An Abundance of Katherines: The Game Theory of Baby Naming

Theoretical and Experimental Analysis of Naming Strategies through the Lens of Game Theory

Introduction

The paper posits a game theory-based approach to analyze the complexities involved in the process of baby naming. Under the assumption that parents prioritize the uniqueness of their child's name, the authors develop a mathematical model to simulate and predict the outcomes of different naming strategies. Despite its humorous undertones, the research draws attention to the understudied area of name selection, integrating theoretical modeling with numerical simulations to shed light on the dynamic and competitive nature of naming practices.

Model Description

Framework and Assumptions

The core of the analysis is built around a model that represents the distribution of names at a given time as a function of their popularity, operationalized through the concept of "uniqueness." The model utilizes a set of parameters and functions to capture parental preferences regarding the desired uniqueness of names. To simplify the analysis, it includes a series of Extremely Reasonable Assumptions (ERAs), such as the disregard for gender-specific names and the notion of myopic parents who possess perfect information about name popularity but lack foresight regarding the impact of their naming decisions.

Name Frequency and Choice Model

At the heart of the model are two critical functions: one representing the frequency distribution of names ($f_i(a)$) and another depicting parental preferences for name uniqueness ($g(\mu)$). The paper meticulously formalizes how parents choose names based on these parameters, emphasizing the satisfaction and stability of name choices as the outcomes of interest.

Satisfiability and Stability

The concept of satisfiability explores whether parents' expectations align with the actual popularity outcomes of their chosen names. Stability, on the other hand, investigates whether the popularity distribution of names remains constant over time, adhering to what is termed the "Dweezil Principle"—the theoretical inheritance of name uniqueness. These components are crucial for understanding the dynamic interplay between parental expectations and real-world naming conventions.

Empirical Simulations

Simulation Overview

The authors conducted simulations using log-normal distributions of parental preferences, diverging from the theoretical power law distributions initially posited. These simulations sought to explore the effects of varying degrees of preference for uniqueness on the resulting name distribution. Findings indicated a marked influence of parental preferences on name popularity distributions, underlining the competitiveness and complexity inherent in naming strategies.

Results and Interpretations

The simulations revealed interesting dynamics; for instance, a collective preference for unique names led to a more evenly distributed but paradoxically unpredictable naming outcome. Conversely, a preference for common names reinforced the popularity of already popular names, potentially leading to a narrower range of frequently chosen names.

Generative AI Experiment

An intriguing aspect of the study involved the use of a generative AI, Kat-GPT, to predict name popularity. This novel approach provided insights into the preferences encoded within AI systems and highlighted significant statistical differences in name popularity based on categorical assignments by the AI, offering a modern perspective on naming trends and their alignment with human naming behaviors.

Future Directions

The paper discusses several avenues for expanding the research, including investigating the creation of new names and the potential for non-myopic parent models. These suggestions underscore the rich potential for further explorations within the naming game, extending beyond traditional boundaries to include considerations of cultural evolution and technological influences on naming practices.

Concluding Remarks

This study offers a rigorous, albeit humorously framed, analysis of the dynamics of baby naming through the lens of game theory. By marrying theoretical modeling with empirical analysis, it provides a multifaceted understanding of the factors influencing naming decisions. Moreover, it opens the door to future interdisciplinary research that could further unravel the social, cultural, and technological facets of naming practices. Through its exploration of naming as a competitive game, the paper invites readers to reconsider the intricacies of a seemingly mundane, yet profoundly impactful, aspect of human behavior and identity formation.