[ultramancool]

> As experiment shows, this is not the optimal strategy, so I don't see why you would call it the "rational" one.

It's rational because if Bob accepts an offer for a positive value of money, even if it's a cent, he gains value from it. Rejecting it just throws that cent away, which he could have had in his pocket, it's irrational to throw away this value.

There's a difference between rational and optimal for a reason though, but you need to feel like you're getting ripped off for that to come into play, you need to feel like you'd rather someone else lose $0.99 than you gain $0.01.

[Kapow]

That only makes sense if you restrict Bob's decision making to consider each game in isolation, without regard to how how rejecting an offer in one game might lead to a higher offer in a future game. At that point, I would call it a different problem entirely, so there isn't much point in comparing the results. I certainly wouldn't label that version of the problem "rational" and the version where Bob considers future games "irrational".

[Tyr42]

But pre-commiting to a strategy of say: "accept if 40 cents or more" could net more coins overall, right?

I agree that if it was a one off game, then that would make sense, but it's an iterated game.