One of the most famous experiments of recent decades, the Ultimatum game, was recently extended to chimpanzees:

This modified game, in which two chimps decided how to divide a portion of banana slices, seems to have revealed the primates’ generous side.

The study, published in Proceedings of the National Academy of Sciences, was part of an effort to uncover the evolutionary routes of why we share, even when it does not make economic sense.

Scientists say this innate fairness is an important foundation of co-operative societies like ours…

She added though that is was not clear that the chimps completely understood the design of the game and that, with just six chimps involved in the study, further evidence would be needed to show clearly that chimps had a natural tendency towards fairness.

It sounds like there is more work to be done to demonstrate consistent effects among chimpanzees. The way to do this is to replicate the game with a variety of chimpanzees in a variety of contexts. There may be two obstacles to this. First, it sounds like it took some time to train the chimps to understand the game, especially since the chimps were not directly offered food as a reward as this had skewed a similar 2007 study. Second, replicating the study elsewhere might lead to different results – kind of like what happens when an experiment changes from involving American undergraduates to other populations in the world.