We find that family stable matchings strongly depend on the structure and

We find that family stable matchings strongly depend

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We find that family-stable matchings strongly depend on the structure and composi- tion of families. In particular, we find that when families are heterogenous in terms of size and when gender is not distributed uniformly across families, inefficient sta- ble matchings may emerge. We also show through examples that the set of shares of surplus that support efficient matchings as stable tends to shrink as competition increases. In particular, for a family partition such that each family is composed of one son and one daughter, the set of shares is minimal. Our analysis builds on the literature of matching theory applied to the marriage mar- ket and the economics of the family, in particular Becker (1973, 1991), and recently reviewed by Browning et al. (2014). The main novelty of our model lies in shifting the decision-making process from individuals to families. To our knowledge, we are the 3
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first to introduce families into the assignment game (Shapley and Shubik 1971) 6 . There is an extensive literature on the economics of marriage examining situations related to arranged marriages under very restrictive assumptions on family structure. Peters and Siow (2002), when they consider parents choosing a premarital transfer to their children and study equilibria in which children use these investments to compete for spouses, use a two-sided market setting, with families composed of one female facing families composed of one male. Actually, a family here can be modeled as an individual making an investment decision prior to the matching decision. Anderson (2003) analyzes the importance of the caste in the evolution of dowry payments with modernization, Anderson and Bidner (2015) formalize the dual role of dowry as both a premortem bequest from parents to daughters and a market clearing price, and Do et al. (2013) analyze the consequences of marital payments on consanguineous marriages when commitments are not credible. In all these papers, however, each family is composed of one child only. By contrast, we model families as arbitrary subsets in a population of males and females. Only a few papers deal with family structure in the matching literature related to marriage. Laitner (1991) explores premarital transfers from parents to their two chil- dren, one son and one daughter, to induce their marriages in a non-transferable utility framework. He restricts attention to symmetric equilibria and focuses on the impact of assortative mating on neutrality results, but he provides a very interesting model of spouse selection by families which would be worth extending 7 . By contrast, we consider a transferable utility framework with arbitrary family structure and study the impact of family decision-making on stable matchings. Our analysis contributes to an expanding literature on the impact of family composi- 6 No theoretical paper in the matching literature explores the matching problem we address. Some papers study many-to-one markets and many-to-many markets (Sotomayor 1999) applied to the marriage market. For instance, Baiou and Balinski (2000) study a matching model in which every
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