Except, nobody really thinks this is the way players would behave in reality. The optimal strategy seems sociopathic; isn’t it worth playing cooperatively in the hope that the other player will do the same thing? (Unlike much real human interaction, standard game theory does not accomodate the “hope” that someone else will play suboptimally: optimal play is to be expected at all times. )
But Ignacio Palacios-Huerta…and Oscar Volij gave the centipede game to skilled chess players. They found that the chess players were far more likely to play optimally; grandmasters always played optimally and took the $4. Hyper-rationality can be a disadvantage. (Or did the experiment discover something else: that chess grandmasters are sociopaths?) Palacios-Huerta and Volij don’t speculate. My guess is that they have discovered something about the rationality rather than morality or empathy of chess players, but I may be wrong. [emphasis mine; parenthetic link about real football omitted]
They should run the same experiment with Tour de France riders.