A generalized cognitive hierarchy model of games

Subjects in simple games often exhibit nonequilibrium behaviors. Cognitive Hierarchy (CH) and Level k (LK) are two prevailing structural models that can predict these behaviors well but they make quite different assumptions on players’ beliefs of their opponents’ actions. This paper develops a generalization of CH and shows that CH and a variant of LK belong to the same family. Under generalized CH (GCH), level k players best respond to level 0 to level k−1 but the perceived proportion of each lower level is obtained by weighting its actual frequency by a parameter α, reflecting stereotype bias well documented in social psychology literature. When α = 1, GCH reduces to CH; and when α =∞, it becomes Level m (LM) in which level k best responds to only the modal level below k (and the modal level may be k−1). GCH also fixes prior ad-hoc assumptions about level 0 by developing a plausible model for it. GCH posits that non-strategic level 0 players are more likely to choose strategies that will never yield the minimum payoff in all possible outcome scenarios. This minimum-aversion tendency captures level 0’s avoidance for dominated strategies and compromise effects welldocumented in the individual choice literature. Using fifty-five 2-player m x n games from four distinct datasets, we show that GCH describes and predicts behaviors better than CH and LK. Structural estimation results show that higher level players exhibit stereotype bias and level 0 players exhibit minimum aversion. Finally, we apply GCH to two new games and find that GCH is able to overcome CH’s inadequacies and predict behavior remarkably well.