The authors note, "People who spend time with young children will know that they often favor themselves when sharing, but surprisingly they endorse equal sharing not just by other people but also in their own case. In our research, we were able to rule out a number of explanations for this early gap between word and deed."
When the researchers gave 3-8-year-olds stickers they valued and asked them about sharing, children of all ages readily asserted that they themselves should share equally, and others should as well. However, when given the chance to actually share, children failed to follow the norms they endorsed until the ages of 7-8. In a second test, older children aged 7-8 correctly predicted that they would share equally, while 3-6-year-olds clearly stated that they would favor themselves while sharing; thus, children of all ages were accurate in predicting what they would do. The study concludes that though younger children know the norm of equal sharing, the importance they attach to it increases with age.
Source: Public Library of Science