We consider two-sided matching markets with couples. First, we extend a result by Klaus and Klijn (J Econ Theory 21: 75–106, 2005, Theorem 3.3) and show that for any weakly responsive couples market, there always exists a “double stable” matching, i.e., a matching that is stable for the couples market and for any associated singles market. Second, we show that for weakly responsive couples markets, the associated stable correspondence is (Maskin) monotonic and Nash implementable. In contrast, the correspondence that assigns (...) all double stable matchings is neither monotonic nor Nash implementable. (shrink)

We consider the problem of choosing the location of a public facility either (a) on a tree network or (b) in a Euclidean space. (a) (1996) characterize the class of target rules on a tree network by Pareto efficiency and population-monotonicity. Using Vohra's (1999) characterization of rules that satisfy Pareto efficiency and replacement-domination, we give a short proof of the previous characterization and show that it also holds on the domain of symmetric preferences. (b) The result obtained for model (a) (...) proves to be crucial for the analysis of the problem of choosing the location of a public facility in a Euclidean space. Our main result is the characterization of the class of coordinatewise target rules by unanimity, strategy-proofness, and either replacement-domination or population-monotonicity. (shrink)