Pareto-optimal matching allocation mechanisms for boundedly rational agents

Abstract

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. Mathematics Subject Classification C78 · D03 · D60I would like to thank Christoph Engel, Olga Gorelkina, Martin Hellwig, Aniol Llorente-Saguer, Michael Mandler, Paola Manzini, and two anonymous referees. I would like to thank David Bielen for thorough research assistance.

Non-Standard Choice in Matching Markets

“…In matching theory, departures from standard preferences have been motivated by bounded rationality, mistakes, indifferences, complementarities, externalities, and peer preferences. 15 Zhang (2021) and Bade (2016) are studies motivated by bounded rationality and therefore are most relevant to our study. Zhang (2021) studies implications of heterogeneous strategic sophistication of individuals under the Boston mechanism and the deferred acceptance mechanism.…”

“…These take the form of shortlisting and ranking schools in school choice, 17 or choosing an assignment after higher priority individuals have made their pick in a serial dictatorship procedure. There is growing evidence on preference-reporting errors and their detrimental effects on mechanism's performance (see, e.g., Rees-Jones (2018), Rees-Jones and Skowronek 15 See, e.g., Bade (2016) and Zhang (2021) for bounded rationality, see Echenique et al (2016) for mistakes incorporated in individuals' behavior, see Erdil and Ergin (2008) and Erdil and Ergin (2017) for indifferences, see Hatfield and Kojima (2010), Pycia (2012) and Hatfield and Kominers (2015) for preferences exhibiting complementarity, see Sasaki and Toda (1996) and Pycia and Yenmez (2021) for analysis of matching problems with externalities, see Leshno (2021) and Cox et al (2021) for peer-dependent preferences.…”

“…As seen in social choice theory, such decisions need not be consistent with maximization of a single preference. 4 See Bade (2016) for a conversation between Sophie Bade and Utku Ünver regarding this hesitancy.…”