Failed to understand "leave both players with nothing"

Here are two players (two chimps). One finds a valuable windfall and gives half of it to the other, who accepts it or not, at least one of the player has something valuable. How can you say "leave both players with nothing?"

Context:
Chimpanzees often share and share alike when cooperating in pairs, suggesting that these apes come close to a human sense of fairness, a controversial new study finds.
Like people, chimps tend to fork over half of a valuable windfall to a comrade in situations where the recipient can choose to accept the deal or turn it down and leave both players with nothing, say psychologist Darby Proctor of Yerkes National Primate Research Center in Lawrenceville, Ga., and her colleagues. And just as people do, chimps turn stingy when supplied with goodies that they can share however they like, the researchers report online January 14 in the Proceedings of the National Academy of Sciences.

More:
http://www.sciencenews.org/view/generic/id/347602/description/Claims_of_fairness_in_apes_have_critics_crying_foul