A Belief-based Theory for Private Information Games

We propose a belief-based theory for private information games. A Bk player forms correct beliefs up to the kth-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 B1 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.