| As Internet advertising environments have become more complex and dynamic,determining the optimal budget level becomes more and more difficult and challenging.Basically,it requires comprehensive understanding of the process of advertising responses in Internet advertising.For decades,the relationship between advertising and advertising responses has been a research hotspot attracting plenty of attentions from both academia and industries.On the one hand,from a theoretical perspective,quite a few dynamic advertising response models have been developed to quantitatively describe the ad-response relationship;on the other hand,from an empirical perspective,the shape of advertising responses has been examined,specifically for the concave and S-shaped responses.Starting from the above two aspects,this research explores the advertising responses of Internet advertising and proposes an optimal budget strategy.The content is specified as follows:Firstly,this paper investigates a generalized form of Vidale-Wolfe(GVW)model.One key element of our modeling work is that the GVW model contains two useful indexes representing the advertising elasticity and the word-of-mouth(Wo M)effect,respectively.And advertising elasticity and Wo M effect are very prominent in Internet advertising environments,especially in the e-commerce market according to existing research.Moreover,some desirable properties of the GVW model are discussed,and a deep neural network(DNN)-based estimation method is presented to learn its parameters.Furthermore,based on three realworld datasets,computational experiments are conducted to validate the GVW model and identified properties.The research outcome shows that(1)both the ad elasticity index and the Wo M index have significant influences on advertising responses,(2)it's against reality to fix the two newly added indexes as constants such as1.0 and 0.5,(3)the two newly added indexes affect the steady-state market share in different ways.Then,this paper empirically investigates the possible shape of responses by the GVW model,with some baseline models for comparison and results verification.In these models,the number of clicks is taken as the dependent variable,advertising expenditure as the focal independent variable and several important advertising factors inherent in search engine advertising as covariates in the extended models.Based on a realworld dataset of about 55000 ads that collected from practical campaigns by a large U.S.electronic commerce retailer,these models are empirically calibrated.Empirical results show that(1)the shape of advertising responses is mixed: concave in major ads associated with the highly competitive situation,and S-shaped in those with the less competitive situation,(2)in the highly competitive situation with a certain amount of advertising expenditure and equal or similar CTR,ads on a lower position receive more clicks than those on a higher position on the search engine results pages;however,in the less competitive situation,the position effect is small and in an opposite direction.Finally,this paper formulates budget allocation decisions as an optimal control problem under a planning time horizon,based on the GVW model.Moreover,some desirable properties are discussed and a feasible solution is provided.Furthermore,computational experiments are conducted to assess the performance of our model and identified properties,based on two real-world datasets obtained from advertising campaigns by two large e-commerce companies on Google Ad Words and Facebook Ads.Experimental results show that(1)the GVW strategy outperforms optimal strategies based on the Vidale-Wolfe model and its derivatives,(2)the nonlinearity feature with respect to the advertising expenditure,raised by the two newly added indexes,exhibits a better adaptability for complex advertising situations,(3)higher ad elasticities(smaller Wo M indexes)empower higher levels of both optimal budget and corresponding market share,and thus higher payoffs. |
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