Symmetries in the lab

Here is slight modification of the example Christoph presented in the last MEDS lunch (I don’t remember the attribution). I am going to describe three games, and, because for my main point I need to think of the game as taking place in the laboratory, I will call the game `an experiment’ and the players `subjects’, denoted S1 and S2. Below are full descriptions of three experiments. These descriptions are also given to the subjects.

Experiment 1: S2 leaves the room. S1 faces a disk divided into two sides and has to chose one side. His choice is recorded (say, marked on the back of the disk). Then the disk is randomly rotated. Then S2 returns and has to chose a side. If both subjects chose the same side, they get one dollar each. Otherwise, they are cast into the lake of fire.

Experiment 2: Same as Experiment 1, except that the disk is not rotated.

Experiment 3: The Experiment is called `Driving in Illinois’. The rest of the game is as in Experiment 2.