The nature of parent-child interactions has gained recognition as yet another economic determinant of fertility behavior. For example the family-based conflictual fertility model developed by Bernheim posits that parents supply cash transfers (bequests) to their children who in turn reciprocate with in-kind services (attention). In such a model family size decisions can be viewed as flowing from 3 different assumptions about the nature of the parent-child exchange. The market exchange assumption based on the equilibrium that would result if parents could buy attention and children could sell their caring capacity leads parents to have a greater number of children in order to increase the resources of the family economy. In contrast the strategic bequest game assumes a noncooperative sequence in which parents ensure attention from children by threatening disinheritance. At least 2 children are required to extract the maximum surplus and if the parent cares only about the quantity of total attention it is advantageous to have as many children as possible. A 3rd solution concept that of core for this exchange setting does not provide an unambiguous characterization of the bequest-attention allocation and is based on the set of Pareto-optimal allocations of the 2 goods. In families where parents have a strong preference for attention provided by as few children as possible the core and the strategic bequest models do not coincide. However as family size increases the market equilibrium strategic bequest and core solution concepts do coincide.
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