Backward induction
Work out the last move first, then the move before it, and keep stepping back until you reach the start.
Often misread asRejecting the conclusion because it feels wrong, as in the centipede game, where the unravelling says stop at once and real players carry on happily for several rounds.
How to see it
Start at the end, because that is the only place the choice is simple
At the last decision there is no future left to think about, so the right move is obvious. Fix it. The decision before it now has a known consequence, so that becomes obvious too. Work backwards to the start and the whole path falls out.
The checkThe procedure is sound given its assumption, which is that everyone is certain everyone else will follow it; the doubt belongs to that assumption, not to the arithmetic.
Try itSolve the centipede game from the end, then ask honestly what you would do at the first node against a stranger. Now identify which assumption you quietly dropped: that they are rational, or that they are certain you are.
Games that show it
Know these first
Leads on to
Easily confused with
Sources
- Zermelo, E. (1913). Proceedings of the Fifth International Congress of Mathematicians, Volume 2, Cambridge University Press, 501-504.
- Osborne, M. & Rubinstein, A. (1994). MIT Press.