A cognitive hierarchy model of games

Players in a game are "in equilibrium" if they are rational, and accurately predict other players' strategies. In many experiments, however, players are not in equilibrium. An alternative is "cognitive hierarchy" ( CH) theory, where each player assumes that his strategy is the most sophisticated. The CH model has inductively defined strategic categories: step 0 players randomize; and step k thinkers best-respond, assuming that other players are distributed over step 0 through step k-1. This model fits empirical data, and explains why equilibrium theory predicts behavior well in some games and poorly in others. An average of 1.5 steps fits data from many games.