An airline loses two identical bags. It asks each traveller separately what the contents were worth, any number between a floor and a ceiling, and will pay both of them the lower figure. Whoever claimed lower gets a bonus; the other pays the same as a penalty. A short, airtight argument says claim the minimum.
If you were going to claim the ceiling, claiming one less is better: you lose one from the payment and gain the bonus. So nobody claims the ceiling. Given that, the same reasoning removes the next figure down, and the next, all the way to the floor.
Every step is valid, and the conclusion is that two rational travellers each claim the smallest number available and walk away with almost nothing, when both could have had nearly the maximum.
Basu (1994) noted what makes this sharper than the centipede. There, the reasoning depends on assumptions about the other player's rationality that their behaviour can undermine. Here it is iterated dominance on a single move, with no beliefs about anyone required, and it still gives an answer nobody accepts.
Iterated dominance is about as safe as game theory gets. This is the case that makes it look absurd.
The centipede's unravelling depends on beliefs: I reason about what you would do, which depends on what you think I would do. Binmore's objection is that once you deviate, my premise about you is refuted and the reasoning no longer applies.
Nothing like that is available here. Both players move once, simultaneously. The elimination is pure dominance: at each stage a claim is removed because it does worse than another whatever the opponent does. No assumption about the opponent's rationality is being used until the very last steps, and by then almost everything has already gone.
The equilibrium does not depend on the bonus. Whether it is one or fifty, the argument runs identically and the answer is the floor. Yet the bonus is what decides both what people do and what these populations do, and the two agree.
A parameter that makes no difference to the answer makes all the difference to the behaviour.
That is the finding, and it is a problem for the equilibrium rather than for the players. A prediction insensitive to the one thing that visibly governs behaviour is not describing what is happening, whatever its logical credentials.
Nothing here reasons, so this is not a population failing to follow an argument. It is a population responding to gradients: when the bonus is small, undercutting gains little and costs the difference, so high claims survive. When it is large, undercutting pays enough at every step to drag the whole population down. The dominance argument is indifferent to that gradient. Evolution is not, and neither, apparently, are people.
Basu's own view was that this shows rationality as economists define it is not what people are doing, and that the gap is not a defect in the people. Others read it as evidence for bounded reasoning, or for limited depth of iteration. What nobody has is an account on which the standard prediction is both correct and useful here.
Everyone plays everyone at random with no memory and no communication. Real subjects reason about opponents to a limited depth, which is a specific cognitive story this model does not contain and which produces similar numbers by a different route.