Because we assume transferable utilities this marital surplus can be divided

Because we assume transferable utilities this marital

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that specify the total surplus from possible marriages. Because we assume transferable utilities, this marital surplus can be divided between the husband and the wife. Thus, by definition, if i and j from two different families form a match, i.e. if μ ij = 1 , we have u i + u j = π ij . Thus, a matching on individuals with families induces family utilities u f = i f u i + j f u j . For instance, when each family is composed of one child only, we have the classical matching model with individuals. Introducing families shifts decision-making on the marriage market from individuals to parents. Parents consider the utility of the fam- ily, which generates some interdependence in the utilities of its members, who would otherwise act individually. They choose partners for their children in such a way as to maximize the utility of the whole family, which may mean arranging a worse marriage 7
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for one child if it enables the other children to marry better. We show in Section 3 that this setting changes stable matchings. It is also noteworthy that, in our frame- work, a matching generates a network of families. In a network analysis perspective, each node or family can be linked to one or more families through marital connec- tions. Two families could be united through several links, as several of their children could be matched. In fact, when families are taken into account, matching can also be considered a model of strategic network formation. This is in sharp contrast with the classical one-to-one matching models on marriage. We do not specifically study the network structure that emerges from this setting, but we discuss in the Conclusion the broader economic and social implications of family links through marriage, based on this network structure. To solve our matching problem, we introduce a new concept of familial stability . Clas- sical matching models on marriage only considering individuals define a matching as stable if there are no two persons, married or unmarried, who would like to form a new union. In other words, if there are no blocking pairs. As a direct extension of this notion, we consider that a matching is stable if there are no two families who would like to form one or several new unions for some of their children. Thus, we say that a matching is family-stable if there are no blocking pairs of families. This definition is consistent with empirical evidence that families negotiate their children’s mariages bilaterally. In their study on the Luo in Kenya, Luke and Munshi (2006) explain that arranged marriages are organized by a matchmaker, or jagam , who is usually one of the man’s sisters, sisters-in-law or other extended relatives. Molho (1994) provides ev- idence of this practice in detailed descriptions of some arranged marriages in medieval Florence. Literally, we say that a matching is family-stable if there are no two families who would like to sever their existing links for one or several of their children to create new ones with the other family, such that the utilities of both families increase, one of which increasing strictly. To state the definition formally, we introduce the notation
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