A mechanism design approach to child custody allocation in divorce

The paper considers a household family comprising of husband, wife and their child. Each parent consumes a private good and contributes voluntarily for a household public good which is child’s welfare. When divorce occurs, the court has an ex ante transfer mechanism for the parents such that truthful revelation of valuation of child’s welfare by each parent becomes strategyproof. Based on this, the sole custody of child is assigned to the parent having the highest value. We find that the transfer mechanism of the court fails to satisfy ex post individual rationality of some types of the parents. We also show that the court’s mechanism bundled with an appropriate child support order achieves higher child’s welfare and satisfies individual rationality only if the non-custodial parent is extremely altruistic in nature. Thus the paper successfully explains widespread prevalence of non-payment of child support from a perspective which was not discussed previously. More significantly, the paper ends with a policy prescription of replacing the conventional child support system by an equivalent amount of transfer from the government to the custodial parent, and shows that it has the potential to correct the intrinsic loopholes of child support.