An Abundance of Katherines: The Game Theory of Baby Naming

TL;DR

The paper frames baby naming as a tractable game where myopic parents choose names to match target popularities $\mu$ under a population distribution $f_i(a)$ and a meta-distribution $g(\mu)$. It analyzes satisfiability and stability, deriving conditions under which naming outcomes align with or diverge from parental desires, and introduces Extremely Reasonable Assumptions to simplify analysis. Through a power-law illustrative example, the authors show how the product of exponents $t\cdot t'$ shapes the evolution of name-frequency distributions, predicting oscillatory shifts for uncommon-name preferences and potential 'naming event horizons' for common-name biases. Complementary simulations and a Kat-GPT experiment illustrate the dynamics and underscore the paper’s playful yet insightful commentary on the futility and unpredictability of naming strategies, with practical implications for automated naming tools and language-model analyses.

Abstract

In this paper, we study the highly competitive arena of baby naming. Through making several Extremely Reasonable Assumptions (namely, that parents are myopic, perfectly knowledgeable agents who pick a name based solely on its uniqueness), we create a model which is not only tractable and clean, but also perfectly captures the real world. We then extend our investigation with numerical experiments, as well as analysis of large language model tools. We conclude by discussing avenues for future research.

Figures (9)

• Figure 1: Name frequencies from the Social Security Administration, for girls born in 2010ssa. Note the rough power-law shape.
• Figure 2: Examples of different parental preferences: a preference for less common names (blue) and preference for more common names (orange).
• Figure 3: Frequency of name Mabel (image from mabel_image_source).
• Figure 4: Examples of naming frequency at time step $i+1$: the original distribution (blue), the distribution after a preference for less common names (orange), and a preference for more common names (green).
• Figure 5: Parent preference distributions used in experiments. Logarithmic x-axis on the right, showing the log-normal distribution shape. Each histogram represents a sample of 1 million parents from the given distribution.