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Analytical Models of Competition with Implications for Marketing: Issues, Findings, andOutlookAuthor(s): Jehoshua Eliashberg and Rabikar ChatterjeeSource: Journal of Marketing Research, Vol. 22, No. 3 (Aug., 1985), pp. 237-261Published by: American Marketing AssociationStable URL: http://www.jstor.org/stable/3151423 .

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JEHOSHUA ELIASHBERG and RABIKAR CHATTERJEE*

The authors review a representative cross-section of analytical models of competition using a framework for competitive analysis developed from a marketing perspective. Models are classified by the substantive issues they address and by the underlying modeling strategy. The implications of the various models are presented and discussed, and a set of empirically testable propositions is given. Some substantive areas that have been neglected by analytical modelers are identified. Other issues that warrant research attention by marketing behavioral scientists and econ-

ometricians are suggested as opportunities for future research.

Analytical Models of Competition with

Implications for Marketing: Issues, Findings, and Outlook

Because of the growing intensity of competition in vir- tually all spheres of business activity, marketing managers are increasingly aware of the need to better un- derstand and cope with their current and potential competitive environment. Henderson (1983) observes that "the success of any marketing strategy depends on the strength of the competitive analysis on which it is based." Taking a marketing research perspective, Parsons and Schultz (1976) recognize that "in highly competitive markets, the problem of predicting the reactions of a firm's competitors to its own marketing plans must rank as one of the firm's most complex and pressing dilemmas." Porter (1980) notes that the critical managerial questions con- cerning competition are:

What is driving competition in my industry or in industries I am thinking of entering? What actions are competitors likely to take, and what is the best way to respond? How will my industry evolve [over time]? How can the firm be best positioned to compete in the long run?

*Jehoshua Eliashberg is Associate Professor of Marketing and Ra- bikar Chatterjee is a doctoral candidate in the Marketing Department, The Wharton School, The University of Pennsylvania.

The authors gratefully acknowledge many helpful comments and suggestions made by the Special Issue Editor and the anonymous JMR reviewers.

The research was supported by the Center for Marketing Strategy Research, The Wharton School, The University of Pennsylvania.

All these scholars express the view that a theoretical basis for analyzing the dynamics of competition in real marketing situations remains to be developed. We believe that such a theoretical foundation is beginning to emerge, as economists, management scientists, and marketing scientists have made significant progress in developing analytical models of competition.

Competitive behavior has been investigated in microeconomic theory under various market structures- pure competition, monopolistic competition, and oligopoly (Scherer 1980). For the economists, the traditional emphasis appears to be on market structure, with market efficiency the major concern. For marketing scholars and managers, the principal focus is on the conduct of the competing firms in the market, recognizing that the activities of one firm affect the performance of other firms in the market. Thus, marketers are primarily interested in competitive models based on an oligopolistic market structure, where the interdependence among the competing firms is recognized explicitly.

The primary objective of our article is to take an initial step in bridging the gap between analytical models of oligopolistic competition and the realities of competitive interactions in the marketplace. In the next section, we present a framework for classifying analytical models of competition. This framework identifies the major issues in modeling competition from a marketing perspective and illustrates various modeling strategies. We then review and evaluate some of the relevant work in the area.

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Journal of Marketing Research Vol. XXII (August 1985), 237-61



JOURNAL OF MARKETING RESEARCH, AUGUST 1985

Next, marketing implications of the analytical models reviewed are presented in the form of empirically testable propositions. We conclude with suggested directions for future research that should be of interest to marketing modelers, econometricians, and behavioral scientists.

A FRAMEWORK FOR CLASSIFYING COMPETITIVE MODELS

The three major dimensions of our framework for classifying analytical models of competition are (1) the objective of the model, (2) the basic assumptions made about demand characteristics, supply characteristics, and competitive activity and the decision-making process, and (3) the mode of analysis.

Objective of the Model: Basic Understanding Versus Decision-Oriented

Models directed at basic understanding study the industry as a whole rather than one specific company. The industry analysis involves such questions as, "Under various scenarios, what is the nature of the dynamic evolution of the industry and the long-run equilibrium strategies?" Decision-oriented models are those with a prescriptive focus. The manager's alternative courses of action are considered, generally in light of the likely action (and reactions) of the competitors. The basic understanding perspective can be used to generate propositions and hypotheses about actual competitive behavior, which then can be tested in an experimental laboratory setting or with industry data. The decision-oriented approach, in contrast, can be used for answering "what if" questions and for improving decision making.

Basic Assumptions: Demand Characteristics

Number of segments and the nature of their interrelationship. Models can focus on competitive interaction in a single segment or in multiple segments. The segments may be independent or interrelated. Each segment requires a unique marketing activity. Interrelated segments are characterized by the influence of marketing activities in one segment on the demand levels in other segments.

Factors affecting primary demand, market share, and brand sales. Competitive actions may produce two effects on consumer demand, an industrywide primary demand effect and a brand-specific market share effect. A primary demand effect (i.e., a nonconstant market size) may be due not only to competitive activities, but also to exogenous factors (e.g., product life cycle). Unlike primary demand, which may or may not be affected by competitive marketing efforts, the market share always is assumed to depend on the competitive activities. Mar- ket share gains for one competitor must imply losses for the other(s).

Uncertainty. Uncertainty may be an inherent element in each of the three major components of competitive models (demand, supply, and competitive activity and

the decision-making process). For the demand component, uncertainty may be present with respect to individual consumer choice as well as various parameters characterizing primary demand, market share, and brand sales. If such elements of uncertainty are assumed to be present, modeling the decision-making process by managers should involve predictions-often guesses-about future demand conditions.

Basic Assumptions: Supply Characteristics

Number of products and degree of their differentiation. Competitive models may focus on a single product or may examine a line of (possibly interrelated) products. The competing brands within each product cate- gory may be homogeneous or differentiated. Most models incorporate product differentiation explicitly or implic- itly.

Barriers to entry. Production-related phenomena such as technological knowhow, raw material availability, specialized labor skills, capital requirements, and the cost structure (economies of scale and experience curve effects) can create barriers to entry. In addition, entry is affected by the potential entrant's perception of the prevailing profitability and its expectation of the incumbent firms' reactions to its entry. Incumbent firms can create barriers to entry through such marketing decisions as limit pricing, product differentiation, and advertising which generates a high level of goodwill. (See, e.g., Scherer 1980, Ch. 8.)

Cost structure. The cost function is determined largely by technology, both in a static sense (in terms of economies of scale) and in a dynamic sense (in terms of learning curve effects.) Economies of scale arise when the average cost declines with output rate. When marginal and average costs depend on (more specifically, decline with) accumulated volume, the firm is said to have a cost learning curve. Competition between existing brands with differential costs may yield interesting marketing implications even when barriers to entry are not considered explicitly.

Uncertainty. On the supply side, uncertainty may have an important role in such elements as the parameters of the production function, the availability of production inputs, and the estimation of production and entry costs.

Basic Assumptions: Competitive Activity and the Decision-Making Process

Number of competitors. The number of competitors in oligopolistic situations may range from two to any finite number (small enough that decisions by individual firms affect the other firms in the market and such effects are recognized explicitly by the others). The competitive situations that have been considered in the literature include competition among existing brands as well as competition against potential firms in the context of new entries into existing markets. The number of competitors and nature of the competitive activity are results of some unobservable decision-making process which

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ANALYTICAL MODELS OF COMPETITION

presumably is taking place. The following aspects of this process have been recognized explicitly and employed in competitive models.

Decision variables and the competitive interaction. Conceptually, the performance of a firm generally is modeled as a function of (1) marketing decision variables assumed to be controlled by the firm, (2) decision variables controlled by each of the other competitors, and (3) external (environmental/situational) factors be- yond the immediate control of the competing firms. These are the essential elements of the competitive interaction. The decision variables can be continuous (e.g., marketing mix variables such as price and advertising expenditures) or discrete (e.g., the decision to enter a new industry).

Informational base and level of uncertainty. Com- petitors may be assumed to make their decisions simultaneously and noncooperatively (i.e., with no collusion), or sequentially and reactively. Simultaneity is not to be interpreted in a temporal context but in the informational context of not having the opportunity to observe the decisions taken by others. In the simultaneous mode of competitive behavior, uncertainty has a crucial role. The assumptions can range from complete information-where each competitor is assumed to be aware and fully in- formed of the mutual interaction, can infer with certainty the best strategies of its rivals, and can act without actually observing the rivals' decisions-to the incomplete information case where uncertainty is inherent in the competitive interaction which leads each competitor to act according to its expectation (but without actual ob- servation) of what the rivals' strategies might be. In the sequential, reactive case, each competitor makes a move only after having an opportunity to actually observe the rivals' decisions. In this case, however, given that the competitors are fully aware of the sequential nature of the process, the competitor who moves first may conjecture how its rivals will react to any of its possible moves, and thus can plan strategies accordingly. This conjecture may be made with certainty, on the basis of some explicit rules, under complete information; or, in the case of incomplete information, the conjecture will be based on the expectation of the rivals' strategies. The classic economic model of simultaneous and noncooperative decision making under certainty is due to Cour- not (1963) and that of sequential and reactive decision making under certainty is due to Stackelberg (Varian 1978).

In uncertain situations, managers rely on experience and prior knowledge to make assessments and predic-

'In the Cournot model, each firm maximizes profits by setting its output, given the output of the other firms; in the Bertrand model each firm maximizes profits by setting its price given the prices the other firms charge. In the Stackelberg model the leader determines the follower's reaction function by assuming that the follower will maximize its profits on the basis of the leader's decision.

tions about competitors' future moves. Over time, new information becomes available which enables managers to revise their earlier assessments. A common approach to modeling this process of learning employs the Bayes- ian decision-theoretic framework (Raiffa and Schlaifer 1961; Winkler 1972). In our review, we classify models that do not consider such uncertainty in the competitive decision-making process as deterministic.

Decision makers' objectives (goals). The traditional objective is profit maximization; however, objectives in terms of sales or market share, as well as multiple (often conflicting) objectives, may be considered.

Decision makers' attitudes toward risk. The decision maker's attitude toward risk determines the impact of uncertainty on his or her decisions. The decision maker can be assumed to be risk averse, risk neutral, or risk prone. Utility theory (von Neumann and Morgenstem 1947) provides a method for explicitly incorporating attitudes toward risk. This approach can be extended to cover multiple criteria (instead of a single objective) by use of a multiattribute utility function (Keeney and Raiffa 1976). The maximand is then the decision maker's expected utility.

Mode of Analysis Level of aggregation. The demand function is essen-

tially an aggregate description of consumer behavior. Two approaches can be taken in modeling the demand for the brand. One is an aggregate approach and the other is a "build up" approach, starting from an individual consumer behavior model and then aggregating across the population, often based on some heterogeneity (segmentation) variables.

Static versus dynamic mode. If the decision variables are inherently dynamic in the sense that they must be made for at least two consecutive time periods, they are modeled explicitly as functions of time and the model is thus dynamic. In such modeling, a differential game approach typically has been employed (Case 1979).

Equilibrium conditions. An important consideration is the examination of equilibrium conditions under different modes of competitive behavior. Equilibrium conditions will prevail in the industry in the long run, after the competitors have made all their transient moves, and each competitor has no incentive to deviate from its strategy as long as it believes that the others will adhere to their strategies. In static models, equilibrium conditions can be derived for a simultaneous and noncooperative mode of behavior (Courot model) and for one- decision-at-a-time under a sequential and reactive mode of behavior (Stackelberg model). Such equilibria are considered static.

In dynamic models, two types of equilibrium strategies are pertinent. Open-loop equilibria will yield strategic trajectories for the decision variables that are functions of time only, whereas closed-loop equilibrium strategies are functions of time and the state of the system at that point in time. In general, the state of the

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system is characterized by the amount and type of information available to the competitors at that point in time when decisions are made. This type of equilibrium strategic behavior captures the adaptive nature of the competing firms. The issue of open- versus closed-loop strategies generally is related to the amount of the prevailing uncertainty. In a deterministic (complete information) situation, open-loop strategies may be reason- able; however, more realistically, in the presence of uncertainty, firms would tend to follow a closed-loop strategy, which would indicate adaptive behavior. In a modeling context, open-loop equilibria are mathematically more tractable to derive. As noted by Spence (1981), however, open-loop equilibrium strategies sometimes provide results that are not substantially different from those obtained by closed-loop strategies.

Analytical versus simulation approach. In deriving implications, mainly from dynamic models, two types of approaches can be taken-analytical or numerical simulation. There are tradeoffs in selecting one of these approaches. With numerical simulation, more complex situations can be modeled, though the findings of such simulations will always depend on the specific values of the parameters chosen for the investigation. In contrast, the analytical approach restricts the complexity of the situation in order to be tractable, but provides findings that are, in the context of the less complex situation modeled, more general.

A REVIEW OF ANALYTICAL MODELS OF COMPETITION

Two considerations were involved in selecting the competitive models to be reviewed. First, the selection was made to demonstrate the various issues and the major streams of research. The second consideration was to present findings of interest to both empirical marketing researchers and practitioners. In Tables 1 through 3 the essential characteristics of the models are briefly summarized2 along the dimensions discussed in the preceding section.

We have grouped the models for review and evaluation as follows.

1. Deterministic models addressing competition among incumbent firms, summarized in Table 1 (this group is sub- divided further in terms of the marketing decision variable(s) considered in the models).

2. Deterministic models addressing competitive entry issues, summarized in Table 2.

3. Models addressing competitive decision making under uncertainty, summarized in Table 3.

The groups of models are not mutually exclusive because some of the models address multiple issues. Our review focuses on fundamental issues and traces how the

2A more detailed discussion of the individual models and their structures is available from the authors in a working paper.

literature apparently has developed. Though the diversity of modeling approaches, their basic assumptions and philosophies, and their findings does not make this task easy, we attempt, wherever possible, to integrate and compare them.

Deterministic Models Addressing Competition Among Incumbent Firms

Advertising and promotion decisions. We begin our review with static models proposed by Friedman (1958), Shakun (1965), and Gupta and Krishnan (1967). We then present two dynamic models (Schmalensee 1978; For- nell, Robinson, and Wererfelt 1984) which focus mainly on steady-state equilibrium conditions, that is, on the long- run state of the system. Finally, we present four fully dynamic models (Bensoussan, Bultez, and Naert 1978; Deal 1979; Thompson and Teng 1984; Erickson, 1985) which provide insights into the competitive interaction at any point in time, in addition to the long-run steady- state condition. The Friedman, Shakun, and Deal models consider advertising expenditures as the sole decision variable, whereas the other models look at advertising and some other marketing variable as the major competitive tools.

Friedman (1958) takes a static equilibrium approach to examining the issue of allocation of competitive advertising expenditures across independent market segments, under various scenarios. Though the number of scenarios that may fit Friedman's model is limited, this work represents one of the first managerially oriented applications of game-theoretic advertising models. The major implications of Friedman's work may provide guidance in testing, cross-sectionally, some hypotheses about the allocations of advertising budgets as well as the issue of parity in advertising allocation strategies among firms with equal and unequal budgets.

Shakun (1965) generalizes Friedman's model by al- lowing for the possibility that the market segments may be interdependent-i.e., the total advertising in one segment, while increasing sales in that segment, may also influence sales in other segments. This model indicates the effect of interdependencies on the equilibrium allocation of advertising expenditures.

Gupta and Krishnan (1967) focus on a single market segment but extend the number of competitors and the number of controllable variables to promotional effort and price. They explicitly consider the impact of differential effectiveness of promotional expenditure per dollar across competitors. Static equilibrium strategies for the competing firms are examined under four different primary demand (market size) conditions. This work has interesting implications in competitive settings, where one competitor has a cost advantage. It indicates conditions under which one competitor may use promotion as its major competitive tool while another uses price; thus, as observed in practice, the two major competitors may use different weapons (even in situations when price and promotion elasticities are identical for the two firms).

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Though the aforementioned static models may yield interesting insights under certain circumstances such as stable conditions in mature industries, they do not explicitly incorporate the inherent dynamics of both sales response and competitive interaction. These dynamic effects are particularly important in advertising competition, where carryover effects must be considered. Fur- thermore, in situations where conditions change rapidly (such as diffusion of new products), static analyses often may be suboptimal. The preceding models, by considering static equilibrium, focus on the final outcome rather than on the dynamic process which may lead to that outcome. Consequently their insights are limited. This is a substantive modeling issue also of relevance to decisions other than advertising, and we defer its discussion to a subsequent section.

Schmalensee (1978) and Forell, Robinson, and Wer- nerfelt (1984) propose dynamic models of advertising, that is, models that explicitly recognize the fact that advertising decisions are made not just once, but contin- uously over some time horizon. Schmalensee examines the scenario where prices are fixed and each firm's unit costs are constant but can differ across firms because of differences in product quality. His model demonstrates the effect of a cost advantage (and hence quality differential) on the equilibrium advertising budgets, market shares, and profits. In particular, Schmalensee shows that, if consumers have incomplete information about the brands (consumers learn by trial, but do not obtain complete information about performance), there are conditions under which the lowest quality brands may have the largest equilibrium market shares, profits, and advertising budgets. This result is contrary to Nelson's (1974) conclu- sion that better brands should spend more on advertising. Fornell and his colleagues, in contrast, are concerned with advertising and promotion as the two major competitive tools. Their model provides implications in terms of ratios of advertising and promotion to total expenditures in equilibrium.

Though these models explicitly consider dynamic issues, their insights are limited because they focus on ul- timate steady-state conditions rather than investigating the full dynamics of the competitive situation.

The models by Bensoussan, Bultez, and Naert (1978), Deal (1979), Thompson and Teng (1984), and Erickson (1985) represent a stream of research that explicitly examines these dynamics. The Deal and Erickson models consider advertising as the only control variable, whereas the other two models examine both advertising and pricing policies.

All four models assume that some performance criterion is maximized over a finite planning horizon. Ben- soussan and his colleagues, Thompson and Teng, and Erickson consider discounted profits. Deal's criterion of performance is based on two objectives that each firm wishes to maximize simultaneously-the profit stream over the planning horizon and the market share at the end of the horizon. The overall performance criterion is

calculated as a linear combination of the two separate objectives, the relative weights being fixed by each firm. Deal and Erickson (for a duopoly) and Thompson and Teng (for an oligopoly) model the competitive mode of behavior, at any point in time, as simultaneous and noncooperative, and they seek dynamic open-loop Nash equilibrium strategies. Bensoussan and his colleagues, in contrast, propose a decision-oriented model from the market leader's perspective, with competitors' reactions to the leader's moves explicitly considered (via some predetermined dynamic reaction functions). Thus, the competitive interaction is modeled in a sequential and reactive manner. To obtain implications, all four models employ a simulation approach.

The four models represent, in our judgment, perhaps the most advanced efforts to address advertising competition issues with marketing implications. However, they are not free of limitations. For example, both Deal and Thompson and Teng model the impact of competitors' decision variables on the firm's sales indirectly (via the remaining unsaturated market) rather than modeling a firm's sales response explicitly as a function of both the firm's and the competitors' variables. Hence, in our view, the impact of competitive action on a firm's sales is only weakly captured. In addition, Thompson and Teng restrict their analysis to a market in which there is a single selling price, decided by the largest competitor. Er- ickson and Bensoussan et al. limit their analyses to some special cases of their models. We also wish to note that though these models represent recent advances in modeling dynamic advertising decisions, future research should be directed toward developing models that provide closed- loop strategies over the brands' life cycles under environmental uncertainty. Some efforts in this direction of which we are aware (e.g., Albright and Winston 1979), though mathematically elegant, are too abstract to provide practical implications to the marketing community.

Product quality decisions. Brems (1958) and Ballou and Pipkin (1980) explicitly recognize the direct control that firms may have over the quality of their products. These models capture scenarios similar to those faced by a firm challenging the market leader, such as Avis, Westinghouse, and Schlitz. One possible posture that these firms can adopt is to bid aggressively for further market share through product quality/product positioning decisions.

Brems examines the impact of the timing of competitive response on a firm's strategy. Two decision variables, product quality and price, are considered from the perspective of a firm planning its offensive strategy. A two-period sequential modeling approach is taken. The first period begins when the attacker makes its move and the second period begins when the defender implements its reactive strategy.

Ballou and Pipkin examine the issue of product positioning in oligopolistic markets under the basic premise that the consumer chooses the alternative having the highest utility. The utility for each product is distributed

241




Table DETERMINISTIC MODELS ADDRESSING

Friedman (1958) Shakun (1965) Gupta and Krishnan (1967) I. Problem Allocation of advertising expendi- Allocation of advertising expendi- Promotional expenditure and pric-

ture over segments ture over coupled segments ing decisions

II. Objective of model: basic understanding vs. decision- oriented

II. Basic assumptions II. 1 Demand characteristics

Number of segments and the nature of their interrelationship

Factors affecting primary demand

Factors affecting market share

Uncertainty II1.2 Supply characteristics

Number of products Product differentiation Barriers to entry Cost structure Uncertainty

111.3 Competitive activity and decision- making process

Number of competitors Decision variables Competitive behavioral

mode Decision makers'

objectives Decision makers' atti-

tudes toward risk Uncertainty

IV. Mode of analysis Level of aggregation

Static vs. dynamic mode of analysis

Equilibrium conditions

Analytical vs. simulation mode of analysis

V. Basic results

Basic understanding

n(> 2); independent

Fixed primary demand Relative advertising expenditure

Not considered

1 Implicit Not considered Not considered Not considered

2 Advertising

Simultaneous noncooperative Maximize sales

Not considered Not considered

Segment (Models I and II) Customer (Models III and IV)

Static Cournot

Analytical Rules for equilibrium allocation

of advertising budget over segments are determined under different scenarios

Basic understanding

2; coupled

Advertising in both segments Relative advertising expenditure

Not considered

2 Implicit Not considered Constant unit cost Not considered

2 Advertising

Simultaneous noncooperative Maximize profit


Segment

Static Courot

Analytical/numerical Impact of coupling effect (i.e.,

the interaction between advertising expenditures on related products) is explicitly incorporated in the equilibrium allocation

Basic understanding

1

Price, promotion (in full model) Relative promotional effort and

price differential

Not considered

1 Explicit Not considered Constant unit cost Not considered

n(> 2) Promotion, price

Simultaneous noncooperative Maximize profit


Market

Static Courot

Analytical/numerical Equilibrium conditions for deter-

mining combinations of price and promotional effort are derived under different primary demand assumptions

randomly across the population. They first derive short- run implications (i.e., assuming no competitive reaction) for markets that are highly competitive and uncompeti- tive. In the long run, given competitive reaction, Ballou and Pipkin claim that the short-run strategies remain optimal under general conditions, though their effectiveness depends on the strength of the competitive response.

The two models provide various testable propositions, but should be considered cautiously. First, the work by Brems assumes that the competitor always responds to the firm's price policy by a price adjustment and to the firm's product quality policy by adjusting product quality. This "head on" reaction strategy may be somewhat restrictive because, as discussed before, it may at times be more effective to respond via a different variable (Gupta

242




1 COMPETITION AMONG INCUMBENT FIRMS

Fornell, Robinson, Bensoussan, Bultez, Schmalensee (1978) and Wernerfelt (1984) and Naert (1978)

Advertisement levels for fimns selling goods of different qualities

Basic understanding

The effect of consumption experience on steady-state advertising and sales promotion

Basic understanding

Market leader's optimal strategy, anticipating the followers' reactions

Decision-oriented

1 1

Fixed primary demand Quality and advertising

Considered only at individual level

1 Explicit Not considered f (product quality) Not considered

n(- 2) Advertising

Simultaneous noncooperative Maximize discounted profit stream (infinite

horizon)


Individual

Fixed primary demand Consumption experience, advertising, promo-

tion

Not considered

1 Implicit Not explicitly addressed Constant unit cost Not considered

n(- 2) Advertising, promotion

Simultaneous noncooperative Maximize discounted profits over infinite

time horizon


Market

Firm's sales depend on firm's and competitors' prices, and current and past advertising expenditures

Not considered

1 Implicit Not considered f (quantity, time) Not considered

n(- 2) Advertising, price

Sequential, reactive Maximize discounted profits over finite time

horizon


Market

Dynamic Coumot

Dynamic Open-loop

Analytical Equilibrium conditions for advertising levels

are established when competing products differ in quality

Dynamic Partial equilibrium based on a priori conjec-

tures by leaders about followers' reactions

Analytical Steady-state results are derived for promotion

and advertising for firms with different consumption experience

Analytical/simulation Leader's optimal pricing and advertising

strategies are derived

and Krishnan 1967). For Ballou and Pipkin's model, the related work on spatial competition suggests that product positioning strategies may be very sensitive to the distribution of consumer preference, the number of firms, and the number of product characteristics.3

3We thank a JMR reviewer for bringing this issue to our attention.

The dynamics of product quality modification decisions are essentially equivalent to the decision about the introduction of new (perhaps improved) brands. Thus, product quality decisions are one of the issues involved in the context of developing an appropriate entry/exit strategy. We examine such strategies in the next sub- section.

Pricing decisions. Four models previously re-

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244 JOURNAL OF MARKETING RESEARCH, AUGUST 1985

Table 1 DETERMINISTIC MODELS ADDRESSING

Deal (1979) Thompson and Teng (1984) Erickson (1985) I. Problem Advertising strategies in a Advertising and pricing strategies Advertising rivalry between com-

II. Objective of model: basic understanding vs. decision-oriented

IH. Basic assumptions II. 1 Demand characteristics

Number of segments and the nature of their interrelationship


Factors affecting market share

Uncertainty 111.2 Supply characteristics


11I.3 Competitive activity and decision- making process


mode Decision makers'

objectives

Decision makers' attitudes toward risk

Uncertainty IV. Mode of analysis

Level of aggregation Static vs. dynamic mode of

analysis Equilibrium conditions


V. Basic results

duopoly

Basic understanding

1 Firm's sales depend on advertis-

ing and sales decay

Not considered


2 Advertising Simultaneous noncooperative

Maximize linear combination of terminal market share and profits over finite time horizon


Market

Dynamic Open-loop

Simulation

Numerical illustrations for deter- mining equilibrium strategies are presented

for new durable goods petitors in a duopoly

Basic understanding

1 Firm's sales depend on its adver-

tising, price, cumulative sales, unsaturated market potential

Not considered

1 Implicit Not considered f (cumulative production) Not considered

n(- 2) Advertising and industry price Simultaneous noncooperative

Maximize discounted profits over finite time horizon


Market

Dynamic Open-loop

Simulation

Equilibrium pricing and advertising strategies are derived over time by a numerical algorithm

Basic understanding

1 Firm's sales depend on advertis-

ing by both firms

Not considered


2 Advertising Simultaneous noncooperative

Maximize discounted profits over finite time horizon


Market

Dynamic Open-loop

Analytical (for fixed primary demand), simulation for general case

Competitive equilibrium in advertising levels is derived in a duopoly using the Lanchester structure

viewed-those of Gupta and Krishnan (1967), Ben- soussan, Bultez, and Naert (1978), Thompson and Teng (1984), and Brems (1958)-all consider price as a (second) control variable. Rao and Shakun (1972) propose a static model that treats price as the only decision variable. The authors examine market-entry pricing (from the new brand's perspective) for a product class where price is the only indicator of quality. Such a model may be applicable for low involvement or fashion products where price is often an important indicator of quality (e.g., gasoline, soap, or clothes). The model yields implications relating the price prevailing in a monopolistic mar-

ket (i.e., before entry occurs) to prices in a duopolistic market (after entry occurs).

When dynamic effects (such as market saturation) are incorporated into a pricing model and price is not modeled explicitly as an indicator of quality in the same manner as in Rao and Shakun's model, the comparison between a monopolist's and duopolist's pricing strategies may yield different results. For example, Eliashberg and Jeuland (1984) develop a dynamic model for innovative goods in a two-period context. The first period is characterized by a monopolistic market and the second period begins when a new firm enters the market, thereby




(Continued) COMPETITION AMONG INCUMBENT FIRMS

Brems (1958) Ballou and Pipkin (1980) Rao and Shakun (1972)

Impact of timing and extent of competitive Product positioning strategy Pricing strategy when new brand enters the response to attacker's strategy market

Decision-oriented Basic understanding Basic understanding

1 Firm's sales depend on prices and quality in-

dexes for both firms

Not considered

1 Explicit Not considered Unit cost proportional to quality index Not considered

2 Price, product quality Sequential reactive

Maximize profits over two-period horizon


Market

1 Not considered

Distribution of utilities across population for firms' products


1 Explicit Not considered Not considered Not considered

n(> 2) Product positioning in preference dimension Sequential, reactive in the long run

Maximize market share


Individual

1 Firm's sales depend on prices (as indicators

of quality-each customer has acceptable price range)


1 Explicit Do not exist Not considered Not considered

Up to 3 (i.e., 2 existing + 1 new) Price Simultaneous: cooperative and noncoopera-

tive cases considered Maximize sales


Individual

Static Partial equilibrium based on a priori conjec-

tures about competitive reaction Analytical

Partial equilibrium conditions are established to determine the effect of competitive response in terms of its extent and timing for price and product quality

Static Partial equilibrium based on no competitive

reaction in the short run Analytical

Product positioning (in terms of width of appeal in a heterogeneous market) implications are derived for high and low levels of competitive intensity

Static Courot for the noncooperative case

Analytical

Equilibrium pricing policies are derived under symmetric and asymmetric conditions of cooperative and noncooperative behavior by different brands

changing the structure to a duopolistic one. Their analysis yields different implications (see next section).

The strength of models such as that of Rao and Shakun is in the attempt to incorporate explicitly the price/perceived quality relationship. Another interesting aspect of their model is its asymmetric approach in that it permits each competitor to follow a different behavioral mode. The model examines the effects of alternative combinations of behavioral modes on equilibrium price conditions, with sales as the performance criterion. The analysis is carried out for up to three brands. The model may be particularly appropriate in situations where co-

operative and noncooperative behavioral modes are present simultaneously, such as the case of a product line offered by the same firm in a competitive market.

Overall marketing mix decisions. Dutta and King (1980), Hauser and Shugan (1983), and Kotler (1965) consider overall marketing mix decisions in competitive settings. Though these authors address different issues using widely different approaches, all appear to have a decision-oriented objective. Dutta and King present a new approach to designing competitive strategies based on metagame analysis. Hauser and Shugan examine the issue of defensive strategies for an existing brand facing

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Table 1 DETERMINISTIC MODELS ADDRESSING

Dutta and King (1980)

Competitive strategy formulation using metagame analysis

Hauser and Shugan (1983)

Defensive marketing strategy against entering brand

Kotler (1965)

Competitive strategies for new product

II. Objective of model: basic understanding vs. decision-oriented


Number of segments and the nature of their interrelationship



Uncertainty

111.2 Supply characteristics Number of products Product differentiation Barriers to entry Cost structure

Uncertainty ml.3 Competitive activity

and decision-making process

Number of competitors

Decision variables

Competitive behavioral mode

Decision makers' objectives

Decision makers' attitudes toward risk


Level of aggregation Static vs. dynamic mode of

analysis Equilibrium conditions Analytical vs. simulation

mode of analysis V. Basic results

Decision-oriented

1 Exogenous (fixed) market size

"Relative position" variables- relative price and quality dif- ferentials

Not considered

1 Explicit Not considered Actual cost structure

Not considered

n(- 2)

Price, product quality

Simultaneous noncooperative

Maximize utility for profit and market share


Market

Static Metagame analysis

Simulation Stable competitive strategies are

derived under different scenarios: managerial judgment is an important input in the process

Decision-oriented

1 Not explicitly considered

Utility distribution for competing brands


1 Explicit Do not exist Product characteristics may affect

cost Not considered

2 major ones (other companies remain passive)

Price, advertising, product quality, distribution

Sequential, reactive

Maximize profit


Individual

Static Partial equilibrium

Analytical Post-entry partial equilibrium

profit-maximizing guidelines developed for a defending firm (assuming that other defending firms remain passive)

Basic understanding

1 Growth rate, seasonality, total in-

dustry marketing effort Firm's relative marketing effort

Not considered

1 Implicit Not considered Constant unit cost

Not considered

2

Price, advertising, distribution

Nine different competitive behavioral patterns

Maximize discounted profits over finite horizon


Market

Dynamic None

Simulation Performance of duopolistic com-

petitors compared under the different combinations of competitive strategies

a new entrant in the market, whereas Kotler presents a dynamic competitive (duopolistic) model for new product marketing which considers price, advertising, and distribution decisions.

Dutta and King's approach provides a framework for competitive strategy formulations using "metagame analysis," which permits the direct utilization of multi-

pie strategic variables and performance measures. Such an analysis explicitly models the "mutual anticipation" process starting with a hypothesized set of specific strategy choices by the players in a competitive situation, and examining the stability of the situation from the point of view of each firm through a theory of rational choices in "metagames" developed by Howard (1971, 1975).

I. Problem

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(Continued) COMPETITION AMONG INCUMBENT FIRMS

McGuire and Rao and Bass (1985) Shakun (1968) Staelin (1983)

The determinants of dynamic industry price and market share paths in an oligopoly; the impact of dynamically optimal nonmyopic vs. myopic strategies.

Basic understanding

1 Price and cumulative output or time (alterna-

tive models) Firm's output is the decision variable

Effect of organizational structure on competition

Basic understanding

2; coupled Advertising expenditures

Effect of product substitutability on channel structure

Basic understanding

Retailer's sales depend on retail prices Retailer's sales depend on retail prices

Relative advertising expenditures


1 Undifferentiated products Cost advantage f (cumulative output)

Not considered

n(- 2)

2 Implicit Not considered Constant unit cost

Not considered

2

Not considered

1 Explicit Not considered Constant unit cost

Not considered

2

Output


Maximize discounted profits over infinite time horizon


Market

Dynamic Open-loop

Analytical/simulation The dynamics of price and market share are

analytically obtained. Numerical results are derived for a duopoly to characterize alternative modes of competition and the effect of a cost advantage. Empirical results sup- port hypotheses regarding the determinants of price dynamics.

Advertising, organizational structure


Maximize profit


Segment

Static Cournot

Analytical/numerical Payoff implications of organizational struc-

ture (centralized vs. decentralized) examined for both symmetric and asymmetric (mixed) cases

Prices (wholesale and retail), vertical integration decision


Maximize profit


Market

Static Cournot

Analytical Profit implications and equilibrium condi-

tions established for different structures as a function of product substitutability

Thus, possible "solutions" to the game are proposed and examined for their stability rather than analytically derived as equilibrium strategies as in the classical game theoretic approach which underlies most of the work in competitive modeling.

Hauser and Shugan develop a model that considers competition in a multiattribute product space. The model

seeks to develop a defensive marketing strategy for a firm facing a new brand in the market, under the assumption that the other competitors remain passive. Though this assumption is somewhat restrictive, it appears tenable for short-term analysis in a situation where the positioning of the new product significantly affects only one of the incumbent firms so that the others have

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Table DETERMINISTIC MODELS ADDRESSING

Lane (1980) I. Problem

H.

II.

Objective of model: basic understanding vs. decision-oriented

Basic assumptions Im. 1 Number of segments and the na-

ture of their interrelationship Factors affecting primary demand Factors affecting market share

Uncertainty 111.2 Supply characteristics

Number of products Product differentiation Barriers to entry

Cost structure Uncertainty

III.3 Competitive activity and decision- making process

Number of competitors Decision variables Competitive behavioral mode

Decision makers' objectives

Decision makers' attitudes toward risk


Level of aggregation Static vs. dynamic mode of analysis Equilibrium conditions


V. Basic results

Product positioning and pricing strategy in market with sequential entry

Basic understanding

1 Fixed primary demand Price and location in product space of firm

and its two neighbors Considered only at individual level

1 Explicit Fixed cost of entry; entry-deterring product

positioning strategies considered Constant marginal cost; fixed cost of entry Not considered

n(- 2) Price, product positioning Simultaneous noncooperative for price, and

sequential reactive for product positioning Maximize profit


Individual Static Cournot for price, sequential entry with fore-

sight for positioning

Analytical Equilibrium product positioning and pricing

strategies established for oligopolistic market with sequential entry

Spence (1981)

Competitive interaction and industry evolution in presence of learning curve

Basic understanding

1 Price, time Firm's output is the decision variable

Not considered

1 Undifferentiated products Cost advantage

f (cumulative output) Not considered

n(2 2) Output Simultaneous noncooperative

Maximize profits over finite time horizon


Market Dynamic Open-loop Nash; closed-loop Nash also in-

vestigated

Simulation The impact of the learning curve and de-

mand growth on market performance and structure is assessed

no particular motivation to make a defensive response or simply take much longer to react.4 This assumption permits consideration of a richer strategic response in terms of pricing, advertising, distribution, and product positioning decisions.

Kotler's dynamic model of a duopolistic market considers price, advertising, and distribution as the variables controlled by the competing firms. It is similar in spirit to Dutta and King's approach, but does not explicitly investigate equilibrium or stability conditions. A firm's

4There is also the implicit assumption that the entrant will not in turn react to the defensive strategy. Technically, the assumption is that the entering and defending firms are in some sort of equilibrium, i.e., the entering firm correctly predicts the target firm's defensive strategy.

marketing strategy is defined as a set of decision rules that adjusts the vector of the three variables from one period to the next over the planning horizon. The major thrust of Kotler's article is to evaluate different classes of competitive strategies, such as (1) nonadaptive (constant marketing mix over time), (2) open-loop, time dependent (providing automatic adjustments dependent on time only), (3) competitive-adaptive (relying on signal- ing or responding to competitive actions), (4) sales responsive (responding to the company's own past sales), (5) profit responsive (responding to "significant" changes in company profits), and (6) completely adaptive (responding to all current developments, including the pas- sage of time, change in one's own and one's competitor's sales and profits, and changes in the competitor's marketing mix). The first five classes of competitive strategies are simulated in pairs (i.e., one strategy for

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2 COMPETITIVE ENTRY ISSUES

Fershtman, Mahajan, Eliashberg and Jeuland (1984) Clarke and Dolan (1984) and Muller (1984)

Dynamic pricing strategy in a two-major-pe- Evaluation of strategies in a two-major-pe- Effect of initial stocks of goodwill riod (monopoly-duopoly) situation riod (monopoly-duopoly) situation

Basic understanding Decision-oriented Basic understanding

1 1 1 Firm's sales depend on rate of diffusion, un- Firm's sales depend on brand prices and con- Firm's sales depend on advertising, goodwill

saturated potential, brand prices sumers' reservation prices stocks, and prices

Not considered Considered implictly at individual level Not considered

1 1 1 Explicit Explicit Explicit Do not exist Cost advantage (not explicitly considered) Goodwill stock

Constant marginal cost f (cumulative output) Constant unit cost Not considered Not considered Not considered

2 2 2 Price Price Price, advertising Simultaneous noncooperative (1) Sequential reactive Simultaneous noncooperative

(2) Price matching Maximize profits over finite time horizon Maximize discounted profits over finite time Maximize discounted profits over infinite

horizon time horizon

Not considered Not considered Not considered Not considered Not considered Not considered

Market Individual/segment Market Dynamic Dynamic Dynamic Open-loop None Open-loop

Analytical Simulation Analytical Optimal pricing strategies investigated when Impact of three alternative pricing strategies Conditions under which final (long-run) mar-

entry of second firm is known with cer- (myopic, skimming, and penetration) is in- ket shares do not depend on the initial tainty, and compared with a myopic strat- vestigated by simulation stocks of goodwill of the competing firms egy for a firm ignorant of the second are established firm's prospective entry

each firm) for a hypothetical market over a 60-month period for the purpose of exploring their properties. The results of the various possible confrontations are mea- sured by total net profits and terminal market shares.

Kotler's simulation-based analysis addresses such questions as:

-Which long-run strategy is best to adopt if a firm wants to guarantee a minimum return regardless of what the competitor does?

-Which long-run strategies are the riskiest? -Which strategies give the greatest profit potential? -If the rival's strategy is known, which policy is best?

The decision rules used by the duopolists investigated by Kotler are not necessarily the optimal response to each other's strategies, and hence no equilibrium conditions are analyzed. However, the simulation approach repre-

sents a useful tool for policy evaluation whenever the firm has some (perhaps confidential) information about the possible behavior (decision rule) used by its competitors 5

The approaches employed in these marketing mix models appear to be flexible and permit exploration of a wide range of competitive scenarios. They can aid managers in exploring various "what if" questions. The models envisage judgmental inputs by managers and require close managerial involvement. Though Dutta and King's model is limited in terms of the number of decision variables considered, its major strength (relative

5For a critique of the economic plausibility of Kotler's model as well as for an investigation of the model's static equilibrium strategies, see Simon (1978).

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Table 3 MODELS ADDRESSING COMPETITIVE DECISION MAKING UNDER UNCERTAINTY

Cyert and DeGroot (1970) Cyert and DeGroot (1973) I. Problem Bayesian analysis of adaptive be- Analysis of cooperation and

havior in duopoly situations learning in a duopoly II. Objective of model: basic

understanding vs. decision- oriented


Number of segments and the nature of their interrelationship



Uncertainty Im.2 Supply characteristics


Im.3 Competitive activity and decision-making process


mode Decision makers' ob-

jectives Decision makers' atti-

tudes toward risk Uncertainty

IV. Mode of analysis Level of aggregation Static vs. dynamic mode of

analysis Equilibrium conditions


V. Basic results

Basic understanding

1 Price

Firm's output is the decision variable

Not considered

1 Implicit Not considered Not considered Not considered

2 Output Sequential, reactive, and adaptive

Maximize total expected revenues over finite time horizon

Neutral

Considered

Market

Dynamic Probabilistic conjectural vari-

ations-alternating decisions

Analytical Bayesian procedure for updating

information about uncertain parameter included in competitor's reactive decision rule. For model structure assumed, it is shown how an optimal sequential decision procedure can re- duce to the myopic decision procedure.

Basic understanding

1 Price

Firm's output is the decision variable

Not considered

1 Implicit Not considered f (output) Not considered

2 Output Sequential, reactive, and adaptive

Maximize total profits over finite time horizon

Neutral

Considered

Market


ations-alternating decisions

Analytical Analysis demonstrates how duopo-

listic competitors move in a rational fashion from a path leading to a noncooperative equilibrium ultimately to the cooperative solution.

Eliashberg (1981)

Analysis of competitive decision making under uncertainty

Basic understanding

Not explicitly modeled Assumed to be embedded in

management's preference

Not considered

Competitors' preferences for various states of the industry are assumed to be provided by management

2 General (discrete) Simultaneous, noncooperative,

and adaptive Maximize expected payoff on

each trial (decision occasion) Effect of different risk attitudes

considered Considered

Market


ations-simultaneous decisions/game theoretic mixed strategies (long run)

Analytical Dynamic behavior in a Bayesian

decision theoretic framework is investigated for different classes of situations. Effect of risk attitude is considered.

to the other two models) is in providing explicit guidelines as to what a stable situation is, and hence what management should anticipate as the most likely scenario.

Output decisions. Rao and Bass (1985) propose a dynamic oligopoly model with the competitive mode of behavior assumed to be simultaneous and noncooperative. Each firm chooses its optimal dynamic strategy with the

objective of maximizing discounted profits over an infinite time horizon. An open-loop equilibrium solution is sought, as in the dynamic models proposed by Deal, Erickson, Fornell et al., and Thompson and Teng. How- ever, unlike those authors, Rao and Bass consider quantity (output) as the decision variable, rather than any of the marketing mix variables. The products of the firms in the oligopoly are assumed to be undifferentiated, so

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that a common industry price obtains. In the general model, the price at any point in time is a function of the current sales as well as the cumulative industry sales.

The authors first derive analytically the dynamics of industry price and market share. Insight into these dynamics is obtained by considering three extreme cases: (1) only demand saturation, (2) only demand diffusion, and (3) only cost learning. Next, numerical simulations in a duopoly are used to evaluate the implications of adopting myopic versus nonmyopic strategies at different levels of learning rate, growth rate, and price elasticity. Finally, the authors generate hypotheses about the determinants of price dynamics and provide some sup- porting empirical evidence by analyzing data from the semiconductor industry.

Rao and Bass obtain several interesting results. How- ever, we believe that, generally, the use of quantity as the decision variable and the assumption of a common industry price are restrictive from a marketing viewpoint. The authors point out that this modeling approach may be appropriate for several industrial products and some consumer products, but not for packaged goods.

Organizational structure decisions. Two important strategic decision areas relating to the organization of the marketing activities are (1) centralized versus decentralized brand management and (2) vertical integration versus an independent distribution system. The issue of organizational structure has been of major concern to business strategists and researchers in organization behavior (Chandler 1962; Lawrence and Lorsch 1967), whereas the channel decision has been considered "among the most critical marketing decisions facing management" (Kotler 1984, Ch. 17). Both of these decisions have been viewed as a tradeoff between control and efficiency. Little attention has been directed toward the impact of competition on these decisions.

Shakun (1968) examines the implications of central- ization in interrelated segments and McGuire and Staelin (1983) study channel structure (the vertical integration issue). Both models take a simultaneous and noncooperative behavioral mode approach in a duopolistic context. In contrast to previously reviewed models which consider continuous decision variables, these models focus on discrete decisions. Shakun's model considers three types of structural situations: (1) both competitors are centralized (i.e., each firm maximizes its total profits in both segments), (2) both competitors are decentralized (i.e, each firm has two managers, each maximizing his or her segment-level profits), and (3) the mixed case in which one firm is centralized and the other is not.

One may expect a priori that any one firm would be better off (in terms of maximizing its total profits) with a centralized structure (because its profits in the two segments are jointly maximized rather than separately maximized). However, Shakun shows that in a competitive market this is not necessarily so. The choice of organizational structure depends intimately on what the competing company chooses as well as the nature of the in-

terrelationship between segments. In a similar spirit, McGuire and Staelin examine the

vertical integration issue in a channel context, assuming two manufacturers each with one retailer who may not be independent of the manufacturer. Again, there are three combinations of channel structures-decentralized, integrated, and mixed. The decision variables for a given structure are the manufacturer's wholesale price and the retailer's price. The competitive interaction is modeled as follows: (1) retailers set prices by maximizing profits in a simultaneous and noncooperative mode of behavior (the Bertrand model; see footnote 1), taking wholesale prices as given, and (2) the manufacturers then set their prices to maximize profits given the other manufacturer's wholesale price (simultaneously and noncooperatively) and the retailers' reaction functions based on their decision rule (leader-follower, Stackelberg model). The fully integrated case becomes a simple Bertrand model. In the mixed case, the integrated firm and the retailer compete as the two retailers in the fully decentralized case, whereas the nonintegrated manufacturer takes into account all responses to its moves when choosing its profit- maximizing wholesale price.

McGuire and Staelin examine the profit implications for firms under different structures, as a function of the substitutability or the degree of differentiation between the products manufactured by the two firms. Then they determine the channel structure implied by static equilibrium conditions for ranges of the product substitutability. They find that for most specifications6 product substitutability does influence the equilibrium distribution structure.

An interesting common implication of the two models is that in some circumstances the choice between the two discrete alternative organizational structures, in light of the competition, takes the form of a prisoner's dilemma game (Luce and Raiffa 1957). In Shakun's model, it is possible that the two firms are best off when both are centralized, even though decentralization is the dominant alternative for each one of them.7 In McGuire and Stae- lin's model, however, both firms are better off with a pure decentralized system than with a pure integrated system.

These models provide interesting implications and testable propositions, but some important factors are not considered. In modeling channels of distribution, factors such as inventory, ordering, and production should be incorporated to capture fully the channel activities. These factors, by their nature, are dynamic and hence call for a dynamic formulation. In addition, it is not uncommon for firms to use both independent and company-owned outlets. The critical question is, "What is the optimal

6McGuire and Staelin examine other possible competitive behavioral modes as well, including a cooperative mode.

7The firm is better off decentralizing (relative to being centralized) whether the competitor is centralized or decentralized.

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mix of company-owned and independent components of the distribution system over time?"8

Summary. In reviewing deterministic models addressing competition among incumbent firns, we note certain basic similarities and differences in substantive modeling and managerial issues among the models. Four models consider a sequential and reactive competitive behavior mode-Ballou and Pipkin (1980), Bensoussan, Bultez, and Naert (1978), and Brems (1958) examine implications from the perspective of the attacker, whereas Hau- ser and Shugan (1983) take a decision-oriented approach from the defender's point of view. The other models assume simultaneous and noncooperative competitive behavior except for the Rao and Shakun (1972) model, which examines the implications of both cooperative and noncooperative behavior in a simultaneous interactive situation. In addition, the models proposed by Hauser and Shugan (1983) and Rao and Shakun (1972) provide insight into marketing decisions in the light of new competitive entry.

Dynamic models permit the explicit incorporation of the inherent dynamics of both sales response and competitive interaction. This feature is particularly important in the case of variables such as advertising, where carryover effects must be considered. Furthermore, in situations where conditions change rapidly (such as diffusion of new products), static analyses often may be suboptimal, though, as Thompson and Teng demonstrate in terms of pricing strategy, myopic (or static) strategies may, under certain conditions, be close to dynamically derived optimal strategies.

Other than those of Hauser and Shugan (1983) and Kotler (1965), the models focus on one or two decision variables. Though in general models incorporating a larger number of marketing mix variables provide richer implications, there are industries or marketing conditions where only a limited number of variables may be used in practice as competitive weapons, because of either regulation (e.g., in pricing or advertising as in the case of certain medical services) or greater effectiveness of one (or a few) variable(s) relative to others. Changing elasticities of different marketing mix variables over the product life cycle (see, e.g., Mickwitz 1959) may imply that the "competitive weapons" should vary over the product life cycle (Buzzell et al. 1972). "Advertising wars" or "price wars" also point to the use of one (or a few) decision variable(s) in particular competitive situations.

Deterministic Models Addressing Competition Against Potential Firms

We review five models whose major focus is on entry or entry-related issues. Lane (1980) examines equilib-

'This issue was raised and discussed in a recent conference on distribution channels, sponsored by the Marketing Science Institute, at Duke University, September 1984.

rium strategies, in terms of product positioning and pricing, in an oligopolistic market with endogenous sequential entry. Spence (1981) also considers sequential entry in a dynamic context (i.e., temporal competition), focusing on the effect of cost decline through learning and intertemporal growth in demand on market performance and structure. Eliashberg and Jeuland (1984) and Clarke and Dolan (1984) address the issue of dynamic pricing strategies in a sequential entry context where the entry date is known, largely from the point of view of the first (monopolist) firm. Finally, a slightly different issue, that of initial goodwill and its possible impact on entry, is considered by Fershtman, Mahajan, and Muller (1984). Two static models focusing on marketing decisions but in an entry-related context (Rao and Shakun 1972; Hau- ser and Shugan 1983) already have been reviewed.

The research stream on spatial competition in the economics literature (e.g., Eaton and Lipsey 1979; Salop 1979) draws on Hotelling's (1929) geographic location framework. Spatial competition in a geographic location sense is, in several respects, similar to spatial competition in multiattribute product space (Lancaster 1979). We focus on the latter because it is more popular in the marketing literature.

Lane's model represents an interesting attempt to combine descriptive and normative perspectives as to how a firm may choose first the product specification to offer (i.e., the product's attributes) and then the price to charge. The model is based on consumers who are heterogeneous in terms of the relative importance of the product attributes in their utility function. Each consumer chooses the product-price combination that maximizes his or her utility function, demanding one unit of output per period. Product positioning decisions by new entrants are made by taking into account the anticipated responses of subsequent entrants. A firm first chooses its product position in a two-attribute space and then chooses its price, assuming that prices of the competitors will not change in response to its actions. A firm incurs a large fixed cost (assumed equal for all firms) when it selects its product position and decides to enter the market. Firms enter the market sequentially, and they know in advance at what point in the sequence they will enter. Lane analyzes two cases, (1) when the number of firms is exogenously specified and (2) when firms are free to enter and hence the number of firms is endogenously determined.

Spence (1981) also focuses on sequential entries by firms with entry times specified exogenously. He examines the influence of the dynamics of cost and demand and entry timing on market performance and structure (in particular, the number of firms). More specifically, Spence focuses on the effect of the learning curve.

Eliashberg and Jeuland (1984) consider a market for innovative goods which saturates over time. The market is monopolistic in the first period and duopolistic in the second period following entry. Each period is formu- lated as a continuous time problem and a differential game

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approach is employed. Price is the major decision variable and the products of the two firms are assumed to be differentiated. Within this framework, comparisons are made between monopolistic and duopolistic market prices and between foresighted and myopic (i.e., a decision maker who discounts the future) monopolists.

Clarke and Dolan (1984) also consider a situation in which a firm has monopoly status for a predetermined period before being joined by a second competitive firm in the market. The authors use a computer simulation approach to address the following questions: "Under what circumstances does the solution of a series of short-run maximization problems imply seriously suboptimal long- run profits?" "When short-term profit maximization does not make sense, are there simple pricing rules that do?" Three pricing strategies are investigated during the monopoly period: (1) the myopic price strategy, (2) skimming strategy, with a price above the myopic price but below the maximum reservation price of consumers in the market, and (3) penetration strategy, based on a price below the myopic price but above unit cost. For the new entrant, two pricing strategies are considered during the competitive period, (1) sequential and reactive and (2) price matching.

In an oligopolistic market for a new product, some firms may have a differential advantage in terms of their initial goodwill. Indeed, such goodwill can constitute a barrier to entry. A legitimate question from a potential entrant's viewpoint might be, "Under what circumstances will the long-term market steady-state condition not be affected by the initial goodwill of each firm?" Fersht- man, Mahajan, and Muller (1984) address this issue.

Lane's model illustrates a major research tradeoff faced by modelers. It provides an equilibrium analysis to a problem similar to that addressed by Hauser and Shugan, but considers fewer decision variables. By not focusing on equilibrium solutions, Hauser and Shugan can include a larger number of marketing mix variables. The strategic implications of Lane's model are clearly valu- able; however, his approach is static because each firm makes only one-time decisions. Issues of entry are typically more important in emerging markets for new products and hence a dynamic approach appears more suit- able.

The dynamic models considered here are not free of limitations. Spence considers a homogeneous market with one price prevailing for all firms at any point in time, determined by the market, and output is the assumed decision variable. Eliashberg and Jeuland assume no learning on the cost/demand side. Clarke and Dolan address nonequilibrium pricing strategies and their simulation approach limits the generalizability of the results. Fershtman and his colleagues do not consider learning on the cost side and focus only on steady-state conditions. Furthermore, all of these models consider the entry time and the competitors' motivations to be known under certainty. It is worth noting that some interesting and important work in which the latter assumption is re-

laxed has begun to emerge recently in the economics literature (Milgrom and Roberts 1982).

Models Addressing Competitive Decision Making Under Uncertainty

In practice, competitive interaction in an oligopolistic situation is clearly characterized by uncertainty about the interrelationships among the firms and the fact that the decisions of each one affect the others. Equilibrium solutions such as those modeled through the simultaneous and noncooperative mode of behavior are based on sim- plified behavioral assumptions that effectively eliminate such uncertainty. As Cyert and DeGroot (1970) observe, one of the main problems with the traditional models is their nonadaptive character.

The importance of competitive adaptability has been emphasized in the marketing literature (e.g., Henderson 1983). Porter (1980, Ch. 3) also stresses the importance of analyzing the competitors to assess their likely strategy changes, their probable response to feasible strategic moves made by other firms, and their probable reaction to environmental changes. In fact, Kotler's (1965) simulation study examines informally the consequences of various strategies including competitive-adaptive and completely adaptive, which touch on the issue of adaptive competitive behavior.

In this section, we review some duopoly models that explicitly address issues of uncertainty and adaptive learning by firms about each others' reactions. The models examined are those proposed by Cyert and DeGroot (1970, 1973) and by Eliashberg (1981). They employ the Bayesian framework, which affords insights into the dynamic evolution of the competitive situation examined.

Cyert and DeGroot (1970) propose a multiperiod model in which firm 2 makes its output decision after learning firm l's output decision. The innovative feature of the model is the use of reaction functions that involve an unknown parameter and a random component. By using Bayesian analysis, the authors show how the firm is able to adapt its decisions as it gains additional information about the unknown parameter from its rival's behavior. In a subsequent article, Cyert and DeGroot (1973) con- tinue this stream of research and develop a model in which the two firms move over time from a path leading to a noncooperative equilibrium to paths leading to equilibria defined by various degrees of cooperation, and ultimately to the cooperative solution. Decisions are made by the two firms in alternating sequence.

Employing the same framework, Eliashberg (1981) analyzes duopolistic competitive decision-making situations, with either competitor facing a choice between two discrete alternative courses of action. This analysis generates four possible outcomes (states) for the industry. For example, one can think of a monopolist and a potential entrant each having two alternative courses of action: attack or keep the status quo for the entrant and defend or do nothing for the monopolist. The four possible states are (entrant's choice first): attack-defend, at-

253




tack-do nothing, status quo-defend, and status quo-do nothing. If some states can be thought of as cooperative/ noncooperative, the model bears similarity to that of Cyert and DeGroot (1973). The competitive interaction mode is simultaneous and noncooperative at any point in time (not sequential as in the Cyert and DeGroot model) and is based on the rival's expected action as perceived by each competitor. The major objectives of this work are (1) to identify conditions under which the system may cycle among all four states, only two states, or be stable in the sense that the same state always prevails, and study the dynamics of the system under cycling and (2) to examine the impact of the competitors' risk attitude on their interactive behavior (see Eliashberg and Winkler 1978 for further treatment of this issue).

The major strength of the preceding three models is that in addition to outcomes, they are concerned explicitly with the competitive and adaptive decision-making process that may lead to various outcomes. These models incorporate explicitly the notions of expectations and adaptability, which are crucial in dynamic and uncertain environments. Their major limitation, in their present form, is that they do not provide implications directly related to various marketing-mix variables.

A BANK OF IMPLICATIONS AND TESTABLE PROPOSITIONS

In this section, we summarize some of the major implications of the models we have reviewed as a set of propositions that can be tested empirically. We catego- rize these propositions in terms of the major managerial issues they address which cut across the various models.

Unit Manufacturing Cost Advantage A firm may have a unit manufacturing cost advantage

because of inherently greater efficiency, because it man- ufactures a lower quality (and hence cheaper) product or, in a dynamic situation, because of faster experience (learning) curve effects.

Proposition 1. A competitor with a cost advantage generally will spend more on advertising and have a larger market share and profits than its rivals (Gupta and Krishnan 1967; Thompson and Teng 1984).

Corollary 1.1. Proposition 1 may hold even when the cost advantage results from inferior product quality, in situations in which consumers have incomplete information about the performance of the competing brands, especially if consumers believe that better brands spend more on advertising (Schmalensee 1978).

Proposition 2. When one firm has a cost advantage, the best policy for the rival firms may be to employ different competitive tools, even when the sales response to the different instruments is identical for all firms. For example, if the lower-cost firm spends more on advertising, its rival's best policy may be to charge a lower price (Gupta and Krishnan 1967).

Proposition 3. Firms with different but constant unit production costs, competing in saturating markets for dif-

ferentiated products, will price their products such that the lower-cost product's price is lower and declines less rapidly over time (Eliashberg and Jeuland 1984).

Proposition 4. In an undifferentiated market where there is a common industry price and the effect of experience on cost is negligible: a. If demand saturation dominates demand diffusion

(e.g., in the decline stage of the product life cycle for durables), the industry price declines monotonically over time. For any pair of firms the lower- cost firm has a higher market share, and the difference in market shares generally widens over time.

b. If demand diffusion dominates demand saturation (e.g., in the early stages of the product life cycle), the industry price increases monotonically over time. For any pair of firms the lower-cost firm has the higher market share, but the difference in market shares generally narrows over time (Rao and Bass 1985).

Proposition 5. In an undifferentiated market where there is a common industry price, demand is independent of cumulative industry sales, and costs decline with experience, the price declines monotonically over time. The ranking of the firms in terms of their respective market shares may change over time, as finms with high costs may find it beneficial to produce more than low- cost rivals (Rao and Bass 1985).

Differential Advertising Effectiveness

A firm also may have a competitive advantage if its advertising is more effective either in terms of its immediate impact on sales or in terms of greater carryover effects.

Proposition 6. The competitor with the smaller sales decay parameter (i.e., a greater long-run effect of a dollar spent on advertising, relative to the rival) will spend more on advertising, particularly during the beginning of the planning period, and will have larger profits over the period as well as a larger terminal market share. It may decrease its advertising during the later part of the planning period, relying substantially on the carryover effect, particularly if profit maximization over the period is more important than terminal market share (Deal 1979).

Proposition 7. If the advertising investment rate is mea- sured in nonmonetary terms (e.g., number of media ads), a firm having a lower unit cost of advertising (e.g., due to more cost-effective media selection) will invest more heavily in advertising (in a nonmonetary sense) and will have higher profits and terminal market share than its rivals (Thompson and Teng 1984).

Proposition 8. In a mature duopolistic market which is in a stable (steady-state) condition, the competitive advertising rate depends on the relative unit contribution and the relative advertising elasticity. Relative market shares also depend on these factors, as well as on relative advertising effectiveness (Erickson 1985).

In particular, if the advertising elasticities are equal, the following corollary is implied.

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Corollary 8.1 Under the conditions specified in proposition 8, the relative market share at steady state is directly proportional to the relative advertising effectiveness, and it also depends on the relative unit contribution. Furthermore, the ratio of advertising expenditures is given by the ratio of the unit contributions (Erickson 1985).

Implications of Sequential Entry in a Competitive Market

Propositions 9 through 11 examine the impact of the second entrant in the .hitherto monopolistic market and compare pre-entry (monopolistic) with post-entry (duopolistic) prices. Propositions 12 through 14 examine the implications of sequential entry, both for individual firms and industry post-entry performance.

Proposition 9. In markets where price is perceived as an indicator of quality and consumers are heterogeneous with respect to the acceptable price range, the equilibrium prices for two brands (i.e., an incumbent and a new entrant) will be on either side of the optimal monopolistic price (that is, one price is higher and the other is lower than the monopolistic price). The de- viation of either price from the monopolistic price increases with the degree of heterogeneity among consumers with respect to their acceptable price range (Rao and Shakun 1972).

Proposition 10. In a new durable good market that saturates over time, in which experience curve (learning) effects are negligible and the innovation effect is dominant, a monopolist anticipating entry will price lower than a monopolist who does not anticipate entry. In general, prices during the monopolistic and duopolistic periods will decline over time (Eliashberg and Jeuland 1984).

Proposition 11. Under the conditions specified in proposition 10, when the first entry occurs the monopolist's price will drop at the point of entry, the extent of the drop being related directly to the degree of product substitutability (Eliashberg and Jeuland 1984).

Proposition 12. In situations where it is difficult (i.e., prohibitively expensive) for firms to change their product positioning strategies once implemented, early firms position their product to appeal to the larger (and more profitable) segments; later firms seek alternative product positions (away from the incumbent firms) to re- duce price competition, appealing to diverse preferences of consumers. Firms entering earlier in the sequence thus choose the most attractive locations (in the multiattribute space) and receive higher profits, even in the absence of a cost advantage (Lane 1980).

Proposition 13. Profits and, in most situations, prices are related inversely to the number of finns entering the market.9 Typically, barriers to entry, due to such fac-

9Exceptions where entry may actually result in high prices for at least one firm are exemplified by situations where price is an indicator of quality (proposition 9) or in certain highly segmented markets (proposition 16).

tors as cost advantage for firms obtained from experience curve effects or the absence of profitable product positioning opportunities for potential entrants, result in entry ceasing after a limited number of firms (around three to six) are in the market (Lane 1980; Hauser and Shugan 1983; Spence 1981.

Proposition 14. In a steady-state condition for consumer nondurable goods markets, the established brands which have built up a stock of consumption experience (1) spend proportionately less on sales promotion as well as on advertising and promotion combined and (2) place proportionately more emphasis on advertising relative to sales promotion than does a newer and/or less established brand that has a lower stock of consumption experience (Fornell, Robinson, and Wernerfelt 1984).

Defensive Strategies The following propositions examine strategies for de-

fending against new products. In addition, firms may employ pre-emptive strategies, if possible, that deter entry in the first place. This issue is addressed by propositions 18 through 20.

Proposition 15. If consumer tastes are uniformly distributed across the spectrum and new entry occurs, it is optimal to (1) decrease price, (2) at the margin, improve the product quality and increase advertising to reposition the brand in the direction of the defending brand's strength, (3) only under certain conditions,10 at the margin, improve product quality and advertise to reposition the brand in the direction of the new product's strength (Hauser and Shugan 1983).

Proposition 16. There may be certain highly segmented consumer taste distributions for which a price increase is the optimal response to competitive entry (Hauser and Shugan 1983).

Proposition 17. Unless it is possible through a pre-emptive distribution or advertising strategy to prevent the entry of a new brand, expenditure on distribution and awareness advertising should be decreased in response to the new entry (Hauser and Shugan 1983).

Proposition 18. In markets where the fixed cost of entry is high and product repositioning is not feasible, the early firms may find it profitable in the long run to employ entry-deterring product positioning strategies. However, when fixed costs are relatively low, the profit- maximizing strategy is to accept the new entrant and adjust accordingly (Lane 1980).

Proposition 19. In consumer nondurable (or highly de- preciable durable) goods markets, where firms have roughly equal and constant product unit costs, the steady- state condition of the market may not be affected by the initial stocks of goodwill (or initial market shares) if the intensity of the competition, in terms of the de-

lOThese conditions are (1) when the competitor is not very strong and can be dominated along the attribute along which its attack is based and (2) when the competitor attacks not only along its strong attribute but along the defender's strength as well.

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gree of product substitutability, is sufficiently low (Fershtman, Mahajan, and Muller 1984).

Proposition 20. Cost advantage gained by learning curve effects may be a significant barrier to entry if the rate of learning is moderate. A very rapid learning rate (or a negligible learning rate) does not necessarily result in any significant long-term advantage for the firms already in the market (Spence 1981).

Offensive Strategies The following two propositions examine offensive

strategic moves initiated by a firm to gain competitive advantage. The competing firms are assumed to react defensively (in a sequential manner) in response to these offensive moves.

Proposition 21. In a leader-follower situation, where the follower's reaction to the leader's moves is determined by two major components-the long-term elasticity, which is a measure of the intensity of the follower's reactions, and a distributed lag function, which is in- dicative of the timing (and spread over time) of the reaction-the leader will be more aggressive in its at- tacking strategy (e.g., by spending more on advertising or greatly improving its product quality) if it expects a less intense and/or more delayed and "diffused" response from its competitor (Brems 1958; Bensoussan, Bultez, and Naert 1978).

Proposition 22. In highly competitive situations, all companies are more likely to adopt niching strategies by specialization; in relatively noncompetitive situations, the dominant market leader (if one exists) is more likely to adopt a broad-based strategy (e.g., brand prolifer- ation) that has universal appeal, whereas other competitors will again seek specialization (Ballou and Pip- kin 1980).

Head-to-Head Versus Differentiated Strategies The following propositions suggest conditions under

which a head-to-head competitive strategy (or "me too" strategy)-i.e., competing firms make similar decisions-may be appropriate, and those under which a strategy different from that employed by the competition may be preferred. Propositions 23 through 26 relate to allocation of advertising over segments, proposition 27 addresses allocation of advertising over time, and proposition 28 examines a "me too" strategy in the context of vertical integration. Finally, proposition 29 considers the profit implications of myopic and nonmyopic strategies.

Proposition 23. In situations where companies compete in several independent market segments, each company allocates its advertising budget to each market segment in direct proportion to the sales potential of that segment (Friedman 1958).

Proposition 24. In a duopolistic situation, if a company knows its rival's allocation of advertising budget among the independent segments, the company's optimal allocation lies between its rival's allocation and the allocation specified in proposition 23 (Friedman 1958).

Proposition 25. In a duopolistic situation where the companies compete for business with several customers (e.g., industrial buyers) and the (single) vendor choice is based essentially on the relative sales promotional efforts of the firms, the firm with the larger budget should allocate its budget over all the customers, whereas the firm with the smaller budget should concentrate only on a fraction of the customers, effectively ignoring the others. This fraction is given by the ratio of the smaller to the larger budget, so that both firms compete on equal terms for business from the customers who are in this fraction of the total market (Friedman 1958).

Proposition 26. In situations where companies compete in several market segments and advertising in one segment negatively influences sales in another, the total advertising expenditure by all companies in any particular segment will vary directly with the degree of influence of advertising in the other segments on sales in that segment, and inversely with the degree of influence of advertising in that segment on sales in other segments. In situations where this influence is positive, the relationship is reversed (Shakun 1965).

Proposition 27. In competitive situations that are symmetric in all respects except that firms differ in their objectives to the extent that some firms place a greater emphasis on maximizing terminal market share (at the end of the planning period) relative to maximizing profits over the period, the competitor that places a greater weight on terminal market share will advertise to a greater extent toward the end of the planning horizon. If this emphasis is sufficiently high, the firm's advertising over the horizon may be monotonically increasing, whereas for firms emphasizing profit maximization, advertising would typically monotonically decrease over time (Deal 1979).

The following proposition holds in situations where each retailer may carry products of only one manufacturer.

Proposition 28. In duopolistic situations, both manufacturers would find it more profitable to use company stores rather than an independent intermediary in markets where the degree of product substitutability is low, i.e., there is less competition at the retail level. Sim- ilarly, control of the distribution system (by imposing sales quotas or setting the retail price) is the best policy for both manufacturers when the degree of product substitutability is low. In contrast, for more highly competitive (substitutable) goods, manufacturers will be more likely to use a decentralized distribution system (McGuire and Staelin 1983).

Proposition 29. In an undifferentiated duopoly market where there is a common industry price and cost learning effects are present, profits for the two competing firms will be lower if both firms pursue nonmyopic optimal strategies than if both firms act myopically. A myopic strategy may be useful only if the other firm is also myopic. If, however, the other firm adopts a nonmyopic optimal strategy, the myopic strategy will be very unprofitable (Rao and Bass 1985).

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Implications of Nonequilibrium Competitive Strategies

In practice, firms often may not use equilibrium strategies, possibly because the complexity of the situation makes it difficult or even impossible to determine such strategies. Instead, companies may use certain ad hoc but intuitive guidelines to determine their competitive strategies.

The following propositions evaluate some strategies that may be considered by managers in such situations.

Proposition 30. A strategy where each competitor sys- tematically seeks to "out appeal" its rival in every possible way in the interest of achieving the larger market share (by setting lower prices and higher advertising and distribution budgets relative to its rival's levels for the previous period) is mutually ruinous. Even when the rival does not use the same policy, such a strategy is generally dominated by other possible strategies (Kotler 1965).

Proposition 31. In market situations characterized by dynamic demand and experience curve effects, simple dynamic pricing rules using no more information than required for myopic price determination may substantially outperform the myopic price rules (Clarke and Dolan 1984).

Proposition 32. In an undifferentiated market where there is a common industry price, profits under nonmyopic optimal strategies would differ substantially from profits under myopic strategies when: a. Cost learning rates are intermediate. b. The market potential is growing over the horizon. c. The demand is highly price elastic (Rao and Bass

1985).

Dynamics of Competitive Behavior Under Uncertainty

The following propositions consider the implications of competitors' uncertainty about their rivals' behavior, and the impact of risk attitudes and learning about each other's competitive behavior over time.

Proposition 33. When competitors are uncertain about each other's reactions but adapt and learn by observing each other's sequential reactive moves over time, it is possible for them to begin their dynamic competitive interaction in a noncooperative behavioral mode but later change their behavior, through learning over time, toward a more cooperative behavioral mode without ac- tively colluding, to the mutual benefit of the firms (Cyert and DeGroot 1973).

Proposition 34. When competitors must select one of two discrete alternative actions and they are uncertain about each other's strategy choice, but learn by observing each other's decisions over time (at each time, the decisions are made simultaneously), the industry may be in a stable competitive situation or cycle among two or all four competitive states (each state is defined by the combination of competitors' actions, e.g., noncooperation and cooperation), depending on the initial preference structures of the competitors with respect to the various possible states (Eliashberg 1981).

Proposition 35. Under the conditions specified in proposition 34, if the cycle is composed of two states its length remains constant, and if the cycle is composed of four states the duration of each cycle increases with time as firms learn more about each other, so that changes from state to state take place more slowly in later cycles (Eliashberg 1981).

Proposition 36. Under the conditions specified in proposition 34, when the cycle is composed of all four states, the less risk averse one of the competitors in the industry becomes, while the other maintains the same attitude toward risk, the longer each cycle will be (Eliashberg 1981).

DISCUSSION AND SUGGESTIONS FOR FUTURE RESEARCH

We have reviewed various analytical models of competition having marketing implications. Our review illustrates the range of issues, tradeoffs, approaches, and implications associated with this area of research. We now discuss several issues that, in our opinion, warrant further attention.

Predictive Validity and Usefulness

Basically, most of the analytical models have been developed to derive certain normative conclusions about competitive outcomes, based on a certain set of assumptions. The logical question is, "How well do analytical models of competition perform in practice?" At this stage, we do not have a clearcut answer. We point out in our review instances in which the implications of some of the models are consistent with commonly observed marketing practice. These and other implications discussed in our review can be tested empirically. We strongly en- courage such empirical work and present a wide range of testable propositions that can be investigated by marketing econometricians. Such empirical work represents the first step toward testing the usefulness of the models.

Testing the propositions does not necessarily require an accurate estimation of the parameters of the model. However, the situation under which a proposition is tested should correspond to the scenario the model delineates. For instance, models concerned with long-run steady- state conditions should be tested with data obtained from mature industries. Testing of propositions in the first stage establishes whether at least the direction of effects pre- dicted by the model is consistent with the empirical data.

The perspective taken here is that the models are par- amorphic (i.e., they provide a prediction under the assumption that the decision maker behaves as though he or she were following some normative decision rule), similar to various consumer preference and choice models that have been employed with success by marketing scientists (e.g., Eliashberg 1980; Hagerty and Aaker 1984; Hauser and Urban 1977). From this perspective, predictive validity does not imply that the model's prediction is based on a valid description of the actual decision- making process and competitive behavior. This potential

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lack of descriptive validity represents a possible short- coming and identifies directions for future research, as discussed next.

Informational, Motivational, and Behavioral Assumptions About the Competitors

The classical Cournot model can be interpreted be- haviorally and dynamically as a decision-making process where each firm is making decisions based on conjectures about the slopes of its rivals' reaction functions. These conjectured slopes are called conjectural variations (Kamien and Schwartz 1981). Competitors that achieve Courot equilibrium are assumed to take the others' strategy as given-i.e., they act according to zero conjectural variations. We note, however, that these conjectural variations are inconsistent because each competitor does in fact react (though it is not assumed to do so) to its rival's action.

In general, conjectural variations may be nonzero. Economists (see, e.g., Bresnahan 1981) have attempted to narrow the number of possible equilibrium outcomes by imposing the additional constraint that the conjectural variations be consistent. Consistency requires that the firm's conjectures about the slopes of the rivals' reaction functions should coincide with the actual slopes. This departure from the assumption of zero conjectural variations represents an attempt to base the model's prediction on more plausible (but still strong) behavioral assumptions. From a marketing perspective, it raises two issues. First, in reality, competitors are almost always uncertain about each other's future moves and reactions; second, competitors in practice may not always act ra- tionally in a mutual consistency sense. Though some modelers (Cyert and DeGroot 1970, 1973; Eliashberg 1981) recognize both these factors when they allow their models to incorporate adaptive learning in a Bayesian framework, more attention should be given in the future to these issues.

The issue of the applicability of the notion of mutual rationality, which is the cornerstone of game theoretic models, in realistic competitive situations where nonra- tional behavior may be expected to occur has sparked an interesting philosophical debate following Kadane and Larkey (1982a), who challenged the traditional approach of game theory and advocated instead the adoption of a moder subjective view of probability for game theoretic applications. (Interested readers are also referred to Har- sanyi 1982a, b; Kadane and Larkey 1982b, 1983; Shubik 1983.) Our views, in terms of modeling competition, follow.

1. From the perspective of basic understanding of competitive markets (i.e., from a "detached" viewpoint), we need a descriptive model based on how competitors believe the others act and how the competitors actually act (more precisely, the modeler's "best" judgment of how they act).

2. From a decision-oriented perspective (i.e., from a con- sultant's viewpoint), two theories are required: a pre-

scriptive theory to guide the "client" firm's decision making and a predictive theory of the competitors' behavior (Kadane and Larkey 1983).

3. In general, a classical game theoretic approach assuming completely rational behavior by all competitors may serve as a good "benchmark" for both purposes. In particular, for decision-oriented models, such an approach may provide a useful first-cut approximation to predicting the rivals' behavior, in the absence of any other basis. This initial conjecture should be revised as information is gained over time by observing the competitors' actual behavior.

As Kadane and Larkey argue, a descriptive model incorporating perceptions of firms about the likelihood of taking certain actions must be based on empirical evidence supported by psychological theory. We believe that empirical and further theoretical work in this area de- serves the highest priority, if richer and more useful competitive models in marketing are to emerge. The need for such work, in our judgment, opens an important research avenue for marketing behavioral scientists. Per- haps a good starting point could be laboratory experi- ments with simple paradigms such as those presented by Rapoport, Guyer, and Gordon (1976), but where the decision making is in a marketing context. The work by Cyert, Feigenbaum, and March (1959), Howard and Morgenroth (1968), and Hogarth and Makridakis (1981) on information processing under competitive conditions, as well as the experimental work in economics (Plott 1982; Smith 1982), is also very relevant in this regard.

Models have been proposed in the marketing literature which explicitly consider competitive reaction, in the form of competitive response elasticities, and which were estimated econometrically through empirical data (Lam- bin, Naert, and Bultez 1975 from a single firm's perspective; Hanssens 1980 from an industrywide viewpoint). In the context of the dynamic competitive interaction process, such an approach might have two limitations. First, the competitor's conjectures about its rivals' reactions at any point of time may not coincide with the econometrically estimated response elasticities. This dis- crepancy would limit our understanding of decision- making processes in competitive settings. Second, when learning takes place and then competitors adapt their behavior, the actual (dynamic) response elasticities would be time-varying and not stationary parameters to be estimated. However, an econometric estimate of competitive response elasticities may also provide a useful "first- cut approximation" to assessing competitors' reactions and decision-making processes.

In terms of modeling the decision makers' preference structure (which determines their motivations), the applicability of multiattribute utility theory was discussed. This approach permits explicit incorporation of,uncertainty, attitudes toward risk, and tradeoffs between different conflicting objectives. In the case of the firm with multiple decision makers, a group utility function must be developed which may not necessarily be a weighted sum of the individual utility functions (Hull, Moore, and

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Thomas 1973; Keeney and Raiffa 1976, Ch. 10). Other approaches to addressing uncertainty and its

management are available. Value maximization models and in particular the Capital Asset Pricing Model (CAPM) have been developed and popularized in the financial literature. Jagpal and Brick (1982) apply the CAPM in developing a marketing mix model under uncertainty. An important difference between the CAPM and expected utility approaches is that the former maximizes the utility of the shareholder whereas the latter (typically) takes the decision maker's (i.e., manager's) perspective. In our view, in a descriptive or predictive context, a model based on maximization of the decision maker's utility is more valid. In a prescriptive context, it is also imperative that the recommendations derived from the model be consistent with the decision maker's objectives if they are to be implemented. Consequently, we favor the expected utility approach, particularly when its greater flexibility and ability to incorporate nonfinancial objectives are considered.

Assumptions About Consumer Behavior

Most analytical models, especially the dynamic ones, begin with aggregate and often oversimplified behavioral assumptions about the consumer. As we observed before, marketing is in a position to incorporate more in- sightful consumer behavior perspectives, based on analysis at the individual level. Such an approach permits explicit consideration of consumer heterogeneity, and consequently provides a more meaningful basis for examining product positioning and segmentation strategies. Not surprisingly, for all three (static) models that explicitly address product positioning issues (Ballou and Pipkin 1980; Hauser and Shugan 1983; Lane 1980) market behavior is developed from the individual level.

It must be recognized that there are always tradeoffs between tractability and richness. Though more elabo- rate consumer behavior models may be desirable, we believe that a higher priority must be given to the issue of the competitors' informational and behavioral assumptions, because competitive interaction is the essence of models of competition.

Coverage of Marketing Decision Areas Our review, summarized in Tables 1 through 3, iden-

tifies certain lacunae in terms of marketing decision areas that have been covered inadequately or not covered at all. In particular, we note the following opportunities for modelers.

1. There are no dynamic marketing models which address the dynamics of multiple entries tracing the evolution of oligopolies.

2. Other than Kotler's (1965) model which takes a simulation approach to evaluating a set of a priori strategic decision rules, we are unaware of models which examine the dynamic nature of the marketing mix (multiple variables) and its impact on existing competitors' performance.

3. In general, except in work by Hauser and Shugan (1983) and McGuire and Staelin (1983) in a channel organization context, distribution has been ignored as a decision variable in a competitive setting.

4. Few models consider product line (as opposed to a single product) and segmentation decisions.

5. There are no dynamic models that examine organization structure/vertical integration issues over the product life cycle.

These are clearly areas of future research for modelers of competition.

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