@article{2ba9d803c20e407d90bf6ce9774589e2,
title = "A Mathematical Model for the Origin of Name Brands and Generics",
abstract = "Firms in the U.S. spend over $200 billion each year advertising their products to consumers, around one percent of the country's gross domestic product. It is of great interest to understand how that aggregate expenditure affects prices, market efficiency, and overall welfare. Here, we present a mathematical model for the dynamics of competition through advertising and find a surprising prediction: when advertising is relatively cheap compared to the maximum benefit advertising offers, rational firms split into two groups, one with significantly less advertising (a ``generic{"}{"} group) and one with significantly more advertising (a ``name-brand{"}{"} group). Our model predicts that this segmentation will also be reflected in price distributions; we use large consumer data sets to test this prediction and find good qualitative agreement.",
keywords = "advertising, consumer behavior, differential games, dynamical systems, economic dynamics, nonlinear dynamics",
author = "Johnson, {Joseph D.} and Redlich, {Adam M.} and Abrams, {Daniel M.}",
note = "Funding Information: This work was supported by the National Science Foundation through Research Training grant 1547394. We thank the Nielsen Corporation for their generosity in making their proprietary data available for scientific research. We also thank Vicky Chuqiao Yang for useful conversations. Funding Information: \ast Received by the editors August 19, 2020; accepted for publication (in revised form) September 20, 2021; published electronically August 4, 2022. https://doi.org/10.1137/20M1360888 Funding: This work was supported by the National Science Foundation through Research Training grant 1547394. \dagger Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208 USA (josephjohnson2020@u.northwestern.edu, adamredlich2020@ u.northwestern.edu). \ddagger Department of Engineering Sciences and Applied Mathematics, Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL 60208 USA (dmabrams@northwestern.edu). Publisher Copyright: {\textcopyright} 2022 Society for Industrial and Applied Mathematics.",
year = "2022",
doi = "10.1137/20M1360888",
language = "English (US)",
volume = "64",
pages = "625--639",
journal = "SIAM Review",
issn = "0036-1445",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "3",
}
