The rotten kid with hyperbolic discounting

Abstract The rotten kid theorem implies that appropriately designed family transfers can align self-interested behavior with household welfare. However, this logic relies on future-oriented decision-making that may be weakened by hyperbolic discounting, a behavioral tendency to give disproportionate weight to immediate rewards. This study extends the rotten kid theorem by incorporating present-biased preferences, intra-household externalities, costly enforcement, and strategic inheritance allocation into a unified framework. The model considers a family head, a present-biased child, and a sibling whose welfare may be reduced by the rotten kid’s opportunistic behavior. The family head chooses current transfers, future transfers, sibling allocation, and the strength of an enforcement mechanism, such as a trust, legal restriction, trustee oversight, or conditional disbursement. Enforcement is not treated as mechanically beneficial; it is costly and is chosen only when its marginal welfare gain exceeds its marginal administrative and behavioral cost. The analysis shows that hyperbolic discounting can weaken the alignment between individual self-interest and family welfare by encouraging excessive current consumption and opportunistic behavior. Incremental and conditional inheritance schemes can mitigate these effects by limiting immediate access to resources, preserving future consumption, and reducing the external harm imposed on the sibling. Under strictly concave utility, such arrangements also support consumption smoothing and a more balanced allocation of resources across household members and time. These findings show how behavioral economics and inheritance design can be combined to address family welfare problems in settings where present-biased preferences may undermine long-term outcomes.