In marriage, men obtain and women surrender parental rights because: (i) by default, an unmarried woman giving birth is the child's only known parent and sole custodian; (ii) a married mother shares custody with her husband and the presumed father; (iii) custody allocation in marriage is fixed; (iv) private contracts on rights over children amount to trade in children and have limited legal validity. As a result: (i) women, not men, marry up; (ii) higher income has opposite effects on men's and women's willingness to marry; (iii) out‐of‐wedlock fertility results when trade is not feasible.