It has been suggested that players often produce simplified and/or misspecified mental models of strategic decisions [Kreps, D., 1990. Game Theory and Economic Modeling. Oxford Univ. Press, Oxford]. We submit that the relational structure of players' preferences in a game is a source of cognitive complexity, and may be an important driver of such simplifications. We provide a classification of order structures in two-person games based on the properties of monotonicity and projectivity, and present experiments in which subjects construct representations of games of different relational complexity and subsequently play the games according to these representations. Experimental results suggest that relational complexity matters. More complex games are harder to represent, and this difficulty seems correlated with short term memory capacity. In addition, most erroneous representations are simpler than the correct ones. Finally, subjects who misrepresent the games behave consistently with such representations, suggesting that in many strategic settings individuals may act optimally on the ground of simplified and mistaken premises.
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