Level-k reasoning
How many rounds of 'they think that I think' a player actually performs, which in practice is one or two.
Often misread asAssuming the clever move is to reason as many levels deep as you can manage, and then losing to people who stopped at level two.
How to see it
How many times round the loop do people actually go?
Level-k describes players by how many steps of 'they think that I think' they take. A level-0 player picks something naive, a level-1 player best responds to that, a level-2 player best responds to level-1, and so on. Most people in most experiments sit at one or two.
The checkThe winning depth is one step above where the population actually is, not as deep as you are able to think.
Try itBefore reading any result, write down your own guess in a pick-two-thirds-of-the-average game played by a room of a hundred strangers. If you wrote zero, you assumed everyone else reasons as far as you do.
Games that show it
- Nested dolls
- The sock
- Beauty contest game
- Traveller's dilemma
Know these first
Easily confused with
Sources
- Nagel, R. (1995). American Economic Review 85(5), 1313-1326.
- Stahl, D. & Wilson, P. (1995). Games and Economic Behavior 10(1), 218-254.