Planning marketing-mix strategies in the presence of interaction effects.

Companies spend millions of dollars on advertising to boost a brand's image and simultaneously spend millions of dollars on promotion that many believe calls attention to price and erodes brand equity. We believe this paradoxical situation exists because both advertising and promotion are necessary to compete effectively in dynamic markets. Consequently, brand managers need to account for interactions between marketing activities and interactions among competing brands. By recognizing interaction effects between activities, managers can consider interactivity trade-offs in planning the marketing-mix strategies. On the other hand, by recognizing interactions with competitors, managers can incorporate strategic foresight in their planning, which requires them to look forward and reason backward in making optimal decisions. Looking forward means that each brand manager anticipates how other competing brands are likely to make future decisions, and then by reasoning backward deduces one's own optimal decisions in response to the best decisions to be made by all other brands. The joint consideration of interaction effects and strategic foresight in planning marketing-mix strategies is a challenging and unsolved marketing problem, which motivates this paper.

This paper investigates the problem of planning marketing mix in dynamic competitive markets. We extend the Lanchester model by incorporating interaction effects, constructing the marketing-mix algorithm that yields marketing-mix plans with strategic foresight, and developing the continuous-discrete estimation method to calibrate dynamic models of oligopoly using market data. Both the marketing-mix algorithm and the estimation method are general, so they can be applied to any other alternative model specifications for dynamic oligopoly markets. Thus, this dual methodology augments the decision-making toolkit of managers, empowering them to tackle realistic marketing problems in dynamic oligopoly markets.

We illustrate the application of this dual methodology by studying the dynamic Lanchester competition across five brands in the detergents market, where each brand uses advertising and promotion to influence its own market share and the shares of competing brands. Empirically, we find that advertising and promotion not only affect the brand shares (own and competitors') but also exert interaction effects, i.e., each activity amplifies or attenuates the effectiveness of the other activity. Normatively, we find that large brands underadvertise and overspend on promotion, while small brands underadvertise and underpromote. Finally, comparative statics reveal managerial insights into how a specific brand should respond optimally to the changes in a competing brand's situation; more generally, we find evidence that competitive responsiveness is asymmetric.

Key words: continuous-discrete estimation; dynamic competition; interaction effects; marketing-mix planning; strategic foresight; two-point boundary value problem

History: This paper was received June 19, 2001, and was with the authors 14 months for 4 revisions; processed by William Boulding.

1. Introduction

American corporations collectively spend over $500 billion on marketing activities; even individual companies such as Procter and Gamble spend several billion dollars on advertising and promotion. Consequently, the optimal allocation of marketing resources to multiple activities--referred to as "planning the marketing mix"--is of paramount importance (see Mantrala 2002 for literature review). In the extant literature, dynamic planning models such as Naik et al. (1998) and Silva-Risso et al. (1999) provide decision-support tools to determine advertising schedules and promotional calendars, respectively. These decision-support models, however, ignore the game-theoretic principle of strategic foresight, a notion that requires the brand manager to look forward, i.e., anticipate how other competing brands are likely to make future decisions, and then reason backward, i.e., deduce one's own optimal decisions in response to the best decisions to be made by all other brands. On the other hand, dynamic game-theoretic models that advocate strategic foresight ignore the role of interactions among multiple marketing activities. Such interactions are central to the marketing-mix concept, which "... emphasizes that marketing efforts create sales synergistically rather than independently" (see Gatignon and Hanssens 1987, p. 247; Lilien et al. 1992, p. 5; also see Gatignon 1993 for a literature review).

The joint consideration of both strategic foresight and interaction effects in dynamic response models represents an important gap in the marketing literature. For example, Fruchter and Kalish (1998, p. 22) acknowledge

 
   "... the limitations of current studies [not] to take into 
   account the interactions among the different instruments. 
   A challenge which we see for a future direction 
   is to develop a model which incorporates interactions 
   between promotional instruments." 

The challenging problems arise for the following two reasons. First, as we show later, in the presence of interaction effects, the optimal plans for all activities are interdependent, thereby requiring managers to account for the interactivity trade-offs in budget allocations. In other words, the optimal level to spend on advertising depends on the optimal level to spend on promotion (and vice versa). Second, managers need to know the joint effectiveness of marketing activities of all other brands to be able to determine their own optimal marketing-mix plans. This demands a new methodology for estimating dynamic models of oligopoly markets using market data. Thus, both the substantive problems--the determination of optimal marketing-mix strategies and the estimation of dynamic models for oligopoly markets--are unsolved research topics because the necessary methodology does not yet exist in marketing, economics, or management science (see Erickson 1991, Kamien and Schwartz 1991, Dockner et al. 2000).

Given this gap in the literature, one cannot answer basic questions of managerial interest: Do advertising and promotion amplify or attenuate their impact on market outcomes (e.g., brand share) when used together? How should managers allocate resources to advertising and promotion in the presence of interaction effects? What is the level of optimal budget and its allocation to promotional activities in the presence of strategic foresight? Is own (or competitor's) brand underadvertising or overpromoting, or both? If brand A's interaction effect increases, should brand B optimally respond by increasing advertising or increasing promotion?

To help answer such questions, we develop two methods: (i) a marketing-mix algorithm to plan optimal marketing-mix strategies and (ii) an estimation method to determine the effectiveness of marketing activities and their interaction effects for each brand in dynamic competitive markets.

The proposed marketing-mix algorithm solves the multiple-player differential game resulting from the dynamic models of oligopoly markets. Specifically, it yields optimal marketing-mix strategies that are (a) in equilibrium across multiple brands and over time, (b) accounts for intertemporal trade-offs across multiple periods (i.e., now versus later), and (c) balances interactivity trade-off among multiple marketing activities (e.g., advertising versus promotion). Because this algorithm solves a general nonlinear two-point boundary value problem, its applicability extends to several differential game models in marketing, not only the Lanchester model that we present for the sake of exposition (see Remark 2 for details). In addition, it …