Cooperative Advertising in a Marketing Channel

This paper examines dynamic advertising and promotion strategies in a marketing channel where the retailer promotes the manufacturer product and the manufacturer spends on advertising to build a stock of goodwill. We assume that sales depend on goodwill and promotion activities and that there are decreasing marginal returns to goodwill. Two scenarios are studied. First, the manufacturer and retailer determine noncooperatively their respective strategies. Second, the game is played à la Stackelberg with the manufacturer as the leader who supports partially the cost of the promotion activities of the retailer. In both cases, stationary Markovian strategies are characterized. These scenarios are examined also in the absence of decreasing marginal effect of goodwill on sales. The results show that, whether or not the goodwill stock has a decreasing marginal effect on sales, the cooperative advertising program is a coordinating mechanism in the marketing channel, i.e., both players receive higher payoffs.     

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.     

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.     

Dynamics of competing with quality- and advertising-based goodwill

Goodwill formation is a complex process and many factors influence the formation of goodwill of a firm. The implications of advertising enabled goodwill formation are reported in several articles in the research literature. In this paper, we extend this stream of research by including quality in the goodwill formation process. We adopt a dynamic model of competition utilizing a differential game approach and derive expressions for open-loop Markovian Nash equilibrium investments in advertising and quality. The insights gained from the analysis of our model and from the equilibrium solutions are presented in the form of research propositions.     

Quality improvement vs. advertising support: Which strategy works better for a manufacturer?

We consider a marketing channel with a single manufacturer and a single retailer, where both advertising and quality improvement contribute to the build-up of goodwill. In a non-coop scenario, the retailer controls the advertising efforts while the manufacturer controls the quality improvements and wholesale price. Although improving quality positively contributes to goodwill, it also increases the production cost, thereby reducing the manufacturer’s profit. In a coop scenario, the manufacturer supports the retailer’s advertising while decreasing his investments in quality. We investigate the conditions under which a coop program is beneficial when such a trade-off occurs. Our results demonstrate that only when advertising significantly contributes to goodwill the manufacturer has an incentive to cooperate and a coop program turns out to be Pareto-improving. Conversely, the retailer is always better off with a coop program. Moreover, the channel is operational- and marketing-driven when quality effectiveness is high independent of advertising effectiveness or when both quality and advertising effectiveness are large. In all other cases, the channel is marketing-driven.     

The stochastic goodwill problem

Stochastic control problems related to optimal advertising under uncertainty are considered. In particular, we determine the optimal strategies for the problem of maximizing the utility of goodwill at launch time and minimizing the disutility of a stream of advertising costs that extends until the launch time for some classes of stochastic perturbations of the classical Nerlove–Arrow dynamics. We also consider some generalizations such as problems with constrained budget and with discretionary launching.     

Advertising a new product in a segmented market

We bring some market segmentation concepts into the statement of the “new product introduction” problem with Nerlove-Arrow’s linear goodwill dynamics. In fact, only a few papers on dynamic quantitative advertising models deal with market segmentation, although this is a fundamental topic of marketing theory and practice. In this way we obtain some new deterministic optimal control problems solutions and show how such marketing concepts as “targeting” and “segmenting” may find a mathematical representation. We consider two kinds of situations. In the first one, we assume that the advertising process can reach selectively each target group. In the second one, we assume that one advertising channel is available and that it has an effectiveness segment-spectrum, which is distributed over a non-trivial set of segments. We obtain the explicit optimal solutions of the relevant problems.     

考虑参考质量效应的“农超对接”供应链动态质量改进策略

在“农超对接”背景下,以“农村合作社+超市”组成的二级供应链为研究对象,考虑消费者参考质量效应对需求的影响,利用微分博弈理论分别求得了成本分担契约、非合作以及集中决策三种情形下供应链双方的最优均衡策略及利润。研究发现:消费者参考质量效应能够激励农村合作社提高农产品质量水平,同时缓解了超市的广告宣传压力,使得超市的广告宣传水平降低;当商誉-参考质量转换程度较大时,决策者会选择以低商誉战略来维持消费者合理的农产品质量期望值,形成了农产品质量低,成员收入少的不良经营环境;成本分担契约不仅提升了农产品质量水平,同时也实现了超市和农村合作社双方利润的帕累托改善,能够缓解超市面对劣质农产品束手无策的不良局面。     

Optimal advertising strategies with age-structured goodwill

The problem of a firm willing to optimally promote and sell a single product on the market is here undertaken. The awareness of such product is modeled by means of a Nerlove–Arrow goodwill as a state variable, differentiated jointly by means of time and of age of the segments in which the consumers are clustered. The problem falls into the class of infinite horizon optimal control problems of PDEs with age structure that have been studied in various papers either in cases when explicit solutions can be found or using Maximum Principle techniques. Here, assuming an infinite time horizon, we use some dynamic programming techniques in infinite dimension to characterize both the optimal advertising effort and the optimal goodwill path in the long run. An interesting feature of the optimal advertising effort is an anticipation effect with respect to the segments considered in the target market, due to time evolution of the segmentation. We analyze this effect in two different scenarios: in the first, the decision-maker can choose the advertising flow directed to different age segments at different times, while in the second she/he can only decide the activation level of an advertising medium with a given age-spectrum.     

Pricing and Advertising of Private and National Brands in a Dynamic Marketing Channel

We consider a marketing channel where a retailer sells, along the manufacturer’s brand, its own store brand. We assume that each player invests in advertising in order to build the brand’s goodwill. One distinctive feature of this paper is the introduction of the negative effect of own advertising on other player’s goodwill stock evolution. We characterize feedback-Nash pricing and advertising strategies and assess the impact of the store brand and national brand’s goodwill stocks on these strategies in different settings. The main findings suggest first that investing in building up some equity for each brand reduces the price competition between them and propels the market power for both. Second, the retailer will pass to consumer an increase in its purchasing cost of the national brand in all situations as no coordination is taken into account to counter the double marginalization problem. Finally, the higher the brand equity of the store brand, the more the retailer invests in advertising.     

Advertising and quality improving strategies in a supply chain when facing potential crises

In this paper, we consider a supply chain that faces a potential brand crisis, with one manufacturer deciding quality improvement and global advertising levels, and one retailer determining local advertising effort. The goodwill model proposed by Nerlove and Arrow (1962) is adopted here under the assumption that when the crisis happens, the companies suffer a sharp decrease in the goodwill. We characterize the feedback Nash equilibrium, and then we compare the corresponding quality and advertising strategies and outcomes with those of the case where the potential crises are absent, and where the companies do not invest in quality. The effects of the instantaneous crisis rate and the short-term and long-term damages are also evaluated. Our results reveal that the pre-crisis quality improvement accelerates the goodwill build-up before the crisis, and also helps the recovery in post-crisis regime. Its twofold function suggests that one of the pre- and post-crisis regimes/instants ought to be matched with more intense investment in both quality and global advertising, depending on the overall effect of instantaneous crisis rate, short-term damage and long-term damage. This carryover effect also brings a non-monotonicity of quality improvement effort and value functions with respect to the instantaneous crisis rate. These properties leave the chance to mitigate the loss by anticipating crisis for both members under certain circumstances.     

Optimal Goodwill Path to Introduce a New Product

We consider the problem of determining an optimal goodwill path for the introduction of a new product in a market, while looking for the maximum foreseen profit. The foreseen revenue depends on the product introduction time and on the goodwill level at the same time. We focus on the advertising costs associated with the goodwill evolution and assume that the cost function possesses some rather general features which are shared by the cost functions of the Nerlove-Arrow type models. The dynamic optimization problem is discussed in the calculus of variations framework. A few examples associated with special cost functions are discussed in detail.     

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.     

Advertising decisions for a segmented market

We consider the problem of choosing the levels of a set of advertising media in order to maximize the firm profit when the market is heterogeneous. Advertising efforts affect the demand of the different segments variably and we assume that the advertising effects on demand over time are mediated by a vector goodwill variable. A first general advertising decision problem is stated and solved in the non-linear programming framework. A preference index is then obtained for the medium selection problem when each segment demand function is linear in goodwill and each medium advertising cost function is quadratic in its level. Finally the theoretical case of disjoint advertising media is discussed.     

Transfer pricing in a dynamic marketing-operations interface

A transfer price mechanism is proposed to coordinate the strategies of the marketing and operations functional areas operating in a dynamic interface environment in a decentralized firm. Marketing and operations are strategic decision-makers in a differential game, in which marketing has price and advertising and operations has production as control variables, and advertising goodwill and production backlog are state variables. A constant transfer price is entered into the objective functionals for marketing and operations, and subgame perfect feedback strategies are derived for price, advertising, and production as functions of the state variables. The feedback strategies allow a solution for the dynamic system involving goodwill and backlog, and the total payoff to the firm, the sum of the payoffs to marketing and operations, is determined as a function of the transfer price. Finally, for certain parameter conditions an interior maximum of the payoff function is achieved, and the optimal transfer price is identified.     

On Controlled Linear Diffusions with Delay in a Model of Optimal Advertising under Uncertainty with Memory Effects

We consider a class of dynamic advertising problems under uncertainty in the presence of carryover and distributed forgetting effects, generalizing the classical model of Nerlove and Arrow (Economica 29:129–142, 1962). In particular, we allow the dynamics of the product goodwill to depend on its past values, as well as previous advertising levels. Building on previous work (Gozzi and Marinelli in Lect. Notes Pure Appl. Math., vol. 245, pp. 133–148, 2006), the optimal advertising model is formulated as an infinite-dimensional stochastic control problem. We obtain (partial) regularity as well as approximation results for the corresponding value function. Under specific structural assumptions, we study the effects of delays on the value function and optimal strategy. In the absence of carryover effects, since the value function and the optimal advertising policy can be characterized in terms of the solution of the associated HJB equation, we obtain sharper characterizations of the optimal policy.     

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.     

Equilibrium Pricing and Advertising Strategies in a Marketing Channel

This paper is concerned with conflict and coordination in a two-member channel of distribution. We propose a differential game model that includes carryover effects of advertising, expressed by a retailer-specific stock of advertising goodwill. Pricing and advertising strategies for both firms are identified under channel conflict as well as coordination. Dynamic advertising policies are designed as stationary Markov perfect strategies. In a symmetric case, these strategies can be determined in closed form, taking into consideration explicitly nonnegativity constraints on advertising rates. We establish a global result for the relationship between the advertising strategies of the two firms under conflict and coordination.     

Public Disclosure Programs vs. traditional approaches for environmental regulation: Green goodwill and the policies of the firm

A Public Disclosure Program (PDP) is compared to a traditional environmental regulation (exemplified by a tax/subsidy) in a simple dynamic framework. A PDP aims at revealing the environmental record of firms to the public. This information affects its image (goodwill or brand equity), and ultimately its profit. A firm polluting less than its prescribed target would win consumer’s sympathy and raise its goodwill, whereas it is the other way around when the firm exceeds its emissions quota. The evolution of this goodwill is assumed to depend also on green activities or advertising expenditures. Within this framework, we analyze how a PDP affects the firm’s optimal policies regarding emissions, pricing and advertising as compared to a traditional regulation. We show that advertising acts as a complementary device to pricing and that emissions are increasing in goodwill. The role of a standard or target level for emissions turns out to be totally different under both policy regimes. In the case of a tax/subsidy approach, this target level only acts as constant who increases or decreases profit by a fixed amount, but it does not affect the policy of the firm. On the contrary, if a PDP is implemented, the target value for emissions enters in an important way in the goodwill accumulation mechanism and determines how the firm reacts to the regulation and what is the time path for the economic and environmental variables. Moreover, this value is also crucial to determine the possibility that a PDP is profit improving. A policy implication of this fact is that regulators should be particularly careful in fixing the emission standard when a PDP is applied. The theoretical results are complemented with a numerical illustration.     

Advertising for a new product introduction: A stochastic approach

We formulate a stochastic extension of the Nerlove and Arrow’s advertising model in order to analyze the problem of a new product introduction. The main idea is to introduce some uncertainty aspects in connection both with the advertising action and the goodwill decay, in order to represent the random consequences of the advertising messages and of the word-of-mouth publicity, respectively. The model is stated in terms of the stochastic optimal control theory and a general study is attempted using the stochastic Maximum Principle. Closed form solutions are obtained under linear quadratic assumptions for the cost and the reward functions. Such optimal policies suggest that the decision-maker considers both the above mentioned phenomena as opportunities to increase her/his final reward. After stating some general features of the optimal solutions, we analyze in detail three extreme cases, namely the deterministic model and the stochastic models with either the word-of-mouth effect only, or the lure/repulsion effect only. The optimal policies provide us with some insight on the general effects of the advertising action. Supported by MIUR and University of Padua.