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.     

Overcoming the drawbacks of a revenue-sharing contract through a support program

In a marketing channel governed by goodwill dynamics, players adjust their pricing and advertising strategies when shifting from a wholesale price contract (WPC) to a revenue sharing contract (RSC). We demonstrate that this shift is not payoff-Pareto-improving when the retailer, who is the player transferring the share of revenues, is myopic. Further, we identify the conditions under which the negative effects an RSC creates may be alleviated when the manufacturer offers a support program. Finally, contrarily to operational coordination instruments such as an RSC, a support program always leads to a payoff-Pareto-improving situation and thus should be preferred by firms to reach coordination.     

The impact of product recall on advertising decisions and firm profit while envisioning crisis or being hazard myopic

The occurrence of a product recall can have a disastrous effect on the firm responsible for the recall. Any major recall by a firm can negatively affect the goodwill of the firm. Consequently, the firm incurs a substantial indirect cost due to decline in sales and loss in profit. Moreover, a competitor’s opportunistic reaction can intensify the recalling firm’s damages. Strategic use of advertising recovers lost goodwill and mitigates the damages made by a product recall. In this paper, using a goodwill based model under a differential game framework, we analyze the equilibrium strategies of two competing manufacturers when either one firm or both can issue a product recall at a random time, and investigate (i) the firms’ equilibrium advertising strategies (ii) analyze the impact of the recall on a firm’s profit (iii) introduce and investigate the effect of “hazard myopia” (a firm’s inability to foresee the crisis likelihood) on a firm’s advertising decisions and profit. Our study finds that the equilibrium advertising strategies of competing firms depend on the impact and likelihood of the recall. Notably, we find that when both the firms are focal firms without the prior knowledge of who will recall first in a planning horizon, adjusting optimal advertising at an appropriate time is essential. Surprisingly, a product-recall with a minor impact can increase the focal firm’s long-term expected profit. On the other hand, hazard myopia can be profitable if the long-term effect of the recall is small. Our findings suggest that advertising levels of firms should differ in pre-recall and post-recall regimes depending on the impact and likelihood of the recall.     

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.     

A goodwill model with predatory advertising

We investigate the dynamic advertising policies of two competing firms in a duopolistic industry, assuming a predatory phenomenon between their advertising campaigns. The resulting model is a differential game which is not linear-quadratic. We show that there exists a Markovian Nash equilibrium, and that it leads to time constant advertising strategies. According to this model, predatory advertising produces a negative externality: the interference between the advertising campaigns decreases the total demand of the market.     

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.     

On the superiority of pulsing under a concave advertising market potential function

The authors study the superiority of advertising pulsing policy (turning advertising on and off in a cyclic fashion) over its uniform (constant spending) counterpart that costs the same under the assumption that sales dynamics follow a modified Vidale–Wolfe aggregate advertising model. The authors show that pulsing can be superior if the product of the concave market potential function and the linear or concave advertising response function is convex in advertising. Similar to previous studies in the literature, the average undiscounted profit over the infinite planning horizon is considered as a performance measure according to which alternative advertising pulsation policies are compared.     

Advertising in a Differential Oligopoly Game

We illustrate a differential oligopoly game where firms compete à la Cournot in homogeneous goods in the market phase and invest in advertising activities aimed at increasing the consumers reservation price. Such investments produce external effects, characterizing the advertising activity as a public good. We derive the open-loop and closed-loop Nash equilibria, and show that the properties of the equilibria depend on the curvature of the market demand function. The comparative assessment of these equilibria shows that the firms advertising efforts are larger in the open-loop equilibrium than in the closed-loop equilibrium. We also show that a cartel involving all the firms, setting both output levels and advertising efforts, may produce a steady state where the social welfare level is higher than the social welfare levels associated with both open-loop and closed-loop noncooperative settings.     

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.     

Persuasive advertising under Bertrand competition: A differential game

We investigate a linear state differential game of advertising, under Cournot and Bertrand competition. A unique saddlepoint equilibrium exists if the marginal cost of advertising is sufficiently low. Bertrand competition entails more intense advertising than Cournot competition, since increasing market size is more important to firms when competition is tough.     

Supply chain coordination through integration of innovation effort and advertising support

This study integrates firms’ innovation and advertising decisions in a two-echelon supply chain, where a monopoly manufacturer sells products to ultimate consumers through an autonomous retailer. Considering that both innovation and advertising contribute to the product demand, we first investigate the optimal equilibriums of channel members under two different game structures: the non-cooperative and cooperative. In the non-cooperative structure, the manufacturer controls the innovation effort and wholesale price while the retailer controls the advertising rate and retail pricing. In the cooperative structure, the manufacturer agrees to share part of retailer’s advertising expenditure. We find that both the optimal operation and marketing decisions are sensitive to effects of innovation and advertising on demand as well as the manufacturer’s cost reduction coefficient due to innovation. Further, we find that the manufacturer always prefers cooperation. Meanwhile, only when the firms’ investments significantly contribute to the market mechanism, does the retailer have incentive to implement a cooperative program. In addition, we further propose a new two-way subsidy policy to coordinate channel members’ business functions.     

Modeling the effect of campaign advertising on US presidential elections when differences across states matter

We provide a stochastic electoral model of the US Presidential election where candidates take differences across states into account when developing their policy platforms and advertising campaigns. Candidates understand the political and economic differences that exist across states and voters care about candidates’ policies relative to their ideals, about the frequency of candidates’ advertising messages relative to their ideal message frequency, their campaign tolerance level, and vote taking into account their perceptions of candidates’ traits and competencies with their vote also depending on their sociodemographic characteristics. In the local Nash equilibrium, candidates give maximal weight to undecided voters and swing states and little weight to committed voters and states. These endogenous weights pin down candidates’ campaign and depend on the probability with which voters choose each candidate which depends on candidates’ policies and advertising campaigns. Weights vary across candidates’ policy and ad campaigns, reflecting the importance voters in each state give to the two dimensions and the variation in voters’ preferences across states.     

Hybrid subgames and copycat games in a pulsing model of advertising competition

Two recent papers,^6,7 introduced the game of pulsing competition (PC) in advertising together with its related subgames of alternating pulsing competition (APC) and matching pulsing competition (MPC) for a duopoly. Following a game theoretic approach in conjunction with a continuous Lanchester model, the above authors basically concluded that when at least one of the response functions is convex, generalising monopolistic advertising pulsation results to a competitive setting might not be adequate. This paper expands the scope of the PC game by incorporating in its structure for the first time in the literature, two versions of a hybrid pulsing competition (HPC) subgame. The article compares the payoffs of the four alternative subgames and provides an analytical solution of a special case of the PC game. In addition, the article also introduces for the first time a variant of the PC game designated by ‘the copycat advertising game’ and shows analytically that for such a game the policy of constant advertising spending over time is optimal for both firms irrespective of the shape of their advertising response functions. The paper illustrates at its end how to solve numerically the expanded PC game in its general form using linear programming and how to derive a solution for a copycat advertising game.     

Signaling advertising by multiproduct firms

We consider the use of advertising expenses as quality signals in multiproduct firms, extending previous results on single product firms. In our model, a firm introduces sequentially two products whose qualities are positively correlated. We investigate whether there exist information spillovers from the first to the second market. We show that, when correlation is high, the equilibrium in market 2 depends on the quality reputation the firm has gained in market 1. Moreover, if a firm with a high-quality product 1 wants to separate from its low-quality counterpart, it needs to advertise more in this market than if the qualities of the two products are unrelated. This advertising level signals not only high quality in the first market, but also the likely quality of the second product. Thus, advertising in the first market has information spillovers in the second market.     

A Competitive Advertising Model: Some Theoretical and Empirical Results

Using a modified Lanchester model, this article demonstrates that the policy of constant advertising spending is superior to a cyclic counterpart, provided that the advertising response functions of competing firms are concave. The competitive model is estimated using filter and non-filter cigarette data. The empirical results suggest the presence of over-advertising and that the relative effectiveness and elasticity of filter cigarette advertising are both higher than those of non-filter cigarette advertising.     

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.     

New product advertising in dynamic oligopolies

The success of the introduction of a new product in a market is very sensitive to the marketing decision variables adopted by the firm. In the present paper we are concerned with the question of new product advertising in a heterogeneous oligopoly market consisting of N firms. A dynamic game is formulated to model strategic as well as sales interactions in such a market. Optimal advertising strategies are identified as open-loop Nash solutions.The comments of two anonymous referees are appreciated. The first author wishes to acknowledge support from NSERC (Grant No. OGP0037342).     

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.     

The effects of advertising,prices and distribution on market share volatility

Although the influence of marketing decision variables on market share has received ample attention in the literature, less is known about their effects on volatility. This study attempts to shed light on this issue by empirically examining the effects of advertising, pricing and distribution, not only on market share but also on its volatility, using an EGARCH model. We argue that establishing a link between management-controlled actions, such as advertising, pricing and distribution, and market share volatility may benefit firms seeking to reduce uncertainty in their market share performance. Application of the proposed model to data on two markets (SUVs and Minivans), suggested that advertising, pricing and distribution significantly influence market share volatility.     

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.