> The game is turned on its head
Is that really true? What has changed? Player B still can't trust that player A will give him 50% of the money outside of the game. Player could turn the tables by claiming he too will steal. Wouldn't that put them back to the original situation?
Consider how your family would treat you if you reneged on a verbal commitment you made on TV. For the vast majority of people, this is a major negative factor. Now add in your coworkers, employers, friends...
Most people are honest most of the time, and especially so when there is a high likelihood of being caught cheating.
https://www.youtube.com/watch?v=y6GhbT-zEfc&feature=relm...
That said, you're right about the fact that reputations matter. They just don't matter to everyone.
It's funny that the one-shot prisoner's dilemma is used so often as an example of rational self-interest leading to suboptimal outcomes or formal modeling failing to capture real behavior. This is true only for the most stylized models and simplest games. Really rational players will choose to restructure the rules and play a better game! Since prisoner's dilemmas were bad games, we figured out how to make credible commitments and overcome them. Since talk is cheap, we developed things like punishment and social norms to enforce commitments.
Adding things like iteration, reputation, and punishment to simple games leads to complex cooperative outcomes that reflect real behavior—and we can model them by adding a few simple rules. I think it's a fascinating and optimistic view of human history: modern market-exchange societies are the outcome of a long process of figuring out how to turn bad-outcome games that encourage defection into positive-sum cooperative ones that benefit everyone. Yet we are still biased to ignore all the cooperation around us and see selfishness (here's one of my favorite papers on this subject: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=929048).
I've also found it a very valuable personal insight. When you find yourself playing a bad game, don't settle for choosing the least harmful payoff. Figure out how to change the rules.
This is why contracts matter. It's clear that both parties would love to sign a contract saying "I'll scratch your back and you scratch my back," if the consequences of not obeying that contract were sufficiently severe, because they see that they can get a mutually better reward. The reason why criminals do better than game theory professors on the prisoner's dilemma game is not necessarily because they act irrationally, but because they're part of a social order which creates and enforces those sorts of cooperative systems, and which doesn't do business with folks who break them.
Note also that he was going to steal at first, but changed his ball at the last second to cooperate. And the other guy lied about stealing, having chosen to split the whole time, never changing his ball.