A Belief-based Theory for Private Information Games

Abstract

We propose a belief-based theory for private information games. A Bk player forms correct beliefs up to the k^th-order, and heuristic beliefs from the (k +1)^th-order onwards. Correct beliefs follow the prior distribution of types, as in standard game theory. Heuristic beliefs ignore the distribution of types and are rather heuristic projections of one own's type onto the rival, of the form "my rival is of my type". A Bk best responds to those partially correct and partially heuristic beliefs. As a result, a B∞ plays the standard game theoretic Bayesian-Nash equilibrium, where the player's entire hierarchy of beliefs is correct, and a B0 plays the Nash equilibrium of the symmetric-type complete information version of the game, where the entire hierarchy of beliefs is heuristic. We ground the belief-based theory on the psychological literature, we illustrate it through a simple yet novel game, we apply it to standard games and we compare its predictions with those of cursed equilibrium (Eyster and Rabin, 2005), which is another single-parameter generalization of the standard game theoretic Bayesian-Nash equilibrium. Despite the two theories are conceptually different, predictions often overlap.

Keywords: common-knowledge, hierarchy of beliefs, private information games

JEL Classification: C72, D83