Market Share Attraction Model Research Articles

An explicit Nash equilibrium for a market share attraction game

In competitive marketing, the speed of generating the best price has become as critical as its reliability. In this study, we aim to design a practical marketing management tool. We consider a non-cooperative marketing environment with multiple substitute products, where total market size is moderately price-sensitive. The price-demand relations are determined by a market share attraction model, where the attraction of each product is a linear function of its price. The product's brand image is reflected in the parameters of this linear function. For the general case of multiple substitute products, we derive explicit expressions for the best-response functions. For the specific case of two substitute products, we derive closed form expressions for the prices at Nash equilibrium. These expressions help managers in changing their marketing instruments other than price, so as to obtain substantial individual profits. We show how our closed form Nash equilibrium enables the examination of the profit loss due to competition. Relevant for practice is the fact that our model can be easily calibrated. We provide a simple procedure for estimating the model parameters.

The optimal delivery time and order quantity in an oligopoly market with time-sensitive customers.

With the development of e-commerce, delivery time is regarded as a key competitive advantage in an oligopoly market, as shortening the delivery time can stimulate demand for products. Many firms adopt a variety of strategies to shorten delivery time, and holding sufficient inventory is reported as an effective way. This study integrates a market share attraction model based on delivery time competition with the traditional inventory model to determine the optimal delivery time and order quantity. With the use of supermodular game method, we investigate the effect of changes in marketing and operations factors on the equilibrium delivery time and order quantity in non-dominated and dominated oligopolistic markets. The results reveal that the equilibrium delivery time and order quantity exhibit a directional response to changes in marketing and operations factors, and the response differs between the non-dominated oligopoly and the dominated oligopoly. Furthermore, under a cooperative oligopolistic market with asymmetry, it is beneficial for the firms with high competitive strength to adopt the delivery time strategy, but it fails to do so for the firm with the low competitive strength. Lastly, numerical analysis suggests that marketing factors play a more important role in affecting equilibrium measures than operations factors.

Dynamics analysis for a discrete dynamic competition model

In this paper, the dynamics of a discrete market share attraction model are investigated. It shows that the system can undergo flip bifurcation and chaos. The stability and bifurcation of a market share attraction model are analyzed by using the bifurcation theory and the center manifold theorem. The system displays complex dynamical behaviors, including period-1, 2, 4, 6, 8, 16 orbits, invariant cycle, a cascade of period-doubling, quasi-periodic orbits, and the chaotic sets. Numerical simulations illustrate the analysis and results.

Stochastic sensitivity analysis of concentration measures

The paper extends the traditional approach to measuring market concentration by embracing an element of stochasticity that should reflect the analyst’s uncertainty associated with the future development regarding concentration on the market. Whereas conventional practice relies on deterministic assessments of a market concentration measure with the use of current market shares, this says nothing about possible changes that may happen even in a near future. The paper proposes to model the analyst’s beliefs by dint of a suitable joint probability distribution for future market shares and demonstrates how this analytic framework may be employed for regulatory purposes. A total of four candidates for the joint probability distribution of market shares are considered—the Dirichlet distribution, the conditional normal distribution, the Gaussian copula with conditional beta marginals and the predictive distribution arising from the market share attraction model—and it is shown how their hyperparameters can be elicited so that a minimum burden is placed on the analyst. The proposed procedure for stochastic sensitivity analysis of concentration measures is demonstrated in a case study oriented on the Slovak banking sector.

Preferred supplier contracts in post-patent prescription drug markets.

In recent years, the expiration of patents for large drug classes has increased the importance of post-patent drug markets. However, previous research has focused solely on patent drug markets. In this study, the authors evaluate the influence of preferred supplier contracts, the German approach to tendering, in post-patent drug markets using a hierarchical market share attraction model. The authors find that preferred supplier contracts are a powerful strategic instrument for generic manufacturers in a highly competitive environment. They quantify the effects of signing a preferred supplier contract and show that brand-name manufacturers are vulnerable to tendering. Therefore, brand-name manufacturers should readjust their strategies and consider including preferred supplier contracts in their marketing mix. In addition, the authors employ a simulation to demonstrate that a first-mover advantage might be gained from signing a preferred supplier contract. Furthermore, their results can be used as a blueprint for decision makers in the pharmaceutical industry to assess the market share effects of different contracting strategies regarding preferred supplier contracts.

Spillovers in Attribute Advertising

AbstractWhen firms advertise a vertically differentiated product attribute, they increase the weight consumers put on that attribute. This creates a spillover effect as one firm’s advertising can increase demand for other firms that also have the attribute. I develop a market share attraction model and find that as spillover increases, firms advertise less. Profit can be increasing or decreasing in spillover depending on the particular industry environment. Spillover lends a “public good” quality to advertising and firms free-ride in equilibrium. An advertising ban has an ambiguous effect on the profits of firms with the attribute, but always increases profits of firms without the attribute.

A dynamic marketing model with best reply and inertia

In this paper we consider a nonlinear discrete-time dynamic model proposed by Farris et al. (2005) as a market share attraction model with two firms that decide marketing efforts over time according to best reply strategies with naïve expectations. The model also considers an adaptive adjustment toward best reply, a form of inertia or anchoring attitude, and we investigate the effects of heterogeneities among firms. A rich scenario of local and global bifurcations is obtained even with just two competing firms, and a comparison is proposed with apparently similar duopoly models based on repeated best reply dynamics with naïve expectations and adaptive adjustment.

Estimating multiplicative competitive interaction model using kernel machine technique

We propose a novel way of forecasting the market shares of several brands simultaneously in a multiplicative competitive interaction model, which uses kernel regression technique incorporated with kernel machine technique applied in support vector machines and other machine learning techniques. Traditionally, the estimations of the market share attraction model are performed via a maximum likelihood estimation procedure under the assumption that the data are drawn from a normal distribution. The proposed method is shown to be a good candidate for forecasting method of the market share attraction model when normal distribution is not assumed. We apply the proposed method to forecast the market shares of 4 Korean car brands simultaneously and represent better performances than maximum likelihood estimation procedure.

Supply chain coordination with shelf‐space and retail price dependent demand and heterogeneous retailers

AbstractWe consider supply chain coordination in which a manufacturer supplies some product to multiple heterogeneous retailers and wishes to coordinate the supply chain via wholesale price and holding cost subsidy. The retail price is either exogenous or endogenous. The market demand is described by the market share attraction model based on all retailers'shelf‐spaces and retail prices. We obtain optimal solutions for the centralized supply chain, where the optimal retail pricing is a modified version of the well‐known cost plus pricing strategy. We further get feasible contracts for the manufacturer to coordinate the hybrid and decentralized supply chains. The manufacturer can allocate the total profit free to himself and the retail market via the wholesale price when the retail price is exogenous, but otherwise he cannot. Finally, we point out that different characteristics of the retail market are due to different powers of the manufacturer, and the more power the manufacturer has, the simpler the contract to coordinate the chain will be. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010

Estimating the Market Share Attraction Model using Support Vector Regressions

We propose to estimate the parameters of the Market Share Attraction Model (Cooper and Nakanishi, 1988; Fok and Franses, 2004) in a novel way by using a nonparametric technique for function estimation called Support Vector Regressions (SVR) (Smola, 1996; Vapnik, 1995). Traditionally, the parameters of the Market Share Attraction Model are estimated via a Maximum Likelihood (ML) procedure, assuming that the data are drawn from a conditional Gaussian distribution. However, if the distribution is unknown, Ordinary Least Squares (OLS) estimation may seriously fail (Vapnik, 1982). One way to tackle this problem is to introduce a linear loss function over the errors and a penalty on the magnitude of model coefficients. This leads to qualities such as robustness to outliers and avoidance of the problem of overfitting. This kind of estimation forms the basis of the SVR technique, which, as we will argue, makes it a good candidate for estimating the Market Share Attraction Model. We test the SVR approach to predict (the evolution of) the market shares of 36 car brands simultaneously and report promising results.

When Five is a Crowd in the Market Share Attraction Model

When Five is a Crowd in the Market Share Attraction Model

When Five is a Crowd in the Market Share Attraction Model

When Five is a Crowd in the Market Share Attraction Model

Analyzing the effects of a brand introduction on competitive structure using a market share attraction model

The introduction of a new brand may change the competitive structure, which concerns the market shares and the marketing instrument elasticities. For example, the new brand can cause intensified price competition and possibly also influence the relative effectiveness of price promotions for the incumbent brands. In this paper, we develop a methodology to statistically test for the various possible changes in the competitive structure, where we focus on weekly scanner data. We develop a market share attraction model with which we can handle a changing number of brands. The usefulness of our approach is illustrated in a simulation experiment where its implementation is compared with various alternative methods. We further develop tests to infer whether there are competitive reactions to an entry. Our illustration to scanner data for the detergent category emphasizes the usefulness of our approach.

On deriving and validating comparative statics of a symmetric model of advertising competition

In this article, a market share attraction model is estimated using a data set of six manufacturers related to the ready-to-eat cereal industry in the US. For each year of the studied period, the market share of each firm is less than 50%, and these market shares are further apart from one another. In the reported application it is demonstrated, for the first time in the literature, that if model parameters change, all rivals in the industry should adjust their advertising spending in a manner consistent with the symmetric competitive structure for which all market shares are equal. Implications of this important finding are discussed. Scope and purpose Using a market share model of advertising competition and following a game theoretic approach, this study examines analytically and empirically the sensitivity of optimal advertising to changes in model parameters in a setting of symmetric competition. The results presented in the paper suggest that the proposed approach is useful for a firm to ascertain how to adapt its advertising strategy in response to changes in the market to maintain or enhance its position.

Multistability and path dependence in a dynamic brand competition model

We introduce a dynamic market share attraction model where agents are boundedly rational. They follow a simple rule of thumb which is based on marginal profits to determine their actions over time. We show that multistability arises, i.e. several attractors coexist. In such a situation the selected long run state becomes path-dependent, and a thorough knowledge of the basins and their structure becomes crucial for the researcher to be able to predict the long run outcome of the economic system. We show that the basins of the coexisting attracting sets might have quite complicated structure. Furthermore, we give insights into the mechanism which is responsible for the creation of complex basins of attraction.

Why is Five a Crowd in the Market Share Attraction Model: The Dynamic Stability of Competition

As economists have increasingly accepted the notion that non-equilibrium behavior may be a reflection of the real world, interest has grown in modeling the emergence of turbulence as well as equilibrium. Earlier work by two of the authors used simulation to conduct a non-equilibrium analysis of a market where customer reaction followed the market share attraction model. These simulations demonstrated that even the relatively simple competitive behavior of optimizing one's own spending levels could lead to surprising instability. Optimizing one's own spending requires either that firms use their competitors' last-period budgets and the MSA model to determine a profit-maximizing budget for the next period or that firms use current dollar marketing-dollar profit response to set budgets for next period. Application of either logic will lead to dynamic instability when the number of competitors exceeds a threshold level of four. This study provides an analytical explanation for the emergence of this instability and demonstrates the relationship between this system of competing firms and the standard logistic map. This work also extends the original model formulation to identify conditions that affect the existence or level of the instability thresholds.

Number of Competitors and Dynamic Stability of Competition: Five is a Crowd in the Market Share Attraction Model

As economists have increasingly accepted the notion that non-equilibrium behavior may be a reflection of the world, interest has grown in modeling the emergence of turbulence as well as equilibrium. It is well established that competitive actions and the associated reactions can destabilize a previously stable market. Earlier work by two of the authors used simulation to conduct a non-equilibrium competitive analysis of a market where consumer reaction followed the market share attraction model. These simulations demonstrated that even the relatively simple competitive behavior of optimizing ones own spending levels while assuming stable competitive behavior can lead to surprising instability. The basic logic of the market share attraction model is easy to accept. Given the amount of work done to fine-tune applications of this model, we believe the logic of the model helps determine the behavior of real firms. As shown in earlier work, however, application of the logic may lead to dynamic instability when the number of competitors exceeds a threshold level of three or four. This study provides an analytical explanation for the emergence of this instability when the number of competitors exceeds three or four. This work will also extend the original model formulation to identify other conditions that may affect the existence or level of the instability thresholds.

Analysis of global bifurcations in a market share attraction model

In this paper we demonstrate how the global dynamics of an economic model can be analyzed. In particular, as an application, we consider a market share attraction model widely used in the analysis of interbrand competition in marketing theory. We analyze the local and global dynamic properties of the resulting two-dimensional noninvertible dynamical system in discrete time. The main result of this paper is given by the study of some global bifurcations that change the structure of the attractors and their basins. These bifurcations are investigated by the use of critical curves, a powerful tool for the analysis of the global properties of noninvertible two-dimensional maps.

Path Dependencies and the Long-term Effects of Routinized Marketing Decisions

The purpose of this paper is to discuss a simulation of marketing budgeting rules that is based on a simplified version of the market share attraction model. The budgeting rules are roughly equivalent to those that may be used in practice. The simulation illustrates the concept of path dependence in dynamic marketing systems and shows how it might result from decision rules potentially applied by marketers and retailers. Path dependence results from positive feedback in dynamic systems that imparts momentum to market choices. Where the potential for path dependence exists, there are implications for defining and measuring long-term effects of marketing decisions in a way that is meaningful to managers and researchers. In the simulations presented we show that limited retail assortments may contribute to path dependence when firms use either percentage-of-revenue rules or “market learning” experiments to set budgets. While other budgeting procedures (e.g., matching competition) may stabilize market share, this stability in the share dimension comes at the cost of instability for budgets and profits.

Order of Entry as a Moderator of the Effect of the Marketing Mix on Market Share

Order of entry has been demonstrated to have a significant effect on market share. A number of explanations for this effect have been suggested in the marketing and strategy literatures. To date, the market share advantage gained by pioneers has typically been treated as a main effect—an automatic regularity. Treating order-of-entry as a main effect implies that there is no penalty on the effectiveness of a brand's marketing instruments for late entry and that a late entrant can compensate for being late by dedicating sufficient marketing resources to their product. In this study, we investigate the influence of order-of-entry into a market on the effectiveness of a firm's marketing mix decisions by asking the question, “Can followers compensate for not being first by their marketing mix decisions?” Also, even if they can compensate for being late, does this effort become increasingly more difficult with later entry? That is, are there asymmetries in the effectiveness of a brand's marketing mix variables that relate to its order of entry into the market, or as has been typically assumed to date, is order of entry strictly a main effect? An asymmetry exists, for example, if the market response to advertising is different for the first entrant versus the second or third entrant. An asymmetry also exists if the effects of, say, a price change by the first entrant on the second entrant are different than the effects on the third entrant. We develop a market share attraction model where the parameters vary as a function of order-of-entry. Our main contribution is in modeling the sources of order-of-entry advantage as asymmetries in the effectiveness of a brand's marketing instruments. Hence, distinct from previous research we explain why there are inherent order-of-entry effects. This paper is potentially of interest to researchers developing market share models and studying the effectiveness of marketing-mix variables. The substantive implication of our results concern directly academics interested in marketing strategy as well as the practicing marketing strategists. We model asymmetries in the market response of early entrants versus late entrants using data from two durables and three nondurables categories. With one exception, all data sets are established from the inception of the category and hence do not suffer from the possible bias of excluding pioneers who have failed. Results show that asymmetries in the effectiveness of a brand's marketing mix variables are an essential source of order-of-entry effects; we find that the main effects of order of entry are minimal. Order-of-entry effects do not necessarily lead to lower shares, but overcoming these effects is not without substantial cost to the late entrant. Our results support previous research that has demonstrated advantages to early entry. In addition, we provide guidelines for how late entrants should compete. Later entry tends to reduce a competitor's price sensitivity, suggesting that they not instigate in a price war with earlier entrants in order to gain share. Order-of-entry tends to decrease response to quality and to promotion. To achieve the same impact on market share, later entrants need a bigger change in quality and need to spend more on promotion. Our data did not support an asymmetric effect on advertising.