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We study optimal advertising and entry timing decisions for a new product being sold in two-segment markets in which followers are positively influenced by elites, whereas elites are either unaffected or repulsed by product popularity among followers. Key decisions in such markets are not only how much to advertise in each segment over time but also when to enter the follower segment. We develop a continuous-time optimal control model to examine these issues. Analysis yields two sets of two-point boundary value problems where one set has an unknown boundary value condition that satisfies an algebraic equation. A fast solution methodology is proposed. Two main insights emerge. First, the optimal advertising strategy can be U-shaped, that is, decreasing at first to free-ride peer influence but increasing later on to thwart the repulsion influence of overpopularity causing disadoption. Second, in markets where cross-segment repulsion triggers disadoption, advertising is only moderately effective, and entry costs are high, managing both advertising and entry timing can result in significantly higher profits than managing only one of these levers. In markets without disadoption, with high advertising effectiveness or with low entry costs, in contrast, delaying entry may add little value if one already manages advertising optimally. This implies that purveyors of prestige or cool products need not deny followers access to their products in order to protect their profits, and can use advertising to speed up the democratization of consumption profitably. This paper was accepted by Juanjuan Zhang, marketing.

This paper investigates contract design by a firm in a supply chain where the quality of the product delivered to consumers is co-created by the quality decisions of the contract designer (platform firm) and the agent (the service provider) whose inputs need to be coordinated. Revenue is a function of the price charged to consumers, the product quality, and a market parameter which may be private information to the service provider. We focus on a contract with payment terms commonly used by large platforms such as Amazon. The platform firm adopts a menu-of-contracts approach to get the service provider to reveal its private information, resulting in optimal quality effort and price decisions that maximize the expected profit of the platform firm. We examine cases where the platform firm should disintermediate the service provider and make and sell the product itself. To study the coordination ability of the proposed contract, we compare the results with those obtained in the case of complete information via various benchmark scenarios.

This paper introduces a model for the diffusion of add-ons that consist of new industrial technologies embedded in mature products. These new technologies are targeted to improve attributes such as the performance, convenience, safety, etc., of the carrier product that incorporates them. Although the rationale for the purchase of the carrier product is driven primarily by mature market factors such as physical wear-out or changing personal needs, the innovative technologies embedded in the design of these products and the advantages they offer provide a competitive edge to the brands that incorporate them. We examine the potential growth of the market share of products that incorporate new technologies within this overall carrier market. We apply our model to the diffusion of green buildings that incorporate better thermal insulation through the use of new materials. For this purpose, we draw on surveys and industry data to estimate the parameters of the model.

Recent studies have revealed that a celebrity9s endorsement of a product or service positively influenced the purchase intention of the consumer. Such findings have created a necessity to identify the specific characteristics of celebrities that most positively influence an advertiser9s target audience. This study offers an innovative model for selecting celebrities that will most effectively endorse a specific product. By implementing adaptive conjoint analysis and genetic algorithms in the advertising process, advertisers will newly approach the method of matching product and celebrity from the perspective of product design.

This paper investigates the use of pricing schemes in subscription services that consist of various combinations of activation, subscription, and cancellation fees. When customers exclusively consider what is directly perceivable, the activation fee starts low and increases as the network grows (penetration strategy), whereas the cancellation fee starts high and decreases as the network grows (skimming strategy). The activation and cancellation fees take various other forms otherwise. The subscription fee remains low at the early stages and increases only when a reasonable number of subscribers is secured. Finally, the authors discuss the theoretical and managerial implications of their findings.

We present a model that forecasts sales and product evolution, based on data on market and industry, which can be collected before the product is introduced. Product evolution can be incremental but can also take place by releasing new generations. In our model adoption of a new product is motivated by attribute improvements (enabled by technology evolution), and firms' attribute improvements strategies are motivated by market growth and directed by market preferences. The interdependency between attributes' improvements and cumulative adoption level makes the problem inherently dynamic. The dependency of attribute levels on adoption levels is assessed using industry and technology analysis. Market preferences and purchase intention response to attribute levels changes are assessed based on a conjoint study. The option of collecting and interpreting data about both demand and supply aspects, before the new product is introduced, enables us to estimate sales and technology progress endogenously rather than to require them as inputs. We demonstrate the method on the hybrid car market.

This paper focuses on the proactive planning of a partial switch of a prescription (Rx) drug brand to over-the-counter (OTC) status within the former's patent-protected life. The planning issues are whether and when to make this switch from the “single-status” Rx drug phase to the “dual-status” Rx+OTC phase with or without the grant of a 3-year market exclusivity period for the OTC drug by the US Food and Drug Administration. We formulate an optimal control problem that leads to a two-phase optimization problem with finite-time horizon involving switching time-dependent switching cost and terminal value. Applying a variational approach, we establish the conditions under which it can be optimal to make the partial switch. Counter to conventional thinking, the grant of market exclusivity is neither necessary nor sufficient for a partial switch before the Rx drug's patent expiry. Further, we show in a functionally specified model-based illustration, involving varying combinations of plausible ratios of OTC and Rx version margins and potential market sizes, that denial of OTC market exclusivity can imply that the firm should advance rather than delay the partial switch, and yield greater savings for Rx drug consumers. Implications for pharmaceutical Rx–OTC switch planners and policymakers are discussed.

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).

We present an analytic approach to address the problem of how sellers can establish and maintain a long-lasting relationship with a buyer and, at the same time, maximize customer lifetime value (CLV). To model the evolution of a relational exchange between a seller and a buyer, we extend a well-known mathematical model of “love dynamics.” The growth of each partner’s commitment to the relationship is a sum of negative and positive terms. The negative term describes each partner’s propensities for opportunism, while the positive terms describe each partner’s trust in the commitment of the other, and the reaction to marketing efforts. The seller controls the evolution of the relationship through social relationships and transactional marketing efforts. The main findings are as follows: (1) Loyal (committed) customers and long-term relationships do not always generate better cash flows, especially when buyers either look for superior current value in each purchase opportunity or are short-term oriented. (2) Without mutual trust between partners, the seller should treat old customers over time as new ones, making the reduction of retention costs impossible. (3) It is only cheaper to retain current customers rather than acquiring new ones if mutual trust between partners overcomes propensities for opportunism and the seller slightly discounts future cash flows.

The dual role of price, as a product attribute signaling quality and as a measure of sacrifice, serving as a benchmark for comparing the utility gains from superior product quality, is now well established in the marketing and economic literature. However, knowledge about their long-run impact and the influence of competition on these effects still remains very sparse. In the current paper, with reference to a dynamic and competitive framework, an analytical model is proposed to help determining optimal decision rules for price incorporating both roles. The main results are as follows: (i) The optimal pricing policy is determined as a Nash equilibrium strategy. (ii) The resulting equilibrium price is higher than an equilibrium that disregards the carryover price effects. (iii) For a symmetric competition, we provide normative rules on how firms should set prices as a function of the perceived quality; particularly, how the price should be set initially, when there is little product familiarity and the perceived quality is low, and how this price should vary as the perceived quality increases. (iv) At steady state, we find that the level of equilibrium margin, in percentage terms, decreases with the elasticity of demand with respect to the brand price, but this decrease is moderated by the elasticity of demand with respect to the brand perceived quality, the cross elasticity of demand with respect to the competitor’s perceived quality and the effect of the competitor’s current price on the firm’s perceived quality deterioration.

In this marketing-oriented era where manufacturers maximize profits through customer satisfaction, there is an increasing need to design a product line rather than a single product. By offering a product line, the manufacturer can customize his or her products to the needs of a variety of segments in order to maximize profits by satisfying more customers than a single product would. When the amount of data on customer preferences or possible product configurations is large and no analytical relations can be established, the problem of an optimal product line design becomes very difficult and there are no traditional methods to solve it. In this paper, we show that the usage of genetic algorithms, a mathematical heuristics mimicking the process of biological evolution, can solve efficiently the problem. Special domain operators were developed to help the genetic algorithm mitigate cannibalization and enhance the algorithm’s local search abilities. Using manufacturer’s profits as the criteria for fitness in evaluating chromosomes, the usage of domain specific operators was found to be highly beneficial with better final results. Also, we have hybridized the genetic algorithm with a linear programming postprocessing step to fine tune the prices of products in the product line. Attacking the core difficulty of cannibalization in the algorithm, the operators introduced in this work are unique.

In this paper, we study the dynamic production location decisions of a manufacturer of a certain branded product. Considering brand-image as a form of goodwill, we extend the well-known Nerlove–Arrow dynamic model by adding both country-image and price. Formulating an optimal control problem for a group of countries in which the cost of production is convexly increasing with country-image, we are able to develop optimal decision rules for a manufacturer regarding the location of production and pricing over time. The resulted optimal policy has a very interesting pattern. Assuming that the demand rises by more than the value of the new brand-image in percentage terms, then, if brand-image is increasing toward a stationary value level, the optimal policy should be to initially locate production in countries with high image and set a high price that signals high quality. Later, the production should gradually shift to countries with lower production costs and lower image and the price lowered until the stationary value level is reached. For brand-images beyond the stationary value level, the location of production should start in a country with low costs and country-image while setting prices that signal relatively low quality. Over time, production should be shifted to countries with gradually higher costs and images while setting higher prices until the brand-image approaches the level of stationary value.

We study the dynamic pricing decisions for competitive network service providers. We assume that each competing firm follows a three-part pricing scheme, which consists of an ongoing membership fee, a usage fee for communications within the networks, and another usage fee for communications across the networks. The difference between the two usage fees is the network-based price discount that allows price discrimination. We study the firms problems as a differential game and establish the optimal pricing policy as a Nash equilibrium feedback strategy depending on only the network sizes (i.e., the number of subscribers). We compare the dynamic network-based discount with the static discount. In the special case of a uniform calling pattern, we find that the firm network-based dynamic discount is always lower than the static discount; we find also that the firm that has a larger network can offer a bigger discount. These results are useful particularly for managers. To get further insights into the dynamic pricing policies, we explore the case of symmetric competition using numerical simulation.

The relevance of transactional and relational marketing variables in relational exchanges is now well established in the marketing literature. However, the knowledge about their relative effectiveness and their optimal mix over time remains very sparse. An analytical model is proposed to help determine optimal decision rules for transactional and relational marketing efforts. Some of the main results are as follows: (a) If the seller benefits from the interaction between the transactional marketing effort and buyer’s commitment, then the seller’s optimal decision rules change over time and depend on the level of the partners’commitment. (b) Otherwise, the seller’s optimal decision rules for the two types of marketing are constant over time. (c) The seller should allocate more resources to relational marketing at the beginning of a relational exchange and, later on, should allocate more resources to transactional marketing.

This study investigates how to dynamically allocate resources with a given budget for advertising through Web portals using keyword-activated banner ads on the Internet. Identifying the factors that affect the potential number of banner ad clickthroughs in each portal, we show that the process of budget allocation between the two types of portals (generic vs specialized) that leads to the largest banner clicksthrough in the long run is an optimal control problem. Using techniques of dynamic programming, we find analytical solutions for the optimal budgeting decisions. Our analysis shows that an advertiser’s optimal portal budgeting depends nonlinearly on the number of visitors who type the same trigger keyword and the average clicksthrough rates, as well as on the advertiser and ad effectiveness. Further, we find that the maximal number of banner clickthroughs from both portals, at time t, depends on the remaining budget until the end of the planning period. The analytical results have useful managerial insight. One of the interesting features of our solution shows that, while a large visitor base may favor the generic portal, other parameters may affect it unfavorably: e.g., lower clickthrough rates of keyword banners from a more heterogeneous audience. Using a specificaction that is consistent with empirical observations, we show that, in the long run, an advertiser must always spend more ad money at the specialized portal.

Defining speed of diffusion as the amount of time it takes to get from one penetration level to a higher one, we introduce a dynamic model in which we study the link between pricing policy, speed of diffusion, and number of competitors in the market. Our analysis shows that, in the case of strategic (oligopolistic) competition, the speed of diffusion has an important influence on the optimal pricing policy. In particular, we find that higher speeds of diffusion create an incentive to strategically interacting firms to lower their prices.

In this paper, we investigate the problem of a dominant company facing entry of a “competitive fringe” (smaller competitor or fringe of smaller competitors). We seek to identify pricing and advertising (or other promotional strategies) that maximize long-term profits for the dominant firm, under possible reactions of the competitive fringe. Two main situations are considered: • The firms in the fringe are price-takers, but they advertise. • The firms in the fringe are not price-takers and advertise. The possibility of a passive reaction, in the case of a very small fringe, is considered as a particular case. We assume that the rate of change of fringe sales is dynamically related to the current sales, price and advertising efforts of both the dominant firm and the fringe. The higher the dominant firm price, the faster fringe entry. The higher dominant firm advertising effort, the slower fringe entry. Fringe advertising and pricing may counterbalance these effects. Formulating a dynamic game, with the dominant firm as a leader and the fringe as a follower, we present a new methodology for providing time-invariant feedback Stackelberg equilibrium. The methodology relies on finding the relationship between the co-state variables and the state variable. The equilibrium solution is obtained in an implicit form by solving a set of two backward differential equations. To show the applicability of our solution to real situations, we use data from the U.S. long-distance market and find optimal decision rules for AT&T facing the entry of MCI and Sprint during the 1980–1990 period. The feedback equilibrium indicates that while AT&T's price is decreasing when fringe (MCI and Sprint) sales increase, the fringe price is increasing. AT&T's advertising is increasing with fringe sales while the fringe's advertising increases and then decreases. The comparison with actual behavior indicates that AT&T has adhered closer to the optimal solution in both price and advertising than the fringe.

This article examines the pricing decision of a provider of network services in the face of a growing market of customer bases that join the network and then have a demand for the service. The authors find the optimal pricing policy consisting of an ongoing membership fee and a usage price that maximizes the sum of discounted profits. Consistent with empirical observations, the authors assume that the average usage demand declines with the number of customers. The authors find that the optimal policy consists of a penetration strategy for the membership fee, low at the beginning, increasing with network size, and a skimming strategy for the usage price, starting high and declining later. The intuition behind the results is that if early adopters are heavy users, it is better to increase network size through a low membership fee and have a high usage price for the heavy users initially.

We introduce a general objective function, which incorporates competitive situations, such as conservative, punitive, and predatory advertising. Linking together the particular situations into a two-parameter family of max–min problems, and using the Lanchester model to describe the dynamics of the market, a bilinear-quadratic differential game is obtained. For this game, we find saddle-point feedback time-invariant advertising strategies and show when these strategies are Nash equilibrium strategies. In an empirical application involving duopolistic competition in the cola market, we find evidence of a punitive motivation for the advertising strategies.

The general approach to adaptive and dual control is to formulate an optimal stochastic control problem. However, for such an approach only mathematical representations of the solution are available which allow little insight into the structure of the optimal controller. Here, an alternative deterministic approach is presented based upon determining a control in which a disturbance attenuation function remains bounded for all allowable ( L 2 functions) disturbances. The disturbance attenuation function is composed of the ratio of an L 2 function of the desired outputs over an L 2 function of the disturbance inputs. This disturbance attenuation problem is converted to a differential game. For this game, the optimal control law, in a closed-form, is obtained by performing a minmax operation with respect to a quadratic cost function subjected to a bilinear system. The resulting controller is time-varying and depends nonlinearly on the state and the parameter estimates vector, and on an associated Riccati-type matrix. We provide insights into the structure of the resulting dual controller and illustrate the method by two examples. One of the examples is an application to marketing, to set promotional spending of a company, considering that the effect of promotional effort on sales is unknown.

This paper considers the nonpreemptive priority queue with MAP(Markovian Arrival Process) arrivals. Since MAPis weakly dense in the class of stationary point processes, it is a fairly general arrival process. Service times of customers of each priority class are independent and identically distributed according to a general distribution function that may differ among priority classes. Using both the generating function technique and the matrix analytic method, we derive various formulas for the marginal queue length distribution of each class. Further, we provide the delay cycle analysis of the waiting time distribution of each class and characterize its Laplace-Stieltjes transform.

This study extends the literature of dynamic advertising competition by allowing oligopoly competition and market expansion that results from advertising. We find how advertising actions affect market development and how, conversely, market development influences advertising policies over time. Modelling the competition by a differential game, we solve for both time-variant closed-loop and time-invariant feedback Nash equilibrium strategies. The time-variant closed-loop strategy depends on a firm's own sales rates and the time-invariant feedback strategy depends on the growth of the market. We discuss the marketing implications of the results. Copyright © 1999 John Wiley & Sons, Ltd.

Satisfaction Guaranteed is defined as a selling policy assuring that no consumer is worse off after purchase. The authors show that for a wide spectrum of guarantee policies, the most profitable policy is a Satisfaction Guaranteed policy. Setting a price equal to the willingness to pay of satisfied customers, but generously compensating dissatisfied customers for all costs involved, this policy can be a “creative device” to capture back-added economic value created for consumers through the guarantee. Comparing this policy with a no-guarantee policy, a Satisfaction Guaranteed policy comes with a higher price in a monopoly market and in a competitive market. Conditions under which selling with a Satisfaction Guaranteed policy is more profitable than selling without it are derived. Although this policy seems to be an attractive offer to consumers, the authors show that because of its high price, it may not. Easy-to-satisfy consumers are better off without the Satisfaction Guaranteed policy.

In many business sectors such as airlines, hotels, trucking, and media advertising, customers' arrivals and willingness to pay are uncertain. Managers must decide whether to quote a price low enough to guarantee early sales, or to quote a higher price and risk that some units remain unsold. In allocating capacity, they face a trade-off between two types of potential losses; (1) Yield loss—selling at a low price, and losing a better price later, and (2) Spoilage loss—waiting in vain to sell at a high price, and losing the opportunity of an earlier low price offer. Yield loss means that consumers who value the product most do not get to use it, and spoilage loss means that valuable products are wasted because no consumers get to use them. Sellers typically hedge against the risk of spoilage loss by selling some units early at low prices, and against the risk of yield loss by blocking some units in hope of selling them later at a high price. In this paper we show that the use of overselling with opportunistic cancellations can increase expected profits and improve allocation efficiency. Under this strategy, the seller deliberately oversells capacity if high-paying consumers show up, even when capacity is already fully booked. The seller then cancels the sale to some low-paying customers while providing them with appropriate compensation. We derive a new rule to optimally allocate capacity to consumers when overselling is used, and show that overselling helps limit the potential yield and spoilage losses. Yield loss is reduced because the seller can capture more high-paying customers by compensating low-paying customers who give up their right to the product. Spoilage loss is reduced because the compensation decreases the price spread perceived by the seller, and as a result, the seller is less anxious to speculate and “block” units. Overselling with opportunistic cancellations assures that the product will be sold to consumers who value it most. This means that “everybody wins”, and resources are allocated more efficiently than in conventional selling.

This paper address the managerial problem of promotional budgeting and media allocation in a dynamic competitive framework. We develop an extended Lanchester model that is able to analyze multi-instrument promotion in an oligopoly. The competitors, each with a different initial position as well as economic value of the market share and communication effectiveness, adopt the strategy of maximizing their net present value of discounted profits, taking the other players' actions into account. The resulting differential game is solved using a novel method, providing both the open-loop strategy and the closed-loop strategy for each firm. We prove that our solution is a global Nash equilibrium. We develop a simple formula, that, when applied to an open-loop strategy, readily generates a feedback strategy. We also show that for both open- and closed-loop strategies, the proportion of the budget allocated to each instrument is invariant with time and depends only on instrument effectiveness. We illustrate the results and provide several managerial rules and discuss their application in practice. Finally, we show that our model favorably compares with other model in the literature in explaining actual data.

Using the Lanchester model to describe the dynamics of the market where two firms compete for customers by advertising, we solve the problem of determining an optimal advertising strategy for maximum discounted profits. We develop both open- and closed-loop strategies and explain the relationship between them. Using a new mathematical approach, we prove that our closed-loop solution is a global Nash equilibrium. The closed-loop strategy is time-variant and depends linearly on the actual market share. The time-variant coefficient incorporates the discount factor, its computation requires the solution of a backward differential equation and a set of two nonlinear differential equations for an initial value problem. The closed-loop advertising expenditures are proportional to the open-loop advertising expenditures and to the square of the competitor's actual market share. This provides a very practical adaptive control rule that allows the manager to adjust the actual advertising expenditure and to deviate from budget. We illustrate the use of our control rule, using data for the period 1968–1984 of the Cola War Marketing implications of the results are provided.

This study extends the time-variant closed-loop strategy of Fruchter and Kalish (1997) to the n-player advertising game. We demonstrate that solving an n-player game using 2 players results in overadvertising.

Given a complex-valued function f which depends on m real variables s_1,\cdots,s_m and n complex parameters A_1,\cdots,A_n , we describe a method of finding the zero set V of all zeros of f in some given set G in R^m when each parameter A_i is allowed to vary in some given set K_i in the extended complex plane \overline{\bf C} = {\bf C} \cup{\infty} . This mathematical tool is applied in the paper to determine the complete space of output (or state) feedback gains, which allows robust stabilization of a linear MIMO system under uncertainty conditions. The system may be continuous or discrete. Also, the stabilization may be "relative," i.e., with safety margins. Design examples are provided.