Pareto-optimal matching allocation mechanisms for boundedly rational agents

Is the Pareto optimality of matching mechanisms robust to the introduction of boundedly rational behavior? To address this question I define a restrictive and a permissive notion of Pareto optimality and consider the large set of hierarchical exchange mechanisms which contains serial dictatorship as well as Gale’s top trading cycles. Fix a housing problem with boundedly rational agents and a hierarchical exchange mechanism. Consider the set of matchings that arise with all possible assignments of agents to initial endowments in the given mechanism. I show that this set is nested between the sets of Pareto optima according to the restrictive and the permissive notion. These containment relations are generally strict, even when deviations from rationality are minimal. In a similar vein, minimal deviations from rationality suffice for the set of outcomes of Gale’s top trading cycles with all possible initial endowments to differ from the set of outcomes of serial dictatorship with all possible orders of agents as dictators.