi.org/10.1038/nature07155
Fehr, E., Glätzle-Rützler, D., & Sutter, M. (2013). The development of egalitarianism, altruism, spite and parochialism in childhood and adolescence. European Economic Review, 64. https://doi.org/10.1016/j.euroecorev.2013.09.006