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.     

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.     

Retail competition and cooperative advertising

We consider a cooperative advertising channel consisting of a manufacturer selling its product through a retailer in competition with another independent retailer. The manufacturer subsidizes its retailer’s advertising only when a certain threshold is positive. Moreover, the manufacturer’s support for its retailer is higher under competition than in its absence.     

A differential game model of the marketing-operations interface

In the development of their dynamic strategies, the marketing and operations functions within a firm have differing objectives, and conflict between the two functions is common. The strategic interdependence involving marketing and operations decisions is modeled as a noncooperative differential game. Demand is assumed to be a function of price and advertising goodwill, and marketing controls price and advertising to maximize its discounted stream of revenue net of advertising costs. Backlogging is allowed, and operations controls production to minimize its discounted stream of production and backlog costs. A feedback Nash equilibrium is derived for the game, which allows a solution of the system of differential equations for goodwill and backlog, and is analyzed to study the nature of the dynamic strategies for price, advertising, and production.     

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 dynamic free-entry oligopoly with sluggish entry and exit adjustments

We study a dynamic free-entry oligopoly with sluggish entry and exit of firms under general demand and cost functions. We show that the number of firms in a steady-state open-loop solution for a dynamic free-entry oligopoly is smaller than that at static equilibrium and that the number of firms in a steady-state memoryless closed-loop solution is larger than that in an open-loop solution.     

Reducing competitors in Cournot-Puu oligopoly

The aim of this paper is to investigate whether an oligopoly given by isoelastic demand function and constant marginal costs converges to a duopoly, that is, all the firms except for two of them will not produce anything in future.     

Optimal pricing and advertising in a durable-good duopoly

This paper analyzes dynamic advertising and pricing policies in a durable-good duopoly. The proposed infinite-horizon model, while general enough to capture dynamic price and advertising interactions in a competitive setting, also permits closed-form solutions. We use differential game theory to analyze two different demand specifications – linear demand and isoelastic demand – for symmetric and asymmetric competitors. We find that the optimal price is constant and does not vary with cumulative sales, while the optimal advertising is decreasing with cumulative sales. Comparative statics for the results are presented.     

The nested consideration model: Investigating dynamic store consideration sets and store competition

The nested logit model has been widely used to study nested choice. A typical example of such nested choice is store patronage and brand choice. An important limitation of the nested logit model is that it assumes that all alternatives at both levels of the nest are available in the choice set of the consumer. While there is a wide literature on the incorporation of restricted choice sets into the logit model, the logical extension of this analysis to nested restricted choice sets has not been pursued in the literature. In this study we develop a nested consideration model that integrates store choice and brand choice incorporating the formation of dynamic restricted choice sets of both stores and brands. We term the model the nested consideration model and derive the related probabilities in a manner analogous to the well-known nested logit model. In an empirical illustration, we find that the nested consideration model shows better prediction than nested logit models (with the same explanatory variables). We find that it is important to account for dynamic store consideration sets rather than static sets or store loyalty measures. We also conduct simulations to demonstrate the importance of the nested consideration set model for correct pricing and store location decisions of business managers.     

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.     

A note on oligopoly exploitation of common-pool renewable resources

This note derives the linear Feedback Nash equilibrium of a differential oligopoly game of exploitation of a common-pool renewable resource, and compares and contrasts it with social optimum. The case of regulated entry by means of a license fee is also considered. Two main results are derived. First, the steady-state oligopoly price can be increasing in the (exogenously given) number of firms. Second, an optimal license fee exists that induces the (endogenously given) number of firms to behave efficiently.     

Delayed effects of cooperative advertising in goodwill dynamics

This paper proposes a tool to control cooperative advertising which increases the goodwill of companies operating in a competitive market. We introduce the lag between advertising exposure and customer reaction in the goodwill dynamics evolved à la Nerlove–Arrow. As a result, we obtain a cooperative differential game with immediate and delayed effects of control variables for which we investigate the optimal solution. We examine the role the pre-coalition programmes and the length of delayed response in generating goodwill.     

A tactical model for resource allocation and its application to advertising budgeting

Models for optimal product positioning have received considerable attention by marketing researchers and marketing scientists over the past decade. Typically, optimizing models take the viewpoint that the manager wishes to find a specific vector of product attribute levels that, in the face of competitors’ product profiles, maximizes the firm’s market share (or, perhaps, return) over some designated planning horizon. This class of models emphasizes long run strategic modeling.In contrast, the authors introduce a tactical, short-term model, called SALIENCE, whose purpose is to allocate sales efforts in such a way as to increase the relative importance of attributes for which the sponsoring firm’s current product has a (possibly temporary) differential advantage. In this case emphasis is on short-run, tactical decision making.We describe the SALIENCE model, both informally and mathematically. The model is applied, illustratively, to a real (disguised) study of overnight air shipment delivery.     

A duopolistic model of dynamic competitive advertising

This paper proposes a differential game model of competitive advertising decisions for non-durable products by extending the Lanchester model and the Deal model of competitive advertising in the literature. The proposed model is compared empirically with the Lanchester model for model fitting and forecast accuracy. It is shown that the model is suitable for an actual market and out-performs the Lanchester model in forecast accuracy. The model provides a sensible modeling alternative to the Lanchester model for the study of dynamic competitive advertising decisions. Necessary and sufficient conditions for open-loop and closed-loop Nash equilibrium solutions to the model are discussed. A numerical algorithm for open-loop and closed-loop Nash strategies to the model is developed.     

Differential game approach to pricing and advertising decisions

This study proposes a model to make concurrent decisions on dynamic pricing and advertising to maximise firms' profitability over an infinite time horizon in a duopoly market. To this end, the Nerlove-Arrow pricing and advertising model is designed in the presence of shifting costs in a dynamic duopolistic competition as a differential game. The Nash equilibrium solution is defined based upon a set of Hamilton–Jacobi–Bellman. Four scenarios are applied for economic interpretations and the efficacy of the model.     

A model of far-sighted electoral competition

A model is described in which candidates adopt positions in sequences of election contests against opponents randomly drawn from a large population. Symmetric steady-state equilibria of the model require rational selection of positions by all candidates against the aggregated behavior of the population, taking into account constraints which an individual's current selections impose on his future selections.     

Price coordination in distribution channels: A dynamic perspective

In this study, we investigate two important questions related to dynamic pricing in distribution channels: (i) Are coordinated pricing decisions efficient in a context where prices have carry-over effects on demand? (ii) Should firms practice a skimming or a penetration strategy if they choose to coordinate or to decentralize their activities? To answer these questions, we consider a differential game that takes place in a bilateral monopoly where the past retail prices paid by consumers contribute to the building of a reference price. The latter is used by consumers as a benchmark to evaluate the value of the product, and by firms to decide whether to adopt a skimming or a penetration strategy.     

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.     

A dynamic competition model of regime change

A dynamic competition model for an oppressive government opposed by rebels is proposed, based on coupled differential equations with constant coefficients. Depending on their values, the model allows scenarios representing a stable, oppressive government and violent regime change. With constant coefficients, there can be no limit cycles. However, cycles emerge if rebels and governments switch characteristics after a revolution, if resources change hands and rebel motivations switch from grievance to greed. This mechanism is proposed as an explanation for the establishment of a new repressive regime after the overthrow of a similar regime.     

On the feedback solutions of differential oligopoly games with hyperbolic demand curve and capacity accumulation

To safeguard analytical tractability and the concavity of objective functions, the vast majority of models belonging to oligopoly theory relies on the restrictive assumption of linear demand functions. Here we lay out the analytical solution of a differential Cournot game with hyperbolic inverse demand, where firms accumulate capacity over time à la Ramsey. The subgame perfect equilibrium is characterized via the Hamilton–Jacobi–Bellman equations solved in closed form both on infinite and on finite horizon setups. To illustrate the applicability of our model and its implications, we analyze the feasibility of horizontal mergers in both static and dynamic settings, and find appropriate conditions for their profitability under both circumstances. Static profitability of a merger implies dynamic profitability of the same merger. It appears that such a demand structure makes mergers more likely to occur than they would on the basis of the standard linear inverse demand.