[Kapow]

>In ROUND100, Alice knows Bob will take whatever non-zero offer she makes.

Wait, how does she know that? Can you explain why you consider that the most rational choice for Bob to make? As experiment shows, this is not the optimal strategy, so I don't see why you would call it the "rational" one.

Also, keep in mind that you're describing an iterative game (where the same people play the same game with the same circumstances repeatedly) and the pirate game is non-iterative, since the players and circumstances change between rounds. As you note, iterative games are much more complicated and the sort of induction used in the pirate game doesn't really work.

[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.