Representing others' preferences in mixed motive games: was Schelling right?

The available experimental evidence suggests that even two-person normal form games with an elementary action space present substantial degrees of cognitive difficulty. We submit that the relational structure of the players' preferences is a source of complexity of a game. We provide a formal classication of order structures in two-person normal form games, based on the two properties of monotonicity and projectivity, and present an experiment on individual ability to construct a representation of bi-ordered sets isomorphic to the preference structure of paradigmatic normal form games. Experimental results support the hypothesis that relational complexity matters. In particular, they support Schelling's intuition that `mixed motive games' are harder to represent than `pure motive' ones. In addition, the experiment shows that most subjects tend to perceive and extract monotonic relations from non-projective ones. We show that individuals' short term memory capacity limitations signicantly affect their ability to correctly represent bi-orders. Some connections with Rubinstein's analysis of binary relations in natural language are also shortly discussed. JEL codes: C70, C72