An empirical study on the Lanchester model of combat for competitive advertising decisions

This paper presents an empirical study on the Lanchester model of combat for competitive advertising decisions. Three issues are evaluated: (i) the specification of the market share response model; (ii) the effect of inflation on the estimation of the response model; and (iii) the performance of competitive strategies. It is shown that (a) the square root function that is used in previous studies is often inappropriate to characterize the market share response model; (b) market share variations are more responsive to current advertising expenditures; (c) closed-loop Nash equilibrium strategies are better competitive advertising strategies for firms to maximize profits than open-loop Nash equilibrium strategies; and (d), finally, general perfect equilibria Nash equilibrium strategies developed by Case are usually not good competitive advertising strategies for firms to maximize profits.     

An Application of Multiple Regression Analysis to the Greek Beer Market

The object of this paper is to present a quantitative analysis of the Greek beer industry, through the use of various single regressions. The first part presents the relationship between advertising and sales through disaggregating advertising outlays, media and firm advertised, while a number of indices referring to advertising effectiveness are also estimated. The second part extends the discussion by presenting an illustrative example with regard to the implied duration interval and its importance in advertising.     

Cooperative advertising models in supply chain management: A review

This paper reviews articles on cooperative advertising, a topic which has gained substantial interest in the recent years. Thereby, we first briefly distinguish five different definitions of cooperative advertising which can be found in operations research literature. After that, we concentrate on vertical cooperative advertising, which is the most common object of investigation and is understood as a financial agreement where a manufacturer offers to pay a certain share of his retailer’s advertising expenditures. In total, we identified 58 scientific papers considering mathematical modeling of vertical cooperative advertising. These articles are then analyzed with regard to their general model setting (e.g., the underlying supply chain structure and design of the cooperative advertising program). After that, we explain the different demand and cost functions that are employed, whereupon we distinguish between static and dynamic models. The last dimension of our review is dedicated to the game-theoretic concepts which are mostly used to reflect different forms of distribution of power within the channel.     

Dynamical analysis of a nonlinear competitive model with generic and brand advertising efforts

In this paper, a new four-dimensional map is proposed to model the dynamical advertising efforts, where both the generic and brand effects for advertisement are taken into account in the model. The marginal profit adapting strategy is used to reflect the interaction among the firms that strive for the optimal profit. When the generic advertising bears a large effectiveness coefficient, the generic advertising efforts will exhibit chaos, which leads to a chaotic dynamics for brand advertising efforts. In this case, we analyze the some properties of steady trajectories that imply rough profiles of the advertising strategies evolution. Furthermore, by rigorous dynamical analysis and numerical simulations, we obtain the feasible set outlining the influence of initial conditions on the global dynamic properties. We first deal with the symmetric system, and then extend the obtained results to more general case, namely, the asymmetric model. For the symmetric model, two firms’ brand advertising expenditures behave synchronization, but the dynamics of generic advertising efforts are dependent upon initial conditions. Meanwhile, for the heterogeneous case, the domain firm in the market needs to contribute all generic advertising expenditures. Our results can have a practical impact on the market evolution, and are therefore beneficial to decision maker.     

Optimal Multi-Period Advertising Budget Allocation within a Competitive Environment

A mathematical model approach is developed for the purpose of aiding advertising and marketing executives in advertising budget allocation decision-making in the face of a competitive environment. Two alternative model formulations are examined to study the dynamic market response to advertising expenditures. These embody numerous realistic characteristics of the advertising phenomenon including carry-over of past expenditures, diminishing returns and saturation effects, response decay in the absence of advertising and product diffusion effects. Through mathematical programming, the model determines the optimal advertising expenditures over a predetermined planning horizon under alternative constraint options (including competitive advertising assumptions). Illustrations of model applications are also presented.     

A network equilibrium framework for Internet advertising: Models,qualitative analysis,and algorithms

In this paper, we develop a network equilibrium framework for the modeling and analysis of competitive firms engaged in Internet advertising among multiple websites. The model allows for the determination of both the equilibrium online advertising budget as well as the advertising expenditures on the different websites. We then specialize the model to the case of fixed online budgets for the firms. The governing equilibrium conditions of both models are shown to satisfy finite-dimensional variational inequalities. We present qualitative properties of the solution patterns as well as computational procedures that exploit the underlying abstract network structure of these problems. The models and algorithms are illustrated with numerical examples. This paper adds to the growing literature of the application of network-based techniques derived from operations research to the advertising/marketing arena.     

Vertical cooperative advertising and pricing decisions in a manufacturer–retailer supply chain: A game-theoretic approach

Manufacturers can increase the advertising expenditures of their retailers by bearing a fraction of the occurring costs within the framework of a vertical cooperative advertising program. We expand the existing research which deals with advertising and pricing decisions in a manufacturer–retailer supply chain contemporaneously. By means of game theory, four different relationships between the channel members are considered: Firstly, three non-cooperative games with either symmetrical distribution of power or asymmetrical distribution with one player being the leader in each case, and one cooperative game where both players tend to maximize the total profit. The latter is complemented by a bargaining model, which proposes a fair split of profit on the basis of the players’ risk attitude and bargaining power. Our main findings are as follows: (a) In contrast to previous analyses, we do not limit the ratio between manufacturer’s and retailer’s margin, which provides more general insights into the effects of the underlying distribution of power within the channel. (b) The highest total profit is gained when both players cooperate. This behavior puts also the customers in a better position, as it produces the lowest retail price as well as the highest advertising expenditures compared to the other configurations.     

Co-op advertising models in manufacturer–retailer supply chains: A game theory approach

In the literature of cooperative (co-op) advertising, the focus of research is on a relationship in which a manufacturer is the leader and retailers are followers. This relationship implies the dominance of the manufacturer over retailers. Recent market structure reviews have shown a shift of retailing power from manufacturers to retailers. Retailers have equal or even greater power than a manufacturer when it comes to retailing. Based on this new market phenomenon, we intend to explore the role of vertical co-op advertising efficiency with respect to transactions between a manufacturer and a retailer through brand name investments, local advertising expenditures, and sharing rules of advertising expenses. Three co-op advertising models are discussed which are based on two noncooperative games and one cooperative game. In a leader–follower noncooperative game, the manufacturer is assumed to be a leader who first specifies the brand name investment and the co-op subsidization policy. The retailer, as a follower, then decides on the local advertising level. In a noncooperative simultaneous move game, the manufacturer and the retailer are assumed to act simultaneously and independently. In a cooperative game, the system profit is maximized for every Pareto efficient co-op advertising scheme, but not for any other schemes. All Pareto efficient co-op advertising schemes are associated with a single local advertising level and a single brand name investment level, but with variable sharing policies of advertising expenses. The best Pareto efficient advertising scheme is obtained taking members' risk attitudes into account. Utilizing the Nash bargaining model, we discuss two situations that (a) both members are risk averse, and (b) both members are risk neutral. Our results are consistent with the bargaining literature.     

Non-linear advertising capital model with time delayed feedback between advertising and stock of goodwill

According to the classical Nerlove-Arrow model, advertising expenditure can be considered as a capital investment to create present and future demand for the firm's products and, hence, to create present and future revenues for the firm. Advertising is assumed to influence via stock of goodwill which cumulatively counts for the effects of the firm's current and past advertising outlays. The paper presents a time delayed feedback model describing the relations between advertising and goodwill. Three different types of effects of advertising upon the dynamics of goodwill are modelled. The advertising policy of the management is incorporated into the model via a non-linear advertising function. The advertising function controls the advertising outlay e.g. by budget constraint and by the actual and target values of goodwill. The behavior of the model is analysed both analytically and numerically. Special attention is given for deriving the stability conditions for the limiting solution. The cases of repelling or chaotic limiting solutions are analysed by bifurcation and state space diagrams. Several numerical examples are given.     

Assessing the effect of advertising expenditures upon sales: A Bayesian structural time series model

We propose a robust implementation of the Nerlove‐Arrow model using a Bayesian structural time series model to explain the relationship between advertising expenditures of a countrywide fast‐food franchise network with its weekly sales. Due to the flexibility and modularity of the model, it is well suited to generalization to other markets or situations. Its Bayesian nature facilitates incorporating a priori information reflecting the manager's views, which can be updated with relevant data. This aspect of the model will be used to support the decision of the manager on the budget scheduling of the advertising firm across time and channels.     

Modelling advertising budgeting and allocation decisions using modified multinomial logit market share models

Previous research suggests that a multinomial logit model of market share (MNL) is inappropriate for equilibrium analyses of advertising competition. This article shows that when employing simple transformations of the advertising effort, the modified MNL model becomes useful in representing situations of diminishing returns to advertising and appropriate for advertising equilibrium analyses without additional difficulties in its empirical estimation. Using the modified MNL model, optimal advertising budgets together with their allocation over time are derived for both the cases of concave and S-shaped attraction (response) functions in a symmetric oligopoly.     

Coordinating advertising and pricing in a manufacturer–retailer channel

Cooperative advertising is a practice that a manufacturer pays retailers a portion of the local advertising cost in order to induce sales. Cooperative advertising plays a significant role in marketing programs of channel members. Nevertheless, most studies to date on cooperative advertising have assumed that the market demand is only influenced by advertising expenditures but not by retail price. This paper addresses channel coordination by seeking optimal cooperative advertising strategies and equilibrium pricing in a two-member distribution channel. We establish and compare two models: a non-cooperative, leader–follower game and a cooperative game. We develop propositions and insights from the comparison of these models. The cooperative model achieves better coordination by generating higher channel-wide profits than the non-cooperative model with these features: (a) the retailer price is lower to consumers; and (b) the advertising efforts are higher for all channel members. We identify the feasible solutions to a bargaining problem where the channel members can determine how to divide the extra profits.     

Optimal dynamic advertising policies in the presence of continuously distributed time lags

The Nerlove-Arrow model of optimal dynamic advertising policies is generalized by incorporating a continuously distributed lag between advertising expenditures and increases in the stock of goodwill. This leads to a control problem where the equation of motion is given by an integro-differential equation. The transitory and steady-state properties of the optimal policies are examined, both for a general lag function and for a gamma distributed lag. The dependence of the steady-state solution on the parameters of the gamma distribution is also investigated. An example is given using specific demand and cost functions.     

Alternative statistical regression studies of the effects of Joint and Service Specific advertising on military recruitment

Three different regression approaches use a large database developed by the Wharton Center for Applied Research (WCAR) to study the effects of Joint versus Service Specific advertising on military recruitment. (Here ‘Joint’ refers to advertising designed to serve recruitment for all four services simultaneously. Service Specific refers to advertising administered separately by each of the four services.) These regression approaches and the data and models are examined with special reference to US Army recruitment. The WCAR study led to a recommendation to replace Service Specific with Joint advertising. This recommendation was called into question by the RAND Corporation in its study that used a different regression approach. A third study that combines regressions with data envelopment analysis (DEA) is presented in this paper. This study utilizes recently developed methods based on DEA which, when incorporated in the regression, make it possible to distinguish between efficient and inefficient performances. The resulting regression yields results that show Joint advertising to be not only less efficient but also to attract potential recruits from the Army to other services. Implications for further research are set forth, which can also cast light on commercial practice by regarding Joint as a type of ‘category advertising’ and Service Specific as a type of ‘brand advertising’.     

A dynamic model for advertising and pricing competition between national and store brands

We study the relationship between the pricing and advertising decisions in a channel where a national brand is competing with a private label. We consider a differential game that incorporates the carryover effects of brand advertising over time for both the manufacturer and the retailer and we account for the complementary and competitive roles of advertising. Analysis of the obtained equilibrium Markov strategies shows that the relationship between advertising and pricing decisions in the channel depends mainly on the nature of the advertising effects. In particular, the manufacturer reacts to higher competitive retailer’s advertising levels by offering price concessions and limiting his advertising expenditures. The retailer’s optimal reaction to competitive advertising effects in the channel depends on two factors: (1) the price competition level between the store and the national brands and (2) the strength of the competitive advertising effects. For example, in case of intense price competition between the two brands combined with a strong manufacturer’s competitive advertising effect, the retailer should lower both the store and the national brands’ prices as a reaction to higher manufacturer’s advertising levels. For the retailer, the main advantage from boosting his competitive advertising investments seems to be driven by increased revenues from the private label. The retailer should however limit his investments in advertising if the latter generates considerable competitive effects on the national brand’s sales.     

Optimal Keyword Bids in Search-Based Advertising with Stochastic Advertisement Positions

US expenditures on search-based advertising exceeded $12 billion in 2010. Advertisers bid for keywords, where bid price determines ad placement, affecting click-through and conversion rates. Advertisers must select keywords, allocating each a proportion of their fixed daily budget. In this paper, we construct a stochastic model for the selection and allocation process. We provide analytical results for the single-keyword problem and examine the multiple-keyword problem numerically. We investigate trade-offs between keywords given varying levels of risk and return. We show the implications of enforcing a probabilistic budget constraint. Our paper provides a critical analysis of the advertiser’s problem that may guide future research.     

National and store brand advertising strategies

As the propensity of premium store brands (SBs) increases, retailers must consider different ways to drive sales besides promotional strategies. With this in mind, we consider a national brand (NB) and a (premium) SB co-existing in a market. Each brand has to decide the amount to invest in advertising its product and the prices to charge its customers, which can be determined separately or in unison. When either advertising expenditures or pricing decisions are set, each brand must keep in mind that the advertising efforts and revenue may spillover between the two brands, customers who intend to purchase the NB may end up purchasing the SB and vice versa. We derive an analytical model of the situations described and characterize equilibrium advertising decisions. We find that the characteristics of a premium SB may depend on which marketing/promoting instrument (advertising or pricing) is the primary method for driving demand; and in some situations an NB may be better off to not advertise at all and instead let the premium SB carry out all of the advertising.     

Bayesian analysis of quantile regression for censored dynamic panel data

This paper develops a Bayesian approach to analyzing quantile regression models for censored dynamic panel data. We employ a likelihood-based approach using the asymmetric Laplace error distribution and introduce lagged observed responses into the conditional quantile function. We also deal with the initial conditions problem in dynamic panel data models by introducing correlated random effects into the model. For posterior inference, we propose a Gibbs sampling algorithm based on a location-scale mixture representation of the asymmetric Laplace distribution. It is shown that the mixture representation provides fully tractable conditional posterior densities and considerably simplifies existing estimation procedures for quantile regression models. In addition, we explain how the proposed Gibbs sampler can be utilized for the calculation of marginal likelihood and the modal estimation. Our approach is illustrated with real data on medical expenditures.     

Models of a Consumer Product Market

Aggregate models of the United Kingdom razor blade market are discussed. During one prolonged period when the market was dominated by two major brands, approximately equivalent in terms of quality, price and distribution, a model based on advertising expenditures alone was remarkably accurate at predicting short-term movements of a brand's market share in periods of both growth and decline. An optimum decay rate of advertising effectiveness was identified. The value of consumer promotions could be estimated from the deviations they produced from the model. To cover longer periods and to encompass brands of widely differing qualities and prices a more complex model was necessary. This has been successful in following long-term trends of market shares of all brands and has contributed towards understanding the market structure. It has shed light on the value of a multi-brand policy and has enabled a retrospective evaluation to be made of the effect of a period of production capacity limitation on market share growth.     

Advertising Budgeting,Wearout and Copy Replacement

In this paper we offer a formulation for the "Copy Life Cycle" phenomenon. In particular, we introduce simultaneously three decision variables, the optimal advertising expenditures during a given planning horizon, the optimal times for copy replacements and the optimal investments in the new copies. The analysis and the solution of the problem is carried out by a mixed optimization technique based on dynamic programming and optimal control theory.