Abstract
We introduce the new notion of the pairwise myopic-farsighted stable set to study stable matchings under the assumption that players can be both myopic and farsighted. For the special case where all players are myopic, our concept predicts the set of matchings in the core. When all players are farsighted, we provide the characterization of pairwise myopic-farsighted stable sets: a set of matchings is a pairwise myopic-farsighted stable set if and only if it is a singleton consisting of a core element. This result confirms the result obtained by Mauleon et al. (2011) with a completely different effectivity function and provides a new special case where the farsighted stable set is absolutely maximal (Ray and Vohra, 2019) and coincides with the Strong Rational Expectations Farsighted Stable Set (Dutta and Vohra, 2017). When myopic and farsighted players interact, matchings outside the core can be stable and the most farsighted side can achieve its optimal stable matching.
Highlights
Experimental and empirical studies in matching markets suggest that agents are heterogeneous with respect to their degree of farsightedness and con...rm the underlying hypothesis that being unsophisticated is correlated with belonging to a disadvantaged group.1 Despite this evidence, the extant theoretical literature on matching markets has only proposed stability concepts assuming that players are homogeneous regarding their level of myopia or farsightedness
A myopic-farsighted improving path is a sequence of matchings that can emerge when farsighted players form or destroy links based on the improvement the end matching o¤ers relative to the current matching while myopic players form or destroy links based on the improvement the matching o¤ers relative to the current matching
A myopic-farsighted improving path is a sequence of matchings that can emerge when farsighted players form or destroy links based on the improvement the end matching o¤ers them relative to the current matching while myopic players form or destroy links based on the improvement the matching in the sequence o¤ers them relative to the current one
Summary
Experimental and empirical studies in matching markets suggest that agents are heterogeneous with respect to their degree of farsightedness and con...rm the underlying hypothesis that being unsophisticated is correlated with belonging to a disadvantaged group. Despite this evidence, the extant theoretical literature on matching markets has only proposed stability concepts assuming that players are homogeneous regarding their level of myopia or farsightedness. Experimental and empirical studies in matching markets suggest that agents are heterogeneous with respect to their degree of farsightedness and con...rm the underlying hypothesis that being unsophisticated is correlated with belonging to a disadvantaged group.. Experimental and empirical studies in matching markets suggest that agents are heterogeneous with respect to their degree of farsightedness and con...rm the underlying hypothesis that being unsophisticated is correlated with belonging to a disadvantaged group.1 Despite this evidence, the extant theoretical literature on matching markets has only proposed stability concepts assuming that players are homogeneous regarding their level of myopia or farsightedness. They show subjects of lower cognitive ability are systematically harmed under Boston and that substantial ability segregation may result, with the top school enrolling up to 45 percent more high ability students than the worst school These results con...rm the underlying hypothesis that being unsophisticated is correlated with belonging to an already disadvantaged group, so that the Boston mechanism would selectively discriminate the weakest students
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