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Bob is given a bar of chocolate by the experimenter. Then he is to propose how he will share the chocolate with Emilly. If Emilly agrees with Bob's proposal, the kids will each get their share. If Emilly disagrees, nobody gets anything.

The experiment demonstrates that Emilly will refuse a profitable share (anything more than no chocolate is profitable for her), if the split Bob proposed would be "unfair".

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up vote 5 down vote accepted

The experiment you are referring to is usually called the ultimatum game, and was first experimentally tested by Güth, Schmittberger, and Schwarze in 1982 [1].

[1] Güth, Werner, Rolf Schmittberger, and Bernd Schwarze. "An experimental analysis of ultimatum bargaining." Journal of Economic Behavior & Organization 3.4 (1982): 367-388. PDF

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