Technical Note—The Generalized Sethi Advertising Model

We propose a flexible yet tractable dynamic advertising model called the generalized Sethi model to capture different market penetration rates across various media and markets via advertising. Specifically, the generalized Sethi model employs a Cobb–Douglas production function of advertising expenditure and the untapped market share with constant returns to scale. It encompasses some standard dynamic advertising models as particular cases. Moreover, the model’s flexibility does not compromise its tractability. We demonstrate it by showing single- and multifirm advertising problems involving Nash and Stackelberg games to admit closed-form expressions for the firms’ optimal advertising strategies and value functions under the generalized model. Sensitivity analysis of the model parameters also yields novel economic insights regarding the firms’ optimal advertising strategies and value functions.

Funding: A. P. Kennedy acknowledges the Hong Kong University Grant Council for their support of him pursuing his PhD at the Chinese University of Hong Kong. S. P. Sethi acknowledges financial support from the Eugene McDermott Chair Professorship. C. C. Siu acknowledges financial support from the Research Grants Council of Hong Kong [Grant “Generalized Sethi Advertising Model and Extensions” (Project UGC/FDS14/P02/20)]. S. C. P. Yam acknowledges financial support from HKGRF-14301321 [Project “General Theory for Infinite Dimensional Stochastic Control: Mean Field and Some Classical Problems] and General Research Fund by the Research Grants Council of Hong Kong-14300123 [Project “Well-Posedness of Some Poisson-Driven Mean Field Learning Models and Their Applications”].

Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2021.0717.