Level-k Reasoning
A bounded-rationality model where players best-respond to lower-level opponents in a hierarchy of strategic depth.
Definition
Level-0 players choose uniformly or heuristically; level- players best-respond to level- opponents. A level- player best-responds to level- and converges to Nash.
The cognitive hierarchy model (Camerer-Ho-Chong) generalizes this with a Poisson distribution of levels.
Intuition
Real people do not do infinite strategic reasoning — they guess, then guess what others guess, stopping at 1-3 steps.
Level-1: "I want the best outcome given that everyone else plays randomly." Level-2: "They think level-1, so I should anticipate that."
Worked example
In the "p-beauty contest" game (Nagel 1995), subjects' choices cluster around level-1 and level-2 reasoning, with very few reaching the Nash equilibrium of .
In the centipede game, level-1 explains early defection; higher levels explain deeper cooperation.
The math
The distribution of levels is often fitted as Poisson with mean in lab experiments.
Level- differs from iterated dominance in that it is a behavioral model, not a normative refinement.
Where it is used
Experimental economics, auction bidding behavior, and financial market speculation.
Foundation for behavioral game theory alongside QRE.
More in Game theory
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