This work aims at filling a gap in the cognitive representation of institutions, starting from Aoki’s account of institutions as equilibria in a gametheoretical framework. We propose a formal model to explain what happens when different players hold different representations of the game they are playing. In particular, we assume that agents do not know all the feasible strategies they can play, because they have bounded rationality; grounding on the works by Johnson-Laird and his coauthors, we suggest that individuals use parsimonious mental models that make as little as possible explicit to represent the game they are playing, because of their limited capacity of working memory and attention. Second, we rely on Bacharach’s variable frame theory: agents transform the objective game into a framed game, where strategies are “labeled” in some sense. In such a context, we argue that a social contract – given its prescriptive and universalizable meaning – may provide a shared mental model, accepted by all players, that allows agents to select a joint plan of action corresponding to an efficient and fair distributioner.