Multi-outlet firms, competition and market segmentation strategies

ELSEVIER Regional Science and Urban Economics 27 (1997) 67-86

ECONOMICS

Multi-outlet firms, competition and market segmentation strategies Jean-Claude Thill* Department of Geography, University of Georgia, Athens, GA 30602-2502, USA Received November 1994; final version received September 1995

Abstract

This paper examines horizontal differentiation between outlets serving a market characterized by a geographic dimension and a quality dimension. It departs from the bulk of the location literature by assuming that some firms own several outlets and serve the market from these multiple locations. The paper contrasts a strategy of homogeneous store quality with a strategy of heterogeneous quality. For both strategies, competition between multi-outlet firms is articulated around two main forces whose interplay controls the geography and value offering of the industry. The reservation price of consumers for shopping at less than ideal outlets pushes outlets apart, whereas the probabilistic nature of outlet patronage fosters the aggregation of outlets. The relative strength of each force changes with the conditions of the market. Simulation results also highlight the impact of market strategies on competitive behavior. The constraint of the same value position has little or no influence on industry-wide differentiation for reservation utilities that are large or small enough. For intermediate reservation disutilities, the constraint serves to preserve the geographic spread of outlets until firms are better off aggregating both in value and geographically.

Keywords: Horizontal differentiation; Spatial competition; Multi-outlet firms JEL classification: D21; L81; M31; R32

* Correspondence address: Department of Geography and National Center for Geographic Information and Analysis, State University of New York, Buffalo, NY 14261-0023, USA. Tel.: +1 (716) 645-2722; fax: +1 (716) 645-2329. 0166-0462/97/$17.00 (~ 1997 Elsevier Science B.V. All rights reserved P I I S0166-0462(96)02131-X

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1. Introduction

In a recent paper by Neven and Thisse (1990), it was found that Hotelling's (1929) principle of minimum differentiation whereby competing firms locate at the center of the market does not provide an equilibrium solution when firms are allowed to differentiate along two dimensions. At equilibrium firms choose to differentiate maximally along one or the other dimension according to the dimensions' relative width. In another model of two-dimensional competition in which firms are allowed to serve the market from several locations, Williams and Kim (1990) show that minimum differentiation prevails in both dimensions when distances has little effect on consumers' utility. 1 This paper examines horizontal differentiation between outlets serving a market characterized by a geographic dimension and a quality dimension. It depends from the bulk of the location literature by assuming that some firms own several outlets and serve the market from these multiple locations. The paper also contrasts strategies of homogeneous store quality with strategies of heterogeneous quality. The concentration of the retail business into a few large multi-store corporations is a well-documented evolution of retail trade of Western countries since World War II (Holland and Omura, 1989). In the United States, decades of a steady increase in the portion of the nation's total retail sales captured by companies with more than one point of sale saw these companies pass the 50% market share in 1982. Another recent evolution in the U.S. retail trade is the relative contraction of the mass market as a consequence of changes in the demographics and affluence of society in the 1970s and 1980s (Sheth, 1983). The marketplace partitioned itself into a variety of submarkets, or segments, with different desires and interests (Frank et al., 1972). Retail companies have responded with strategies of market segmentation, where target customer groups are identified by similar buying requirements and expectations (Dibb and Simkin, 1991) as opposed to the conventional, undifferentiated marketing strategy of aggregation which treats the entire market as homogenous (Weinstein, 1987). Concentration on one of several possible segments of the market is a segmentation strategy that numerous retailers, including grocers Food Lion and Aldi, and electronics and appliance retailer, Circuit City, have mastered with great success. In the three cases mentioned, the company has developed and perfected a single retail concept (i.e. an identity or image) and store format that fits well the targeted markets. Certainly an important consideration for the adoption of a homogeneous store quality is in the advertising effort to develop and maintain the targeted store image over a large market. A n o t h e r segmentation strategy for success is that of market differentiation, i Prices are exogenous in this model.

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which consists in tailoring promotional, price and merchandising strategies to several specific market segments (Weinstein, 1987). Currently, many large and medium-size retail companies use this approach, including KMart, Tandy, Dayton-Hudson, The Limited, The Gap, ComputerLand, Winn Dixie, Safeway, and A&P. These retailers have established a portfolio of store formats for specific markets, often operating under different names and with a large autonomy from each other. With the advent of computerized information technology and powerful relational databases for personal computers, many retailers have even resolved to push the concept of market differentiation to its limits by tailoring individual stores to suit the tastes and needs of their shoppers. Market differentiation is often coupled with a physical differentiation of products sold in different outlets to create a fully fledged strategy of heterogeneous store quality. That the standard single-store location theory does not necessarily apply to situations where individual retail outlets are part of larger organizations run according to collective strategies, follows common intuition. Ghosh and McLafferty (1987, p. 127) find that the traditional theory and methods of retail location fail for ignoring the impact that an individual store might have on other outlets in the market area operated by the same firm. Establishing a network of two or more o u t l e t s . . , requires systematic evaluation of the impact of each store on the entire network of outlets operated by the firm and considerations of the system-wide store-location interactions.

In essence, decision-making in multi-establishment firms involves some degree of centralization to maximize system-wide goals (for instance, total profit), which may affect the performance of individual stores of the chain. Competitive strategies are adopted in the best interests of the chain as a whole but are implemented locally, which grants a great deal of flexibility to adapt to the conditions of the competitive environment of each establishment. In this paper we seek to characterize structures of horizontal differentiation that result from competition between firms that control several retail outlets and resort to market segmentation strategies. For this purpose, an address modeling framework is used. This approach is based on Lancaster's (1966) paradigm that preferences are defined over the characteristics of choice alternatives. (See Archibald et al., 1986, and Anderson et al., 1992, for a more complete discussion of address models.) In marketing theory, where choice alternatives are brands, brand attributes are the relevant characteristics, while in location theory, characteristics are the geographic coordinates of stores or firms. The address of an alternative is its location in the space defined by the relevant characteristics. In our problem, the two approaches are combined in the sense that the address of stores consists of

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their geographic location and their quality or value position. Each consumer also has an address which is given by the geographic location and value orientation of his or her most preferred alternative. Each firm selects a single address for each of its outlets that maximizes it total profit with no prior information on the move of rival firms (zero conjectural variation hypothesis). Prices are fixed and uniform. Teitz (1968) was probably the first author to devote more than casual attention to competition between multi-outlet systems. One of the problems he discusses is that of firms engaged in pure location competition on a line segment. The lack of equilibrium prompts him to pursue a leader-follower framework ~ la Stackelberg. With this alternative concept of competitive behavior, competing stores appear to alternate along the market according to a dispersed pattern at equilibrium. Ghosh and Craig (1984) report similar results. Still in the location tradition, Williams and Kim (1990) have presented a model of competition between retail systems in which the distribution of consumer demand among stores is represented by a production-constrained spatial interaction model and firms seek store locations and floor spaces that maximize profit under the zero conjectural variation assumption. A significant result of this two-dimensional model is the existence of a dispersed configuration of stores for a high deterrence of distance and of a clustered configuration when the impact of distance on store patronage weakens. Even stores that are part of the same chain a r e pulled together as the repulsion forces that drive them apart are overcome. Anderson and de Palma (1992) have used a discrete choice model for the demand side, which has been proved by Anderson et al. (1992) to be an isomorphism of address models. The nested logit model allows them to capture the loyalty of customers to firms. They show that a decline in substitutability among firms causes more firms to enter the market, each offering fewer products, while the opposite occurs in the case of reduced substitutability among products of the same firm. However, inter-firm and inter-product substitutabilities are assumed exogenously, with the implication that firms are constrained in their ability to differentiate themselves from others and in their ability to set the level of differentiation of their products that best suits the current conditions of the market. In another multi-store, two-firm problem of two-dimensional horizontal differentiation, Thill (1992a) found that the degree of differentiation among outlets involved in strategies of heterogeneous quality may be substantially smaller along the geographic dimension than along the quality dimension. Simulation results indicated that outlet differentiation is critically dependent on consumers' willingness to shop at outlets away from their ideal points and on the probabilistic nature of store patronage. While the latter fosters agglomeration, the former inhibits it. In this paper we rely on the same

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modeling f r a m e w o r k to expand on our previous analysis. First, we p e r f o r m s o m e c o m p a r a t i v e statics under a strategy of heterogeneous quality to d e t e r m i n e the role of m a r k e t structures. Specifically, we vary the n u m b e r of outlets that serve the market, the n u m b e r of firms and their relative sizes. Subsequently, the analysis is also conducted for a scenario of h o m o g e n e o u s store quality. This permits us to investigate the interplay between segmentation strategies and multi-outlet firm competition by contrasting inter-outlet differentiation under the two strategies of m a r k e t segmentation. T h e p a p e r is organized as follows. In Section 2 we set out the modeling f r a m e w o r k of the p r o b l e m , discuss its behavioral relevance and present the numerical algorithm used to simulate competitive behavior. Section 3 deals with competition under strategies of m a r k e t differentiation: outlets part of the same chain m a y adopt different value positions. The scenario of m a r k e t concentration in which stores of the same chain are bound by a c o m m o n value position is treated in Section 4. The p a p e r concludes in Section 5 with c o m m e n t s on the significance of our results and venues for future research.

2. The address model of chain competition Let us consider the m a r k e t for a given line of merchandise in a certain geographic territory. This m a r k e t is served by J firms that directly c o m p e t e with each other. Each firm j ( j = 1 . . . . . J ) in this industry operates a given n u m b e r of outlets K ( j ) . Altogether K outlets are open in the market: K = K(1) + K(2) + . . . + K ( j ) + ' " K ( J ) , with K / > J . E a c h outlet k is defined by a geographic location gk along a b o u n d e d line of length G and a value position v k . The value offered by a store to consumers reflects the quality of the shopping experience at the store as it is perceived by customers. It is a composite index related to various store characteristics, including merchandise quality and selection, service level, ambiance, and fashion orientation (Ghosh, 1990). Possible value positions range f r o m 0 to V on a line segment. The vector (gk, Vk) defines the address of outlet k in the address space G x V. For the purpose of our analysis, the address space is a square of dimensions 50 x 50. No two outlets can have the same address in the space, z Prices are fixed and equal at all locations. O n the consumer side, preferences are defined over all possible outlet

2 As a reviewer pointed out, only an identical geographical address is objectionable. However, this infeasibleness is extended here to the value dimension to preserve a certain symmetry in the problem and, thus allow for a comparison with other two-dimensional location models. Limited simulations by the author suggest that relaxing the constraint on value addresses would not alter the general conclusions of this research. However, it explains some of the non-convergent cases.

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addresses, i.e. G × V. An individual's address (or ideal point) is given by his or her ideal bundle of relevant store characteristics (i.e. geographic location and value position). Any mismatch between one's own geographic location and most preferred value orientation, and the geographic location and value position of the patronized outlet results in a disutility for the consumer. A uniform distribution of consumers along the geographic dimension is assumed. In addition, consumers differ by their tastes or preference for value offered by outlets. The diversity of favorite value combinations is assumed to be represented by a uniform frequency distribution over the interval (0, V], which is identical at all geographic locations. For notational convenience, the density of consumers on the geographic line is set equal to V. Hence, each unit of the address space has a number of consumers normalized to unity. Under the assumptions presented above, consumers perceive a disutility for not shopping at their own address in G × V. Following the relevant literature (Schmalensee and Thisse, 1988), it is postulated here that the disutility of individual i located at (gi, vi) shopping at outlet k located at (gk, vk) is given by the weighted Minkowski distance: U i -- Uk

2)

.

In this expression we follow the location theory conventions that the individual's transportation cost function is linear in its argument. However, disutility along the value dimension is quadratic, as is usual in product positioning models (e.g. Pessemier, 1980; Neven, 1985; Ben-Akiva et al., 1989). It has been argued in the behavioral geography literature that various internal and external considerations of feasibility and familiarity constrain the set of outlets actually considered in the choice process (Burnett, 1980; Desbarats, 1983). The formation of the individual choice set can be conceptualized in various ways (Thill, 1992b). It is done here by assuming that only outlet addresses that are close enough to the individual's ideal point are deemed acceptable. More specifically, an outlet has a non-zero probability of being selected, and therefore being in one's choice set, if and only if the loss of utility that would be incurred by shopping at this outlet instead of at one's ideal point does not exceed a certain threshold or > 0. All other outlets are excluded from consideration. This largest acceptable disutility (or reservation utility) is identical for all individuals. The choice set C i of individual i is then defined by

Ci = {gk, vl,)ldik < or}.

(2)

In line with a vast literature on store patronage behavior (see Hubbard's,

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1978, review, for instance), it is assumed that all the outlets in the choice set have a non-zero likelihood to be visited. Luce's (1959) strict utility postulates that the probability that a choice alternative will be chosen is equal to the ratio of the utility associated with that alternative to the sum of the utilities for all the alternatives in the available choice set. Luce's premise is loosely adapted here to the concept of an ideal point and to the loss of utility resulting from buying at an outlet away from this point. The probability of choosing outlet k is defined by the ratio of the expected disutility of choosing an outlet other than k to the sum of the disutilities for all the outlets in the choice set. Formally, the probabilistic choice rule for this case is the following:

if {k} C C~,

P,~=.~ (Ni-1)j~ec, d,j'

[?:

(3) if if

k ~ C~ , C i = {k},

where N i is the number of outlets in the choice set. This is illustrated in Fig. 1 with a hypothetical choice set containing three alternatives. Choice probabilities are plotted against the disutility from outlet 1, holding the disutility from outlets 2 and 3 constant at 3 and 5, respectively. One can readily check that the choice odds Pi~/Pi2 a r e not independent from the characteristics of a third alternative. Hence this choice model is free of the so-called property of 'independence from irrelevant alternatives' (IIA). (See H a y n e s et al., 1988, for a discussion of this property in the context of spatial choice problems.) In the context of this research, this is an advantage because it allows for choice probability ratios to depend on the size of the choice set and on the level of differentiation of outlets in the choice set, so that choice probabilities and choice set generation are more intimately related. It is worth stressing that many conventional choice models, such as the logit and spatial interaction models, are affected by IIA. This drawback is also shared by more faithful adaptations of Luce's theorem such as P~k = (0 -- di~)/~j (0 - do), with 0 arbitrarily large. The reservation utility tr plays a key role in determining choice probabilities. It defines the extent of the choice set of each individual and delineates the potential market area of each outlet. Market areas are diamond-shaped with curved sides when or is small enough. The long diagonal is parallel to the geographic dimension G. If outlets are scattered over the address space and ~r is small enough, the market areas are exclusive tributary areas. With the specification of the disutility function adopted here, this happens for o-~< 2.5. With a larger reservation utility, market areas

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Choiceprobability 60% [ ................................................................... 50%

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inevitably encroach on each other. For tr/> 14, all m a r k e t areas overlap considerably for any realistic address configuration of the industry. All the outlets c o m p e t e all over the address space. Competitive behavior and industrial structures are invariant to the disutility threshold for or > 14. It remains to determine the expected profit of each firm. All consumers are assumed to buy one unit, if at all, of the product sold by the industry. T h e r e f o r e , the expected aggregate d e m a n d of outlet k is given by

qk =

E

iEG×V

Pik,

(4)

where Pik is the choice probability given by (3). In turn, the total profit of a firm is obtained as the sum of the profit of each of its outlets. If set-up costs are assumed to be zero and uniform marginal costs are scaled so that m a r k - u p is unity, then profit is K(j)

1I/= E qk" k=l

(5)

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Each firm selects outlet geographic locations and value positions that maximize its total profit. A Nash equilibrium is reached when no player can increase its profit by unilaterally modifying its outlet addresses. Earlier research by this author and others (Economides, 1986; Hanjoul and Thill, 1987) stressed the computational difficulty of analytically solving competition problems in two-dimensional address models. A simulation approach is employed here as in Thill (1992a). For any given parametric specification of the model, the computer algorithm searches for an address configuration of each competitor that is a stable equilibrium. The properties of this algorithm are now briefly discussed. The algorithm iteratively seeks one firm's best reply to the other firms' best replies. It proceeds as a discrete grid search of the address space at a unit resolution. Failure of the algorithm to converge is taken to imply that no 'stable' equilibrium exists (Moulin, 1986). The grid search does not evaluate all the possible solutions in the grid, but rather proceeds according to a vertex-substitution heuristic rule (Teitz and Bart, 1968) to reduce computation time. The principle of this heuristic rule is the successive substitution of grid cells not currently occupied for those that are currently occupied until no increase in profit can be found. The heuristic requires a starting solution. Although the vertex-substitution is very robust (Rosing et al., 1979), it may lead to sub-optimal solutions. It may also indicate that an equilibrium exists, when that is actually not the case, or vice versa. To alleviate these problems and to reduce the dependency of the behavior of the system on the starting solution, the simulation of each address problem is repeated with six randomly selected starting solutions. Because the address grid is fairly coarse and the solution algorithm is heuristic rather than exact, repeated simulations can produce different solutions. It turns out that, in all instances, solutions exhibit very similar differentiation properties. T h e r e f o r e , in what follows it is sufficient to report only the average results for each series of six runs. Simulation series differ by the number of firms in the industry as well as by the number of outlets. The number of outlets K varies from 3 to 5, while the number of firms J ranges from 2 to 4. A total of nine different combinations of outlet numbers and firm numbers will be considered. Finally, Thill (1992a) revealed that the outcome of the game is strongly dependent upon the parameter tr. To explore this relationship further, tr will be allowed to vary incrementally from 2 to 14 in each simulation series T h e degree of differentiation between outlets is described by two statistics that measure the degree of spread/concentration of outlets in each dimension. These statistics, denoted Lg and L v respectively in the geographic dimension and the value dimension, are computed as the ratio of the observed mean Euclidean distance between pairs of outlets to the corresponding mean that is expected under the assumption of random dis-

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tribution of outlets. When the statistics have a value of 1, the simulated conditions match those predicted for random location. Values less than 1 suggest a clustering of outlets, while values greater than 1 imply that a degree of regularity is present. Finally, the reader can easily check that, for a perfectly regular or maximally spread distribution, Lg equals 1.33 with three outlets, 1.25 with four outlets, and 1.20 with five outlets) Mutatis mutandis for L~.4

3. Equilibrium positions In our earlier work with four outlets and two firms of equal sizes (K(1) = K ( 2 ) = 2 ) (Thill, 1992a), it was found that, for small disutility thresholds, firms capitalize on consumers' unwillingness to shop at outlets far from their ideal point by setting up local monopolies all over the address space and by placing their outlets so as to maximize cannibalization of sales. See Fig. 2(a) and Table 1. We establish that the behavior of the system is controlled by the interplay of two forces. On the one hand, forces of repulsion between outlets, which act at the extensive margin, are induced by the constraint set on the extent of choice sets and market areas. On the other hand, antithetic forces are induced at the intensive margin by the probabilistic allocation of individual demand to outlets. 5 The latter attraction forces are bound to develop between all outlets, including outlets of the

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Fig. 2. Address configurations with a strategy of heterogeneous value position: K(1) = K(2) = 2. /X = firm 1 outlets; • = firm 2 outlets. 3 For instance, three regularly distributed outlets are located respectively at 1/6, 1/2, and 5/6 of the length of the address line. The mean outlet-to-outlet distance is 0.44, whereas it would be 0.44 for a random distribution. 4 For reasons noted above, values of Lg and L v are averaged over the number of converging runs. 5 The agglomerative effect of a stochastic destination choice rule is thoroughly discussed by A n d e r s o n et al. (1992, ch. 9) for single-outlet firms on a one-dimensional space.

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Table 1 Differentiation statistics with a strategy of heterogeneous value position: K ( 1 ) = K ( 2 ) = 2 o-

Lg

Lv

2 3 4 5 6 7 8 9 10 11 12 13 14

0.67 0.04 0.14 0.04 0.08 0.04 0.04 0.10 0.07 0.12 0.04 0.04 -

1.06 1.04 1.02 0.97 1.00 1.08 1.13 0.72 0.51 0.29 0.24 0.04 -

Note: - indicates failure of the algorithm to converge in all six runs.

same chains. As the threshold tr is increased, attraction forces gain m o m e n t u m over repulsion forces and competitive processes lead to a progressive clustering of the address configuration of outlets. Numerical evidence of the outcome of this behavior can be found in the inverse relationship between or, and Lg and L V (Table 1). We can now highlght the fundamental differences between the geographic and value address dimensions for the scenario of reference K(1) = K(2) = 2 by comparing Lg and L v. Simulation results summarized in Table 1 and Fig. 2 are used for this purpose. According to the magnitude of the tr disutility threshold, we obtain three cases. First, if ~r is very small (less than 2), Lg and Lv are fairly large, although L v is larger than unity while Lg is smaller. While outlets show a tendency towards maximum differentiation along the value dimension, their geographic distribution is significantly more compact than if locations were random. This is consistent with the behavioral interpretation of the competitive process that was proposed above, since marginal disutility is higher along the value dimension than along the geographic dimension and, in turn, choice sets and market areas extend farther along the latter dimension. Secondly, for ~ values greater than 2 but less than 9, Lg values are close to zero and L v values are about unity. This situation is characterized by the minimum differentiation of outlets at the center of the geographic dimension, which is a consequence of larger choice sets and market areas, and by the pairwise clustering of outlets at the first and fourth quartiles of the value dimension (Fig. 2). A similar pairing of outlets was also found by Eaton and Lipsey (1975) in an oligopoly problem of pure spatial competition on a b o u n d e d linear market with inelastic demand. In essence, higher reservation

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utilities tilt the balance of attraction and repulsion forces towards the clustering of outlets. As the marginal disutility in the value space exceeds that in the geographic space, market areas stretch farther in the latter than in the former. In turn, the broader overlap of geographic market areas triggers competition at the intensive margins, which leads to the geographic aggregation of outlets at the center of G. However, only a partial agglomeration in the two clusters occurs along the value space. The pairing of outlets of competing firms gives them the opportunity to encroach on the market areas of rival outlets with minimum cannibalization of sales of the other outlet of the chain. Perfect clustering of value positions requires higher disutility thresholds. Thirdly, for or values greater than 9, L g is still close to zero while L v decreases monotonically toward zero. In other words, outlets remain clustered at the center of the geographic space and adopt increasingly similar value positions with larger o-. As a result, minimum differentiation of all outlets, whether they belong to the same firm or not, on both dimensions is achieved for large disutility thresholds. Once again, this clustered configuration is consistent with the mechanisms of spatial competition advanced above whereby agglomerative forces at the intensive margin dominate repulsion forces acting at the extensive margin. Let us now undertake some comparative statics on address slutions with respect to the number of firms serving the market and their size. Simulation on each of the remaining eight market configurations is conducted in a similar fashion as for K(1) = K(2) = 2. We observe first t hat, in all eight cases, outlets tend to locate away from each other on both dimensions for low disutility thresholds. Also, differentiation is greater along the value dimension that in the geographic space. In addition, as or increases, outlets agglomerate first on the geographic dimension and, subsequently, on the value dimension. Finally, in all cases for which the simulation model provides solutions, it is found that, while outlets cluster together at the center of the geographic dimension, they form two clusters containing one, two or three outlets each according to the simulation case, and located about the first and fourth quartiles of the value dimension. This is illustrated by Table 2 for the case K ( 1 ) = 2 , K ( 2 ) = K(3) = 1 and by Table 3 and Fig. 3 for the case K(1) = 3, K(2) = K(3) = 1. 6 Note that, in these two cases, a three-outlet cluster develops along with a two-outlet cluster for intermediate or values. For the latter case, Fig. 3(b) shows that two of the outlets in the three-outlet cluster belong to the same firm. This demonstrates the intensity of the attraction forces unleashed by the competitive processes modelled here. Another interesting feature of this case is that the three-outlet cluster is located in the first third of the value 6 D e t a i l e d n u m e r i c a l results are a v a i l a b l e for the o t h e r cases f r o m t h e a u t h o r .

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Table 2 Differentiation statistics with a strategy of heterogeneous value position: K(1)= 2, K(2)= K(3) = 1 o-

L8

Lv

2 3 4 5 6 7 8 9 10 11 12 13 14

0.66 0.08 0.06 0.11 0.10 0.12 0.04 0.04 0.02 0.10 0.04 0.04 0.04

1.05 1.04 1.00 0.98 1.04 1.08 1.13 0.56 0.16 0.23 0.04 0.04 0.04

d i m e n s i o n r a t h e r t h a n in a q u a r t i l e , like t h e c o m p a n i o n t w o - o u t l e t cluster. B y its n u m e r i c a l d o m i n a n c e , t h e t h r e e - o u t l e t cl u st er is a b l e to slide t o w a r d s t h e c e n t e r o f t h e m a r k e t a n d c a p t u r e a l a r g e r m a r k e t s h a r e , w h i c h is to be split t h r e e ways. T h e s a m e s i t u a t i o n is also o b s e r v e d in o t h e r cases w h e r e a t h r e e - o u t l e t c l u s t e r f o r m s , t h a t is w h e n five o u t l e t s s e r v e t h e m a r k e t . T h e r e f o r e , t h e c o m p a r a t i v e statics results s h o w t h a t firms' c o m p e t i t i v e b e h a v i o r is strikingly similar, i r r e s p e c t i v e o f t h e n u m b e r o f o u t l e t s in t h e m a r k e t , o f t h e n u m b e r o f f i n n s a n d o f t h e i r r e l a t i v e sizes. W h i l e an i n c r e a s e in i n d i v i d u a l s ' c h o i c e sets p r o m p t s o u t l e t s to s e e k t h e p r o x i m i t y o f o t h e r s in Table 3 Differentiation statistics with a strategy of heterogeneous value position: K(1)= 3, K(2)= K(3) = 1 Lg

Lv

2 3 4 5 6 7

0.67 0.18 0.21 0.10 0.21

0.99 1.08 0.93 0.87 0.82

8

-

-

0.01 0.02 0.11 0.06 0.06 0.06

0.23 0.13 0.04 0.04 0.04 0.04

9 10 11 12 13 14

Note: - indicates failure of the algorithm to converge in all six runs.

J.-C. Thill

80

Regional

a) 0 : 2

Science a n d U r b a n E c o n o m i c s

27 (1997) 67-86

c) 0=10

b) 0=6

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Fig. 3. A d d r e s s c o n f i g u r a t i o n s with a strategy o f h e t e r o g e n e o u s v a l u e position: K(2) = K(3) = 1. z~ = firm 1 outlets; • = firm 2 outlets; O = firm 3 outlets.

K ( 1 ) = 3,

the address space, the trajectory to minimum differentiation is slower along the value dimension than along the geographic dimension.

4. Equilibrium with constrained value positions In this section we study competition between multi-oulet firms under the constraint that outlets in the same chain adopt the same value position. For the sake of comparison, the presentation follows that of Section 3: first, the simulation case where K ( 1 ) = K ( 2 ) = 2 is discussed, then we present some comparative statics results, and finally we draw a parallel between the strategies of heterogeneous and homogeneous value positions. Results for K(1) = K(2) = 2 are summarized in Table 4 and Fig. 4. Once again, three cases can be identified on the basis on the magnitude of or. First, Table 4 D i f f e r e n t i a t i o n statistics w i t h a strategy of h o m o g e n e o u s v a l u e position: K ( 1 ) = K ( 2 ) = 2 tr

Lg

Lv

2 3 4 5 6 7 8 9 10 11 12 13 14

1.01 1.04 0.88 0.74 0.72 0.77 0.68 0.62 0.64 0.23 0.06 -

0.97 0.96 0.76 0.60 0.52 0.36 0.20 0.12 0.04 0.04 0.04 -

N o t e : - indicates failure o f the a l g o r i t h m to c o n v e r g e in all six runs.

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a) 6=2

b) ~)=6

c) 0:10

so

so~

so

40

40 i

40

30

30 -

30 >

20

20

20-

lo

lO

lO

lo

20

=o a

40

so

~o

20

30 a

4o

so

lo

2o

30

~o

so

a

Fig. 4. Address configurations with a strategy of homogeneous value position: K(1) = K(2) = 2. A = firm 1 outlets; • = firm 2 outlets. if or is small enough (3 or less), both Lg and L v are close to unity, which indicates that outlets have no tendency to agglomerate on either dimension. As a matter of fact, they spread over the address space insofar as they can establish local monopolies. Mechanisms at the extensive margin dominate competitive processes• Note that the differentiation behavior of outlets along one dimensions closely mirrors that along the other. Secondly, for tr E [4, 10], Lg decreases from 0.88 to 0.64 as cr increases, while L v drops m o r e sharply from 0.64 to 0.04. The interpretation goes as follows• Larger disutility thresholds p r o m p t outlets to locate closer to one a n o t h e r in the two-dimensional space• The same holds true in each of the two address dimensions, but the pace of outlet agglomeration with higher tr is not independent of the dimension. The differentiation statistics show that the agglomeration of outlet positions in the value space is achieved when or reaches 10, whereas geographic clustering is still to come. This m a y seem surprising since marginal disutility in the value space exceeds that in the geographic space. In fact, the homogeneity of value positions places one firm's outlets in a situation where they c o m p e t e directly for the same customers• The best response is for them to stay far enough apart f r o m one a n o t h e r to reduce m a r k e t cannibalization, but still be able to cut into the other firm's proximal market• Finally, the third case develops when the disutility threshold is greater than 10. We then observe low Lg and L v which is a tight clustering at the very center of dimensions G and V. Processes at the intensive margins now offset those at the extensive margins and drive outlets to identify themselves as closely as possible with others in the market. An analysis of comparative statics with eight other model specifications reveals that the conclusions drawn on the reference case, K ( 1 ) = K ( 2 ) = 2, are robust. They are not contrived by the n u m b e r of outlets serving the markets by the n u m b e r of firms, nor by their sizes. This can readily be seen in Fig. 5. A few c o m m e n t s on these two cases will be m a d e h e r e a f t e r . For

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J.-C. Thill / Regional Science and Urban Economics 27 (1997) 67-86 b) 0=6

a) 0=2

c) 0=1o

so

4o

ao

2o

1o

tO

20

30 G

40

50

10

20

30 G

40

SQ

10

20

30

40

G

Fig. 5. Address configurations with a strategy of homogeneous value position: K ( 1 ) = 3 , K(2) = K(3) = 1. Z~ = firm 1 outlets; • = firm 2 outlets; ~ = firm 3 outlets.

reasons of space limitation, simulation results for the remaining cases are not reproduced here, but can be obtained from the author. Fig. 5(b) shows that, for intermediate disutility thresholds, a two-outlet cluster forms about one of the extreme quartiles of the value dimension. In both cases the outlets of the cluster in question belong to single-outlet firms• Such partial clustering of outlets is also found under the same conditions with K ( 1 ) = 2 and K ( 2 ) = K ( 3 ) = K ( 4 ) = 1. Partial clustering may develop when only two or more single-outlet firms serve the market. In other instances the homogeneity of value positions effectively prevents outlets from forming clustering unless consumers' reservation disutility is large enough. We now turn to a comparison of heterogeneous and homogeneous value positioning in terms of their impact on the geography and value structure of the industry. First, we find from the extensive simulation work reported above that, for the family problems considered here, the complexity of competition processes under either strategies of market segmentation boils down to the strained interaction between two main considerations that foster attraction and repulsion between outlets in the address space, namely consumers' probabilistic destination choice and their reservation disutility. Indeed, we observe that the general patterns of differentiation of outlets obtained by varying consumers's disutility threshold, all other things being equal, are the same under both strategies. The level of outlet differentiation decreases in the geographic dimension and in the value dimension as ~r increases, i.e. as the dominance of extensive margin effects of reservation utility is superseded by that of intensive margin effects of destination choice uncertainty. This is not to say that the adoption of one strategy over the other is inconsequential. For o - = 2 and K ( 1 ) = K ( 2 ) = 2 Fig. 2(a)), for instance, outlets cluster in two separate geographic locations with homogeneous value positioning, but at four distinct locations otherwise. The most conspicuous

J.-C. Thill / Regional Science and Urban Economics 27 (1997) 67-86

83

differences between the two strategies are found, however, for reservation disutilities that are not too small nor too large. In such instances, we noted earlier that with a strategy of homogeneous value position, outlets aggregate on the G dimension only if they also aggregate on the V dimension. Assuming a strategy of heterogeneous value position, the inverse holds true: minimum geographic differentiation is a necessary condition for the adoption of indentical value positions in the industry at large. The basis for such incongruity is in the constraint that the former strategy imposes on value positions. Indeed, as already mentioned, firms are better off spreading their outlets in the geographic space. Agglomeration is not a viable option here because it would entail outlets cutting into each other's sales with little impact on the other firm's market. Interestingly, we observe that neither strategy of market segmentation is limited to solutions of minimum or maximum differentiation. A wide range of solutions characterized by various intensities of differentiation may develop. Also, since firms have two strategic variables at their disposal, the interplay between geographic location and value allows them to blend different behaviors in each dimension. Specifically, simulation results indicate this to be the case when consumers' reservation utility is such that competition at the intensive margins is sufficiently intense to prevent maximum differentiation of outlets, but not strong enough to produce a central agglomeration. Depending on the strategy of market segmentation that is implemented, outlets will either have a tendency to select similar value positions but distinct geographic locations, or vice versa. Firms take advantage of the differential marginal disutilities along the geographic and value dimensions by maximizing differentiation of their outlets in the dimension along which market cannibalization can be reduced without compromising the ability of their outlets to compete at the intensive margins with outlets operated by other firms. It is worth stressing here that this is a very general result in the context of this research. In the particular case where marginal disutilities are identical in the two dimensions, i.e. when the parameters associated with value and geographic differences in the weighted Minkowski distance (1) are identical, the behavior of firms becomes perfectly symmetrical in terms of their strategic choices. Simulations show that solutions in the geographic space are the same as those in the value space. In all other instances, solutions are bound to be asymmetrical provided that reservation disutility is not too small or too large.

5. Conclusions

This paper discussed non-cooperative address behavior between multioutlet firms. Firms choose the geographic location and value position of

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each of their outlets given a certain strategy of market segmentation. The paper looked specifically at the strategies of market concentration and market differentation. The analysis confirms that the competitive process between multi-outlet firms is articulated under both strategies around two main forces. The reservation price of consumers for shopping at less than ideal outlets pushes outlets apart, whereas the probabilistic nature of outlet patronage fosters the aggregation of outlets. The relative magnitude of each force changes with market conditions. It was found that the level of outlet differentiation decreases in the geographic dimension and in the value dimension as the dominance of extensive margin effects of reservation utility is eroded in favor of a dominance of intensive margin effects of patronage uncertainty. Irrespective of the strategy adopted, outlets seek maximum geographic and value differentiation with low reservation utilities. However, for high reservation utilities, Hoteling's principle of minimum differentiation holds in both dimensions. The latter was also established earlier by Williams and Kim (1990) for a problem where marginal disutilities are identical in the two strategic dimensions. The former result appears to rule against Neven and Thisse's (1990) expectation that maximal differentiation along all dimensions will not be an equilibrium. For intermediate values of reservation disutility, the simulations suggest that minimum value differentiation is a necessary condition for the aggregation of outlets at the center of the geographic space under a strategy of market concentration. The opposite is true when firms are not constrained to offer the same value in all their outlets. This is reminiscent of the Neven and Thisse (1990) result, although in a more complex model. In both studies, firms are unlikely to choose similar differentiated strategies in all strategic dimensions. The results also highlighted the impact of market strategies on competitive behavior. The constraint of the same value position has little or no influence on industry-wide differentiation for reservation disutilities that are large or small enough. In cases of intermediate reservation disutilities, the constraint preserves the geographic spread of outlets until firms are better off aggregating both in value and geographically. The problems of multi-outlet competition examined have assumed that all firms serving the markets adopted the same marketing strategy. A natural extension of this research would be the situation where some firms follow a strategy of heterogeneous value positions while others choose to adopt the same value position throughout the organization. Other promising directions for future research may include economies of scope and consumer loyalty to chains of outlets whose value positions are close. With respect to the former, A n d e r s o n (1985) found that clusters of outlets, whether belonging to the same firms or to competing firms, is not an equilibrium. It remains to determine the robustness of this conclusion with a finite consumer reservation utility and a probabilistic outlet patronage.

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Acknowledgements The author acknowledges the financial assistance of NSF grant SBR9 3 0 8 3 9 4 . C o n s t r u c t i v e c o m m e n t s b y K. S t a h l a n d t w o r e f e r e e s o n a n e a r l i e r v e r s i o n o f this p a p e r a r e g r a t e f u l l y a p p r e c i a t e d .

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