Rotten kid theorem

Gary Becker's rotten kid theorem is a thought experiment in economics. It posits that family members, even if they are selfish, will act to help one another if their personal incentives are properly aligned. The theorem is one of the most famous theorems within family economics, and applied mechanism design.

In his original work, Becker paints a hypothetical situation in which children will receive gifts of money income from a wealthy, altruistic parent to make them happy. One of the children is a selfish, "rotten", child who would take pleasure in harming his sibling. However, if he chose to actually hurt his sibling, the altruistic parent would help the victim, and curtail help to the wrongdoer. That way, the altruist would function as a means of transferring utility between the rotten kid and his sibling. In the process the parent would also bring about an incentive not to wrong the sibling in the first place, because any utility robbed of the sibling would be automatically taken away from the rotten kid.

The theorem relies on multiple assumptions. First, the altruistic parent has to be wealthy enough to compensate for any wrongdoing by the rotten kid. Secondly, he has to be a pure, rational altruist, with full knowledge of the personal utility of both the rotten kid and his sibling. Thirdly, the altruist would have to be fixed in his own income. And so on.

The theorem has proven widely influential in the economic analysis of family life, and beyond that, other regarding economic institutions in general. It has done so especially in the economical analysis of unconventional and nonmonetary economic institutions, traditionally and especially in the popular sphere regarded as being outside the ambit of the economic science. Thus today it is a standard example of the novel contribution to economic literature that the so-called nonstandard economics has brought about.

Further applications

The theorem can be applied to inheritance as well, in expectation. There it suggests that a parent who plans to bequeath his estate in accordance to his children's needs and equity, might want to delay until the children are older, or possibly until after his demise. This is because if parents plan to will their children money in accordance with their needs, the real outcome of their behavior over their lifetime cannot be measured beforehand. Thus, the perfect incentive for the child to behave well towards his siblings can only be realized at the very end of the altruistic parent's life. In this application, the independent earnings of the various siblings can also be taken into account, without breaking the grounding logic of the theorem.

See also

• Game theory
• Marginal utility
• Family:
  • Identified patient
  • Cinderella effect
  • Dysfunctional family

References

• Becker, Gary S. (1974). "A Theory of Social Interactions". Journal of Political Economy. 82 (6): 1063–1093. doi:10.1086/260265. JSTOR 1830662.
• _____ (1991) [1981]. A Treatise on the Family (Enlarged ed.). pp. 9–11, 13, ch. 8, 11.
• Bergstrom, Theodore C. (2008). "Rotten Kid Theorem". The New Palgrave Dictionary of Economics (2nd ed.).