So if you picked "keep" you have a chance at an extra $125,000. But you also look like a selfish bastard on national TV, you'll probably lose a lot of friends, and whatever relationship you had going with your housemate (I assume there was something, I didn't watch the show) is now gone. I think those outweigh the extra hundred-odd grand.
The moral of the story is that ongoing relationships can break the prisoner's dilemma. This could be anything from an emotional relationship to a business contract to mere public scrutiny. The prisoner's dilemma is really only a dilemma if it is a true one-shot game, or if the monetary amounts are enough to overcome these other factors.
It would be interesting to simulate the prisoner's dilemma through AI agents and see if they develop a sense of trust over time. Maybe they would adopt a cooperative strategy eventually.
There is an iterated version of the prisoner's dilemma and you don't need a clever AI to win. The name of the strategy is tit for tat and it basically wins over the long run.
The moral of the story is that ongoing relationships can break the prisoner's dilemma. This could be anything from an emotional relationship to a business contract to mere public scrutiny. The prisoner's dilemma is really only a dilemma if it is a true one-shot game, or if the monetary amounts are enough to overcome these other factors.