An advertising game with multiplicative interference

Two competing manufacturers provide a homogeneous market with substitutable products and want to maximize their profits. Each firm may advertise its brand, with a positive effect on its own brand and negative on the competitor's one. Moreover, each firm may choose an advertising medium to use among several available media. We assume that the advertising effect on demand is mediated by the goodwill variable and that a competitor's interference may be represented as a proportional reduction of the virtual goodwill. We model the manufacturers' problem as a noncooperative game under complete information and discuss the existence and features of its Nash equilibria.     

Using several advertising media in a homogeneous market

We propose a variety of models to represent the joint effect of several advertising media on the demand for a product in a homogeneous market, and discuss the associated profit maximization problems. An advertising productivity function represents the combination of several media and, together with demand and advertising cost functions, determines the features of the associated profit problem. We distinguish between additive and nonadditive advertising productivity functions, then between smooth and nonsmooth ones. The demand function may either be linear or not. We observe how different models may exhibit either synergy or interference effects. In some cases we obtain explicit optimal solutions.     

Pure-strategy Nash equilibria in an advertising game with interference

Two manufacturers produce substitutable goods for a homogeneous market. The advertising efforts of the two manufacturers determine the demand for the goods and interfere negatively with each other. The demand of each good is a piecewise linear function of the product goodwill, and the latter is a linear function of advertising efforts. In a game with two competing profit-maximizing manufacturers who have access to a set of several advertising media, the pure-strategy Nash equilibria are characterized and their existence is shown.     

Using mixture‐amount modeling to optimize the advertising media mix and quantify cross‐media synergy for specific target groups

One of the critical decisions in media planning is how to allocate advertising efforts across different media. While studies indicate that marketers can create positive synergy effects by spreading their effort across several media, there is little understanding of how much should be invested in each specific medium to optimize advertising results. In this study, we apply a novel methodology, mixture‐amount modeling, which allows advertisers to determine the optimal allocation of advertising effort across media as a function of the total advertising effort. Moreover, we test how the optimal allocation and the resulting response change for consumers with distinctive media usage patterns and varying degrees of product category experience. Based on these results, we quantify the potential synergy between media and calculate the synergistic capacity for specific target groups. We apply the model to data from 52 beauty care advertising campaigns that ran on TV and in magazines in the Netherlands and Belgium. We determine the optimal allocation of advertising investments (measured through Gross Rating Points) to maximize campaign recognition. Our findings support the existence of positive synergistic effects between magazine and TV advertising and illustrate that these effects depend on consumers' media usage and product category experience.     

Game theoretic analysis of pricing and vertical cooperative advertising of a retailer-duopoly with a common manufacturer

This paper considers competition of duopolistic retailers, who sell substitutable products supplied by a single manufacturer offering a vertical cooperative advertising program. The price-dependent component of the demand function is derived from the consumers’ utility function in order to avoid logically inconsistent results. Additionally, each supply chain member can increase the costumers’ demand by advertising. By means of game theory, we get the following results: (a) Retailer competition harms all players, but is beneficial to the consumers. (b) Stronger competition is followed by less advertising. (c) Channel-leadership is not always advantageous to the manufacturer, and—likewise—retailers can also be better off when accepting followership. However, as our analysis shows, the increased complexity of the model under consideration reaches the limits of an analytical solution. Therefore, we give a brief outlook on non-nalytical solution methods for Nash and Stackelberg games, that could be used in future research, in the end of our paper.     

A communication mix for an event planning: a linear quadratic approach

The communication mix is a relevant decision issue for an organization that plans the advertising campaign for a fixed future event. It is assumed that the objectives of the organization are to minimize the cost of the advertising campaign and to drive the final demand as close as possible to a target value. Two different advertising channels are available: the first affects deterministically the consumers’ demand, whereas the second presents some stochastic aspects which are out of decision-maker’s control. Some recent mathematical developments on the stochastic linear quadratic control problem allow to formulate and solve some interesting instances of the problem. A comparative analysis of the efficiency of deterministic and stochastic controls is done and the optimal feedback policies are discussed. The trade-off between efficiency and risk of an advertising channel is essential to understand the features of the optimal solutions.This study was supported by MIUR and University of Padua.     

Advertising and production of a seasonal good for a heterogeneous market

We bring some concepts from market segmentation, which is a fundamental topic of marketing theory and practice, into the statement of an advertising and production problem for a seasonal product with Nerlove–Arrow’s linear goodwill dynamics. We consider two kinds of situations. In the first one, the advertising process can reach selectively each segment. In the second one, one advertising medium is available which has a known effectiveness spectrum for a non-trivial set of segments. In both cases we solve, using the Pontryagin’s Maximum Principle conditions, the optimal control problems in which goodwill productivity of advertising is concave and good production cost is convex. Two special cases are discussed in detail.     

An Experimental Design for Measuring Advertising Payoff

A model is described to assist retail management in developing an effective advertising strategy. The difficulties of advertising decision-making are reviewed and the nature of the particular marketing problem is outlined. It is shown how market research is used to construct an effective appeal and choice of media. An experiment, using a split-plot design, is then performed to estimate the payoff of advertising. This provides a clear framework for developing advertising decisions and for their implementation and control.     

A joint dynamic pricing and advertising model of perishable products

Advertising and dynamic pricing play key roles in maximizing profit of a firm. In this paper a joint dynamic pricing and advertising problem for perishable products is investigated, where the time-varying demand rate is decreasing in sales price and increasing in goodwill. A dynamic optimization model is proposed to maximize total profit by setting a joint pricing and advertising policy under the constraint of a limited advertising capacity. By solving the dynamic optimization problem on the basis of Pontryagin’s maximum principle, the analytical solutions of the optimal joint dynamic pricing and advertising policy are obtained. Additionally, to highlight the advantage of the joint dynamic strategy, the case of the optimal advertising with static pricing policy is considered. Numerical examples are presented to illustrate the validness of the theoretical results, and some managerial implications for the pricing and advertising of the perishable products are provided.     

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.     

Optimal media planning for multi-products in segmented market

Promotion is an essential stage of any product life cycle. All firms either concerned with single or multiple products promote their products. Advertising is the most dominated form of promotion for most of the products. Our research focuses on firms which produces a multiple range of products and advertise them using available media options. The budget constraint forms the major restriction. The existing research in media allocation of multiple products ignores the market segmentation and formulates the media plan assuming all segments alike. In this paper we formulate a media planning problem for allocating the available budget in multiple media that are found suitable for the advertising of multiple products considering marketing segmentation aspect of advertising. The objective is to maximize the total reach in all the segments. Goal programming technique is used to solve the problem. A case study is presented to show the real life application of the model.     

Signaling Quality: Dynamic Price-Advertising Model

This paper extends the existing quality-signaling literature by investigating the roles of price and advertising levels as quality indicators in a dynamic framework. Considering perceived quality as a form of goodwill, we modify the well-known Nerlove-Arrow dynamic model to include price effects. In our model, price is used both as a monetary constraint and as a signal of quality, while advertising spending is used only as a signaling device, and thus purely as a dissipative expense. Utilizing optimal control, we determine optimal decision rules for a firm regarding both price and advertising over time as functions of perceived quality. The results indicate that, when prices act as monetary constraints and are reduced to increase demand, the firm should use the signaling role of advertising by increasing spending to accelerate perceived quality increases. In cases when the value of the perceived quality goes up together with the increase in the perceived quality by more than the demand, in percentage terms, the firm should increase the price (use its signaling role). At steady-state, we find that the level of optimal profit margin relative to price decreases with the elasticity of demand with respect to the brand price. However, higher elasticity of demand with respect to the firm’s perceived quality and/or a higher impact of price (advertising) lead/leads to a higher optimal profit margin (advertising spending) relative to price (revenue).     

风险中性零售商的合作广告策略与订货模型

考虑了由一个制造商与一个零售商构成的单期二阶段供应链是否进行合作广告的博弈问题.面对市场需求的不确定性,零售商从制造商处订购报童类型产品销售给消费者,零售商具有风险中性的行为特征.通过不合作广告与合作广告两种情形,制造商与零售商进Stackelberg主从博弈,得到了均衡解,比较后发现,合作广告下的最优解及利润总是优于不合作广告下的最优解和利润,告诉了上下游企业采用合作广告的广告策略.最后,通过数值算例,给出了需求敏感系数对最优决策的影响,同时也论证了有关结论.     

The gravity p-median model

In this paper we propose a new model for the p-median problem. In the standard p-median problem it is assumed that each demand point is served by the closest facility. In many situations (for example, when demand points are communities of customers and each customer makes his own selection of the facility) demand is divided among the facilities. Each customer selects a facility which is not necessarily the closest one. In the gravity p-median problem it is assumed that customers divide their patronage among the facilities with the probability that a customer patronizes a facility being proportional to the attractiveness of that facility and to a decreasing utility function of the distance to the facility.     

Advertising Response Functions and Media Planning

In the first part of this paper the definition and use of advertising response functions are examined critically. It is shown that advertising response functions cannot be regarded as models of the advertising process whose parameters are known, that only a small section of the complex functions often postulated is relevant to media planning, that measures of advertising impacts or exposures are relative rather than absolute, and consequently that the “response function” only shows a notional relationship between advertising response and exposure, which normally needs to be calibrated to the advertising appropriation.In the second part a media planning system which utilizes a “control parameter” rather than a “response function” is described. The main feature of the “control parameter” is that it adapts itself so that an appropriate relationship between response and exposure is used, whatever the appropriation. Other features of the system are described.     

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.     

On a cooperative advertising model for a supply chain with one manufacturer and one retailer

, , ,  and  recently studied a game-theoretic model for cooperative advertising in a supply chain consisting of one manufacturer and one retailer. However, the sales-volume (demand) function considered in this model can become negative for some values of the decision variables, and in fact, this does happen for the proposed Stackelberg and Nash equilibrium solutions. Yue et al. (2006) acknowledge the negativity problem and suggest two constraints to fix it; however, they do not incorporate these constraints into their mathematical analysis. In this paper, we show that the results obtained by analyzing the advertising model under the constraints suggested by Yue et al. can differ significantly from those obtained in the previous papers.     

On the impact of advertising initiatives in supply chains

Advertising plays an important role in affecting consumer demand. Socially responsible firms are expected to use advertising judiciously, limiting advertising of “bad” products. An example is the advertising initiative adopted by several major food manufacturers to limit the advertising of unhealthy food categories to children. Such initiatives are based on the belief that less advertising will lead to less consumption of these unhealthy food categories. However, food manufacturers usually distribute products to consumers through retailers whose advertising is not restricted by those initiative programs. In this paper, we examine the effectiveness of such advertising initiative in a leader–follower supply chain with one manufacturer and one retailer. We assume that both the manufacturer and the retailer can choose to participate in the advertising initiative by reducing their advertising levels. The problem is formulated as a Stackelberg game. We show that the effectiveness of the advertising initiative critically depends on the leader’s participation in the initiative. If the leader is willing to reduce the advertising level below a threshold, the market coverage of the product can drop significantly. On the other hand, if only the follower participates in the initiative, the market coverage is likely to expand in the majority of cases. Managerial implications of this research are also discussed.     

Dynamic resource allocation in a multi-product make-to-stock production system

We consider optimal policies for a production facility in which several (K) products are made to stock in order to satisfy exogenous demand for each. The single machine version of this problem in which the facility manufactures at most one product at a time to minimise inventory costs has been much studied. We achieve a major generalisation by formulating the production problem as one involving dynamic allocation of a key resource which drives the manufacture of all products under an assumption that each additional unit of resource allocated to a product achieves a diminishing return of increased production rate. A Lagrangian relaxation of the production problem induces a decomposition into K single product problems in which the production rate may be varied but is subject to charge. These reduced problems are of interest in their own right. Under mild conditions of full indexability the Lagrangian relaxation is solved by a production policy with simple index-like structure. This in turn suggests a natural index heuristic for the original production problem which performs strongly in a numerical study. The paper discusses the importance of full indexability and makes proposals for the construction of production policies involving resource idling when it fails.     

Joint Price and Lot-Size Determination When Supplier Offers Incremental Quantity Discounts

This paper considers the joint pricing and the lot-size determination problem faced by a retailer when he purchases a product for which the supplier offers incremental quantity discounts. Two common demand functions are considered: (1) the constant price-elasticity function, and (2) the linear function. A procedure is provided for each case for calculating the optimal price and the lot-size.