Cognitive Hierarchy Model
See (Camerer et al., 2004) for a nice introduction using Keynes’ “beauty contest” game.
In the cognitive hierarchy model, each player believes that they understand the game better than other players. Decision rules reflect an iterative process of strategic thinking.
The CH model consists of iterative decision rules for players doing \(k\) steps of thinking, and the frequency distribution \(f(k)\) (assumed to be Poisson) of step \(k\) players.
Step 0 thinkers assume that the other players behave randomly according to some probability distribution. Step \(k\) thinkers assume that their opponents are distributed according to a normalized Poisson distribution, from step \(0\) to step \(k-1\), but ignore the possibility that some players may be doing as much or more.