A note on sibling rivalry and good-kid, bad-kid equilibria

Abstract

When parents with concave utility reward good behaviour on the part of their children with a share of the marginal utility they derive from good behaviour, a decrease in good behaviour by kid i causes kid j to increase the amount of good behaviour he/she supplies in equilibrium. This may explain why simultaneous good-kid behaviour is rare and also why children try to get their siblings into trouble.

Keywords:

• sibling rivalry
• kid behaviour
• bribery

JEL Classification:

• D1
• H3
• C7

Acknowledgements

The author is grateful to Dale Lehman, Dong Li, Brenda McDaniel and Glen Robinson for helpful discussions and to Canh Le, Burak Onemli and Daigyo Seo for expert research assistance.

Notes

¹Stein (1990) argued that the ‘good child’ and the ‘bad child’ are deeply rooted in our cultural and religious traditions (e.g. Cain and Abel).

²Becker (1974, 1981) pioneered the use of microeconomics to model social behaviour, including family interactions.

³See Chang and Weisman (2005) and the references cited therein for a discussion of sibling rivalry.

⁴Mander (1991, p. 374) discussed the importance that children attach to winning in contests between siblings, ‘but if this was not possible, the goal became not to allow the other to win, if necessary by sabotage.’

⁵Whereas the analysis could be extended to more than two children, the literature indicates that sibling rivalry is more pronounced in smaller families (Leung and Robson, 1991, p. 315). In addition, the assumption regarding the additivity of good behaviour could be relaxed, but this would only increase the mathematical complexity of the analysis without changing the fundamental insights.

⁶See, for example, Bernheim et al. (1985).

⁷Francis Bacon (1999, Chapter IX) observes, ‘For he that cannot possibly mend his own case will do what he can to impair another's’.

⁸This is closely related to the idea of enforcing group discipline by using agents to monitor other agents (Varian, 1990). In similar fashion, the Grameen Bank model of microlending uses group liability to induce loan repayment by individual borrowers. See Levinson (2003) for a comprehensive treatment of group sanctions as a means to discipline the behaviour of individuals in the group.

⁹See Holmstrom (1979) and Rogerson (1985).