What was the experiment where a person is given something and then has to share it with another person
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 &amp; Organization 3.4 (1982): 367-388. PDF