A little bit of game theory goes a long way. But something like that wouldn't work for very long before someone came along who was only faking it.

There are a bunch of related videos of this show as well. It can be interesting to try to predict the outcomes to see just how good your internal lie detector really is.

EDIT: Also, don't miss one of the comments. BCR came up with the clever solution of passing one of their balls to the other player. That's quite the game breaker, though, so it probably wouldn't be allowed. I guess I should also mention that this is technically a variant of the PD, and that I change the title because almost nobody would know what the story was about otherwise.