Level-k thinking
Also known as: Level-k reasoning
People reason only a few steps deep about what others will do.
What it means
A model of strategic thinking in which players are characterized by how many rounds of iterated best response they perform: a level-0 player acts naively or randomly, a level-1 player best-responds to level-0, a level-2 player best-responds to level-1, and so on. It captures the empirical fact that human strategic reasoning is shallow, typically stopping at one to three levels rather than reaching full equilibrium. The framework explains systematic deviations from Nash play in beauty-contest and other games and predicts behavior better than assuming common knowledge of rationality. It matters because it replaces the unrealistic infinite-regress of classical theory with a bounded, measurable account of how people actually anticipate others.
Examples
In the guessing game, a level-1 player assumes others pick 50 at random and best-responds with about 33, never iterating further.
A rival cuts prices before Christmas, so you cut yours to undercut them — and stop there, never asking what they will do once they see your new price.
In poker, a beginner plays her own cards, a better player plays what the beginner holds, and a good player plays what that second player thinks. Few go further.
First described in Nagel (1995); Stahl & Wilson (1995).