Representing Others' Preferences in Mixed Motive Games: Was Schelling Right?

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Abstract
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 classification 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 significantly affect their ability to correctly represent bi-orders.

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