In direct competition between national brands of consumer packaged goods (CPG), one brand often has a large local share advantage over the other despite the similarity of the branded products. I present an explanation for these large and persistent advantages in the context of local competition on perceived quality or brand image. The main result of the analysis is a relation between varying degrees of product similarity and equilibrium outcomes of local share advantages. Namely, I find that asymmetric quality positioning and associated local share advantages emerge especially when competing brands are objectively similar. Conversely, local share asymmetries based on brand positioning occur less when brands are dissimilar. This paper provides two reinforcing intuitions for this result. First, if brands are objectively similar, different levels of investment in local quality perceptions co-exist in equilibrium in the same market, because this investment is often borne as fixed cost. Also, early movers will invest in high perceived quality, whereas late movers have less incentive to invest because of demand sharing and increased price competition. Second, if the local advantages are shared by competitors across markets, the persistence of these advantages is reinforced by multimarket contact. Even when local brand building is free, firms may not want to improve perceived quality in their “weak” markets if it initiates retaliation by the competition in their “strong” markets. The increase in multimarket profits from collusion is large when the products are similar, because price competition looms large.
1 Introduction
Brands of consumer package goods (CPG) in the United States often lack meaningful product differentiation on attributes other than brand labels and would be difficult to correctly identify based on taste tests alone (Carpenter et al. 1994; Trout and Rivkin 2000). If two products are physically identical, except perhaps for brand labels, utility maximizing consumers should be relatively indifferent between them. All else equal, therefore, demand for such brands should be similar or at least not systematically different.
However, this simple intuition does not hold for CPG industries in two ways. First, within markets, it is not true that seemingly similar brands have the same market shares. To the contrary, there exist strong local asymmetries. Second, across markets, the same national brand of repeat purchase goods often has very different market shares, even after controlling for the influence of regional or local brands. Market dominance is often limited to a subset of local markets. Consider Fig. 1, which shows market shares for the two largest manufacturers of brands of Mexican salsa, Campbell and Frito-Lay, who sell the Pace and Tostitos brands, respectively. Both brands originate in Texas and offer highly substitutable products. The figure demonstrates that the two firms have very different shares within markets. Across markets, the two firms seem to divide the domestic U.S. market in two territories, one for each brand. Tostitos dominates along the East Coast, whereas Pace leads west of the Mississippi. While local market-shares are clearly not constant across markets, they are in fact constant in the medium term across time.1
Fig. 1
Market shares of two leading manufacturers of mexican salsa
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Bronnenberg et al. (2006) show that these patterns are commonplace in CPG industries such as coffee, mayonnaise, margarines, pickles, hotdogs, etc. Given any one market and given the similarity of most national brands in the aforementioned categories, the question addressed in this paper is: Why do large local market advantages emerge in the face of little product differentiation, and what sustains them? The answers provided in this paper are twofold and focus on the interaction of product similarity (horizontal differentiation) and firms’ efforts to influence perceived quality (vertical differentiation).
First, when providing high perceived quality comes at a cost, not all firms may invest in high quality, although it is profitable for those who do ultimately invest. This seems consistent with what happens in many CPG industries: in each local market, a single or a small number of brands invest in quality perceptions through advertising and distribution whereas other products do not invest and play a fringe role (Bronnenberg et al. 2006). I find that the first mover is the one who invests in high quality.
Second, when several firms have their own region of local dominance where they are the sole provider of high perceived quality, local monopoly power raises multimarket profits above those when all firms are symmetric, i.e., with “average” share and high quality perceptions in all markets. Thus, firms have an incentive to coordinate across markets. It has been argued (Karnani and Wernerfelt 1985) that such multimarket coordination is at work in at least some CPG industries.
Common to these two explanations, I find that the lower the degree of product differentiation, the more likely unequal perceived quality and market shares emerge in a given market and persist. Namely, I show that a lower degree of horizontal product differentiation increases the incentive for the seller of high quality products to maintain high quality and at the same time decreases the incentive for the seller of the lower quality product to close the quality gap. In effect, by endogenizing local perceptions of product quality, the main finding of this paper is that when two products are objectively similar, market shares for these products will more likely be different. Conversely, when products are different, market shares are similar across geogra phy, in the sense of globally reflecting objective quality differences rather than strategically managed perceptions of quality.
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In terms of contribution, this paper aims, first, to offer a simple theoretical argument for why (the regionalization of) market dominance emerges in CPG industries and why it persists. My model offers a very simple interpretation of regionalization of market dominance when local share asymmetries span multiple contiguous geographical markets. This happens when there is regionalization of moving first in choosing quality, e.g., through gradual rollout by sellers from different geographic origins. Second, the paper aims to make a contribution to the literature on horizontal and vertical differentiation (d’Aspremont et al. 1979; Neven and Thisse 1990; Shaked and Sutton 1981) by outlining how the willingness to invest in the local vertical attribute depends on the relative importance of the horizontal product attributes or the manufacturer’s capacity to horizontally differentiate. Third, an additional contribution of the paper is that it solves the quality competition game within a logit demand system. Theoretical predictions from this demand system may be more directly testable in future empirical research.
The remainder of this paper is organized as follows. The next section reviews how consumers take non-product attributes such as advertising and distribution as perceptual cues for product quality in CPG industries. Section 3 discusses a family of demand models with local quality perceptions. Section 4 establishes the basic relation between profits, perceived quality and prices in a single market framework. Section 5 shows how asymmetric choices about local perceived quality emerge. It also links these results to sequential entry. Section 6 shows how market share asymmetries can be sustained in a multi-market setting, even when improving quality perceptions is free. Section 7 discusses several empirical examples and interprets the main results in the context of packaged goods. Section 8 concludes with future research directions.
2 Consumer quality perceptions
Although physical product characteristics are important determinants of quality perceptions, in this paper, brand advertising and distribution support such as shelf-space are allowed to impact perceived quality also. There is ample support for a link between advertising and quality inferences. For instance, Kirmani and Wright (1989) find a positive relation between advertising and consumer expectations about product quality. Further, brand awareness is often a determinant of choice, especially for low involvement decisions (Bettman and Park 1980; Hoyer and Brown 1990; Park and Lessig 1981). In addition, there is a large and important literature in economics linking persuasion advertising to inferences about product quality (Bagwell 2007; Caves and Greene 1996; Comanor and Wilson 1974) and willingness to pay (e.g., Sutton 1991).
There are also studies linking brand distribution and retail support to inferences about brand quality. Simonson (1993) argues that consumers construct preferences for non-durable goods at the point of purchase. In this context, consumer may take large shelf space allocations for brands as a cue that these brands are popular in a given local market. Therefore, more shelf space and retailer support likely leads to the perception of higher quality for CPG. Even if consumers do not acquire brand information themselves (Dickson and Sawyer 1990; Hoyer 1984), broad distribution and shelf space allocations may indirectly allow them to rely on the quality assessments of others.
In sum, while consumers in different markets may face the same physical product when considering a nationally distributed brand, perceptions about the quality of these brands are co-determined by local advertising and distribution (retailing) strategies of firms. Noteworthy in this context is that the U.S. is partitioned in more or less discrete population centers across which there is little consumer arbitrage,2 and across which advertising and distribution strategies can be varied by firms. This set of conditions permits local branding strategies. The next section considers a model in which 2 firms can control quality perceptions locally.
3 Model
3.1 Demand
Utility
I use an “address model” of consumer demand. In this model, consumers h are characterized by a position zh in a K-dimensional attribute space in ℝK. Consumers’ ideal points \(\mathbf{z} _{h}\ \)are not observed by the firm, but their distribution across h is known. Products i = 1,2 are also characterized by a position \(\mathbf{z} _{i}\in \mathbb{R}^{K}\) in the attribute space, and this position is known to all. Consumers h have a quadratic disutility for distance between ideal points zh and the location of products zi (d’Aspremont et al. 1979). Utility for brand i by household h = 1,...,Nm in market m is specified by
where Yh is income of household h. The local quality attribute aim is a quality perception that is influenced by positioning in the distribution and communication channel and is controllable at the market level. pim is the price of the product in market m. The scalar μ measures the consumer’s disutility of products being far away from his ideal point and is a measure of horizontal differentiation.
Quality perceptions
I use the term quality perceptions to allow for the idea that aim is not just driven by objective product characteristics but also by local investments by the firms in regional advertising or shelf-space allocations by retailers.
Brand positions in the physical attribute space
I assume that there is one physical attribute \(z_{i}^{k}\) (K = 1). The physical attribute, zi, is common to all consumers in a market. To rule out a demand-focused explanation of asymmetries, I initially assume that the location of products and consumers is symmetric around zero. Owing to the presence of the multiplier μ, it can be assumed without further loss in generality that the position of brand 1 is given by \(- {\frac12} \) and of brand 2 by \(+ {\frac12} \).
Location of consumers’ ideal points in attribute space
The consumer ideal points zh ∈ ℝ represent the idiosyncratic component of utility. I assume the logistic density for the location of consumers
Consumers choose that alternative that maximizes their utility. Demand for product i among Nm consumers in market m is thus obtained by finding the support of the consumer distribution, Eq. 2, for which product i has the highest utility, Eq. 1. The utility components Yh and \(z_{h}^{2}\) do not affect choice (they are common to alternatives). Given the symmetric positions, the utility component \(z_{i}^{2}\) (i = 1,2) also drops out of the utility comparisons. What remains is the interaction zhzi of the location of consumers and products. Thus the location of the consumers enters the utility comparison as a linear term, and demand is given by a logit model (see, e.g., Anderson et al. 1992).
For convenience and because its role turns out to be largely passive, markets are all of equal size and total market size is normalized such that Nm = 1.
The logit demand formulation has broad appeal in both theoretical (e.g., Anderson et al. 1992), as well as empirical work (e.g., Berry et al. 1995). It is noted that with a uniform distribution for g(z), a linear demand structure is obtained. The results of our analysis generalize to this linear demand model. If μ approaches 0, the demand model in Eq. 3 becomes a vertical model (also called the neoclassical model—see Anderson et al. 1992, p. 45).
Because I initially wish to separate margin and multi-market contact effects from demand expansion, the model used here does not account for an outside good. This may be justified by realizing that for many mature categories such as coffee, Mexican salsas, and alike, demand expansion in response to price changes is small (Nijs et al. 2002). It can be shown that the main results of the analysis generalize to the case of demand with an outside good, as long as that outside good is not too large.
3.2 Supply
Marginal costs cim are assumed to be constant and independent of perceived quality. Instead, the cost of creating quality perceptions through advertising and/or distribution is fixed (see, e.g., Anderson et al. 1992; Bagwell 2007; Sutton 1991). Investments in perceived quality are denoted K(aim) and may depend on aim.
4 Analysis
4.1 Perceived quality and prices.
Of initial interest is how perceived quality, aim, affects prices, pim, and profits, πim. In this section, firms compete by first simultaneously deciding how much to invest in quality perceptions aim. Conditional on these choices, firms next simultaneously set prices. For now, firms can increase perceived quality at no cost. Thus, the fixed cost Kim is initially zero. Later this restriction will be lifted.
The profit function for brand i in market m is \(\pi _{im}=\left( p_{im}-c_{im}\right) \cdot s_{im}-K_{im}.\) Given the sequence of decisions, prices are solved first. Caplin and Nalebuff (1991) have shown that a unique Bertrand–Nash equilibrium in prices exists for the demand system in Eq. 3. The first-order condition (f.o.c.) for firm i is equal to
The price equations are implicit because the right-hand side of the expression for the markup contains prices pim, and perceived quality aim (through sim). Using the last equation to solve for sim and substituting in the profit function gives that at optimal prices
Define the local perceived quality gap as am ≡ a1m − a2m. Two useful dependencies of local prices and – in view of Eq. 6 – of profits on this quality gap are:
Proposition 1
(Optimal Prices)
1.
The price of brand 1 increases and that of brand 2 decreases in am.
2.
The price increase (decrease) is never larger than the increase in the perceived quality differential, i.e.,
$$ 0<\frac{dp_{1m}^{\ast }}{da_{m}}<1,\text{ and }-1<\frac{dp_{2m}^{\ast }}{ da_{m}}<0 $$
Thus, the price for either brand increases as its perceived quality advantage over the other brand widens. However, neither brand will adjust its price in equal measure to improvements in perceived quality. Consumers get at least part of the utility stemming from the perceived quality improvement. For a related result, see Anderson et al. (1992), and Anderson and de Palma (2001).
The next proposition considers the comparative statics in the second-stage of the game to provide intuition for the effects of the vertical attribute on pricing and profits, and provides the basis for the main results in the paper.
Proposition 2
(Perceived quality) Prices and profits are convex in the perceived quality gap, am.
Namely, first, as the perceived quality gap between two brands widens, the marginal effect of am on prices and profits increases.3 Proposition 2 therefore implies that low perceived quality brands are less impacted by an increase in perceived quality, than high perceived quality brands are impacted by a comparative decrease. As a consequence, the latter is willing to pay more for sustaining a perceived quality gap than the former is willing to pay for closing it, thus providing an important motivation for why asymmetries may emerge in the market.
Second, in the case of multiple markets, firms can set aim in each market. By Jensen’s inequality, the convexity result then implies that two firms, competing on M markets, would prefer to have a distribution of market-specific quality gaps am over an average vertical positioning difference of \(\bar{a}=\frac{1}{M}\sum a_{m}\) in each market.
Before showing that these two arguments can produce stable market outcomes, it is useful to formalize and discuss the interaction of horizontal differentiation μ and vertical differentiation am = a1m − a2m in the model I consider.
Proposition 3
(Interaction) The marginal effect of quality improvements on profits diminishes in horizontal differentiation for the quality leader but increases for the brand lagging in perceived quality, i.e.,
To illustrate this proposition, consider two extreme cases. First, for μ very small (limiting to 0), the leading firm will price its quality advantage almost completely to the market and still capture all demand. Thus, \(\dfrac{d\pi _{im}}{da_{im}}\) approaches 1 for this firm. For the firm that has the lower perceived quality and zero demand, increasing its quality has no consequence (the quality leader would just drop its price and still get all demand), i.e., \(\dfrac{d\pi _{im}}{ da_{im}}\) approaches 0 for the firm that lags in quality. Thus, when products are similar, the lagging firm has no incentive to invest in quality, whereas the leading firm has a positive pay-off to investments in quality.
Second, for μ > 0, there are customers to whom the lower quality product is preferred because it is closer to their ideal points. The perceived quality leader now sets prices taking into account not only the perceived quality advantage but also the adverse quantity effect of pricing too high. The marginal effect of a quality improvement on prices and profits is therefore less than 1. For the lagging firm, the effect of a quality improvement is no longer 0 but positive. I subsequently show (in Proposition 5 below) that in the limit, as μ→ ∞ , the marginal effect of a quality improvement on profits becomes equal for both the leading and the lagging firm and has value 1/3.
Combining these cases, Proposition 3 implies that as μ increases from 0 to infinity, the marginal effect of perceived quality improvements by the high quality provider on profits continuously decreases from 1 to 1/3 in the case of the higher quality brand and increases from 0 to 1/3 in the case of the lower quality brand.
In sum, when there is little horizontal differentiation, the incentives to maintain/dissolve differences in perceived quality are very different for the high vs. the low quality firm. In contrast, if there is sufficient horizontal differentiation, then the player with the high perceived quality has the same incentive to maintain the quality gap as the low perceived quality player has to close it. It is this contingency that makes that asymmetries in quality choices depend on the existing degree of horizontal product differentiation.
4.2 The case of a single market and free quality improvements
Before showing the existence of asymmetric equilibria and their dependence on μ, I first present the results of a benchmark case against which to compare other results later. In this benchmark case, firms compete in a single market and fixed cost is zero (K = 0). In this case, firms will end up positioning symmetrically at the highest possible quality level (say aH).
Proposition 4
(Single Market) In the single market equilibrium both firms position at aH and charge a price of c + 2μ. Profits are equal to μ − K.
That is to say, given Proposition 1, both brands choose to set perceived quality as high as possible. As a consequence, both brands set equal prices and have equal market shares. The role of μ in this case is that, as expected, profits and prices rise in the degree of horizontal differentiation.4 In other words, if horizontal differentiation is effectively absent, price competition will drive margins to zero.
I now consider how the above result can be avoided as a function of several realities of brand competition in packaged goods industries: (i) absence of strong horizontal differentiation, (ii) quality perceptions are costly to obtain and are borne as fixed cost, (iii) firms meet in multiple geographic markets and may have a first mover advantage in all or part of these markets.
5 Local asymmetries from competition in costly quality perceptions
5.1 Prices
Consider a single market (drop the subscript m momentarily) and fixed cost \(K\left( a_{i}\right) \) that depends on the local level of perceived quality ai. The costs \(K\left( a_{i}\right) \) represent investments in quality positioning (e.g., through advertising or incentivising retailer support). Consumer response to investments in quality perceptions is assumed to be a step function (e.g., Villas-Boas 1993). This implies that firms consider two levels of perceived quality, say aℓ or ah, with ah > aℓ. The assumption of a step function is made for simplicity. From the literature on pulsing, S-shaped response functions are known to produce similar policies (see e.g. Dubé et al. 2005; Little 1979). aℓ is to be interpreted as the quality perception that is obtained when the firm makes no investment. The assumption that K(aℓ) = 0 ensures that more than one firm enters in the market. Demand is non-zero, even at zero investment in a, e.g., investment in advertising (see, e.g., Little 1979) or distribution.
As before, firms first set perceived quality aim simultaneously and next choose prices. Demand for brand i is given by Eq. 3. In a single market context, profit for each of the manufacturing firms is equal to
Consider first the case where brand 1 is positioned at ah while brand 2 is positioned at aℓ. When is this an equilibrium? For brand 1, profit at the optimal prices computed above equals \(\pi _{1}^{\ast }=\mu \Phi -K\left( a_{h}\right) ,\) with \(\Phi = \dfrac{s_{1}}{1-s_{1}}\). The ratio Φ is the ratio of the demand for the high perceived quality brand over the low perceived quality brand, i.e., \(\Phi \equiv \Phi \left( a_{h},a_{\ell }\right) \). Proposition 1 implies that Φ > 1, because the brands are priced such that consumers receive at least a part of the utility stemming from quality improvements. Suppose firm 1 considers changing its position from ah to aℓ. If so, it will share the market evenly with firm 2 (which is also positioned at aℓ) and, from Eq. 9, its profits would equal μ − K(aℓ). Thus, firm 1 will not position at aℓ as long as \(\mu \Phi -K\left( a_{h}\right) >\mu -K(a_{\ell })\).
Firm 2, positioned “low,” will not reposition if the payoff of sustaining aℓ is larger than that of repositioning to ah. This implies that \(\mu \Phi ^{-1}-K\left( a_{\ell }\right) >\mu -K(a_{h}).\) By combining these results, and substituting that \( K\left( a_{\ell }\right) =0\) neither firm has an incentive to deviate from asymmetric positioning as long as
Note that \(\mu \left( 1-\Phi ^{-1}\right) <\mu (\Phi -1)\) because Φ > 1. Thus, there always a level of fixed costs \(K\left( a_{h}\right) \) that makes asymmetric positioning an equilibrium.
Symmetric positioning
With symmetric positioning at aℓ , the profits for both firms are \(\pi _{i}^{\ast }=\mu -K(a_{\ell }).\) If either firm repositions to ah, profits of that firm will be μΦ − K(ah). Thus, if \(K\left( a_{h}\right) >\mu \left( \Phi -1\right) ,\) then repositioning will not occur and a symmetric equilibrium with both firms positioned at aℓ holds. Following similar logic, a symmetric equilibrium at ah is obtained when it is not profitable for either firm to reposition to aℓ. This happens when \(K\left( a_{h}\right) <\mu \left( 1-\Phi ^{-1}\right) .\)
The following proposition applies.
Proposition 5
(Costly quality perceptions—single market)
1.
(a)
Both brands position symmetrically at ah if \(K\left( a_{h}\right) <\mu \left( 1-\Phi ^{-1}\right) .\)
(b)
Brands position asymmetrically with one at ah and the other at aℓ if \(\mu \left( 1-\Phi ^{-1}\right) \leq K\left( a_{h}\right) \leq \mu \left( \Phi -1\right) .\)
(c)
Both brands position symmetrically at aℓ if \(K\left( a_{h}\right) >\mu \left( \Phi -1\right) .\)
2.
(a)
The range of cost \(K\left( a_{h}\right) \) over which asymmetric positioning is an equilibrium decreases monotonically in μ,
In sum, when it is cheap enough to position at ah, all firms will do so, whereas when it is too expensive, neither firm will. However, over an intermediate range of cost of investing in quality, one brand will position at ah and the other at aℓ. Thus the cost of “branding” K(ah) can cause an asymmetric equilibrium between firms to emerge in a single market. The asymmetry is due to the differences in returns on investment in perceived quality between the high quality and the low quality player discussed in Section 4.
The second part of the proposition says that asymmetric positioning of brands occurs under more general conditions on cost when the degree of horizontal differentiation diminishes.5 The range \(\left\{ \mu \left( 1-\Phi ^{-1}\right) ,\mu \left( \Phi -1\right) \right\} \) in the second part of the proposition marks the upper and lower limit on costs \( K\left( a_{h}\right) \) for which asymmetric market shares will result. This range can thus be interpreted as a measure of the generality with which an arbitrary cost function K(a), a > 0, obeys \(\mu \left( 1-\Phi ^{-1}\right) \leq K\left( a_{h}\right) \leq \mu \left( \Phi -1\right) .\) If it is wide, any cost differential will support an asymmetric market outcome. The proposition states that when products are objectively the same, when \(\mu \ \) approaches 0, the range is widest. Conversely, if horizontal differentiation is more substantial, the cost range will narrow, reducing the support for asymmetric equilibria, and in the limit eliminating it completely.
The proposition above provides an argument for the emergence of asymmetric market shares, but makes no prediction about who will choose ah and who will choose aℓ. I next consider the case where instead of making simultaneous decisions in perceived quality, firms set perceived quality sequentially and next compete on price simultaneously. With these assumptions, I seek to capture the scenario where one firm is the leader in quality choices, but conditional on quality positioning, a Nash pricing game is being played.
Proposition 6
(Sequential moves)
1.
(a)
If \(K\left( a_{h}\right) <\mu \left( 1-\Phi ^{-1}\right) ,\) both firms will choose ah and moving first has no impact on equilibrium outcomes
(b)
If \(\mu \left( 1-\Phi ^{-1}\right) \leq K\left( a_{h}\right) \leq \mu \left( \Phi -1\right) \) the first mover in quality will set perceived quality at ah and the late mover will set perceived quality at aℓ.
(c)
\(K\left( a_{h}\right) >\mu \left( \Phi -1\right) ,\) both firms will choose aℓ and moving first has no impact on equilibrium outcomes
The first and third case simply echo Proposition 5 that when it is sufficiently costly (cheap) to invest both players will play aℓ\(\left( a_{h}\right) .\) However, the second case conveys that when asymmetric equilibria occur, it is always advantageous for the first mover to choose the higher quality perception ah. Consequently, the follower will choose aℓ.
5.3 Graphical interpretation and discussion
In the preceding section, I found that when otherwise undifferentiated firms compete on perceived quality, vertical differentiation emerges endogenously. Figure 2a illustrates this finding from the result that profits are convex in perceived quality differences a1 − a2. In this example, if firm 1 is positioned at a1 = ah, and firm 2 is positioned at a2 = aℓ, then the profit for firm 1 is equal to C ( = μΦ). At this combination of quality levels, profits for firm 2 are A ( = μΦ − 1). If both firms have the same level of quality then both of their profits are equal to B\(\left( =\mu \right) .\) The maximum investment firm 2 is willing to make for repositioning to ah is the difference in profits B − A, whereas the maximum investment firm 1 is willing to make to remain at ah is equal to C − B. Therefore, as long as the cost to produce ah is between B − A and C − B, different choices of perceived quality are an equilibrium. The second part of proposition 5 implies that the difference between the intervals C − B and B − A decreases in μ.
Fig. 2
Convexity of profits in quality and asymmetric equilibria. a One market. b Two markets
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Thus, the existence of different market shares for brands selling close substitutes within a market, can be explained as the competitive outcome of making investments in perceived quality, e.g., through local brand building. The local distribution of perceived quality depends on the primitives in the model: (i) the cost of high perceived quality \(K\left( a_{h}\right) \), (ii) the degree of horizontal product differentiation μ, (iii) and order of entry. My results can be summarized as follows:
Quality costs
A benefit of assuming an step response in aim is that only two levels of perceived quality need to be considered and that the results in this section can be derived with an arbitrary cost function. Yarrow (1989) considers the specific case of \( K\left( a\right) =\exp (a),\) and also finds that asymmetric quality choices may emerge. He does not consider the geographic patterns in CPG brand competition, the effect of sequential quality choices, or as we do momentarily, multimarket contact.
Horizontal differentiation
Asymmetric choices of perceived quality emerge more generally when goods are horizontally undifferentiated. The intuition behind this dependence on μ is that when goods are undifferentiated and quality perceptions are expensive to obtain, there is only “room” for one high quality player in the market. The low quality player realizes there is nothing to gain from imitating the high quality player. In CPG industries, where demand expansion is small compared to gains from substitution, copying the high quality player would result in lower demand and lower margins than the high quality player currently has. These beliefs about expected profits from quality improvements effectively turn the investment in perceived quality by the first mover into a “barrier to copy”.
Order of entry
When firms move sequentially in setting quality perceptions, the asymmetric equilibria are characterized by the first mover taking the higher quality positioning. In Moorthy (1988), the asymmetric equilibrium is also interpreted to offer a possible advantage to the first entrant. However, in my case, a first mover advantage in perceived quality only emerges strategically when μ is small enough, i.e., only when products that are horizontally similar. In cases with a higher degree of horizontal differentiation, the analysis suggest that perceptual differences will be absent or competed away. Perhaps consistent with this prediction, Golder and Tellis (1993) report that first mover advantages are larger and more persistent for non-durable products than for durable products.
Products are objectively similar in many CPG industries. But, at some cost, perceived quality, retail support, or brand awareness of these products can be adjusted. Our arguments suggest that brand competition under this set of circumstances fosters the emergence of asymmetric brand shares within a market. In addition, these quality adjustments can be made at a local level. CPG products are rolled out gradually over geography and the identity of firms who can choose first whether to invest in quality or not, often differs across different regions (see, e.g., Bronnenberg et al. 2006). In turn, our arguments suggest that this set of circumstances fosters the emergence of asymmetric brands shares across markets.
5.4 The vertical model
A special case occurs when μ = 0. This section points out that the prices and quality levels from the logit demand model when μ ≥ 0 are right continuous in μ so that the pure vertical case is a limiting case of the logit demand system already analyzed.
If μ = 0, the demand model in Eq. 3 becomes the following vertical model
where demand is shared between the two players if consumers have the same utility for the two products. Demand for firm 2 is the complement of s1 . What is the outcome of the quality-game in this case? Assume again that a two stage game is played, wherein quality is chosen first and prices second . We maintain the same assumptions about perceived quality, i.e., quality perceptions can be ah or aℓ with ah > aℓ, and with aℓ the resulting quality perception when no quality investments are made (\(K\left( a_{\ell }\right) =0\)).
Consider a candidate equilibrium where one player chooses ah and charges an arbitrary amount less than ph = c + ah − aℓ, whereas the other sets quality at aℓ and charges pℓ = c. At these prices, demand for the first firm is 1 and the demand for the second firm is 0.
Given the asymmetric choices for quality, can either of the players improve their profits by changing price? The first player will not raise prices because it will loose its demand to the second player. It will also not cut prices because doing so decreases margins but does not raise demand which is already 1. The second player will not lower prices for it would sell under cost. It will not increase prices because profits will not rise from doing so. Consequently, neither has a profit incentive to choose a different price, i.e., the prices are subgame perfect.
Next, consider quality choices. At the candidate equilibrium, the first player will capture all demand. At the price ph = c + ah − aℓ, it makes a profit contribution (before fixed cost) of \(\left( p-c\right) \cdot s=a_{h}-a_{\ell }\). So, as long as the investment in quality does not exceed ah − aℓ, the first player will invest in high quality perceptions. In contrast, the second player will not invest in quality, because at the quality chosen by firm 1, it can maximally charge c and hence its profit contribution is 0. It will effectively sit idle, positioning at aℓ and charging c but not actually sell anything. Thus, in the pure vertical model, asymmetric positioning is an equilibrium.
These prices and qualities of the vertical model turn out to be equal to the limiting prices and qualities of the logit model. This can be checked as follows. Equation 8 shows that the optimal price under logit demand is \(c+\mu /\left( 1-s\right) \). From the definition of Φ, we can rewrite this as \(c+\mu \left( 1+\Phi \right) \) for the high quality player and \(c+\mu \left( 1+\Phi ^{-1}\right) \) for the low quality player. Using the proof of Proposition 5, it can be shown that these prices tend to c + ah − aℓ and c (the asymmetric prices in the vertical model) as μ approaches 0 . The quality choices derived in Propositions 5 continue to hold in the case when μ = 0. Namely, the central condition on cost in Proposition 5, that is \(\mu \left( 1-\Phi ^{-1}\right) \leq K\left( a_{h}\right) \leq \mu \left( \Phi -1\right) ,\) limits to \(0\leq K\left( a_{h}\right) \leq a_{h}-a_{\ell }. \) Indeed, from the discussion above, if the cost for the high quality player is in this interval, an asymmetric equilibrium exists. In the same vein, it is easily checked that the result from Proposition 6 continues to hold, except that the first case in this proposition never applies at μ = 0.
In sum, the logit demand model with quality choices continuously approaches the vertical model as μ limits to 0. This section demonstrates that in addition to demand, the asymmetric equilibrium prices and quality levels implied by the logit demand model also limit to those of the vertical model as products get more and more similar, i.e., as μ limits to 0.
6 Sustaining historical asymmetries through multi-market contact
An independent but reinforcing argument for the results in the previous section arises from the practice, common in the domestic CPG sector, that firms meet each other in multiple markets. This creates the possibility of coordination between firms (Bernheim and Whinston 1990). To provide an analytic foundation for a discussion about collusive multi-market equilibria, I make the following assumptions.
First, there are two firms, two markets, and again two levels of perceived quality: high (ah) and low (aℓ).
Second, as is usual in a multi-market contact framework, firms are allowed to interact repeatedly over time (Bernheim and Whinston 1990; Karnani and Wernerfelt 1985),6 and, in this case, for an infinite number of periods.
Third, each firm is endowed with one market in which it is the sole provider of a high perceived quality product and one market in which it is the sole provider of a lower perceived quality product. This pre-existing condition is exogenous to the analysis. The subsequent analysis therefore applies to the local advantages of the type previously derived, but it is noteworthy to observe that it also applies to a broad class of other local advantages, including those that are fleeting.
Fourth, to demonstrate that multimarket contact and repeated interaction broadens the cases where asymmetric equilibria occur, I rule out the cost explanation of the previous section and consider the case where firms can increase perceived quality at no cost, i.e., \(K\left( a_{h}\right) =K\left( a_{\ell }\right) =0\). This constitutes the scenario where single market firms are tempted in the short run to choose a high perceived quality level ah. The idea behind this assumption is that if asymmetries are sustainable in a multimarket setting, even if it is free to improve quality, they will surely be sustainable if it is costly to improve from a low to a high perceived quality brand.
Firms each maximize multi-market profits by choosing perceived quality aim first and setting prices pim next. Figure 2b shows the profit functions π of firms 1 and 2, in a two-market scenario. In the market where firm 1 is positioned at ah (and firm 2 at aℓ) it makes a profit of C. In the other market it is positioned at aℓ (and firm 2 at ah) and makes profits of A. However, if it is free to do so, firm 1 will be tempted to improve quality in the market where it is lagging, because this increases its current multimarket profit (i.e., B + C > A + C). I assume that the consequence of not colluding is to remain positioned symmetrically in both markets at ah forever. First, this is optimal in the short run, if ah comes at no cost. Second, this is consistent with the idea that when firms have eliminated the perceived quality gap between two brands, such a gap is not easily recreated. In sum, firms in this argument are represented as trading off the benefits of an immediate profit improvement in their lagging market from A to B with future profit deterioration in strong markets from C to B.
Let π ∗ denote multimarket profits with asymmetric positioning, i.e., \(\pi ^{\ast }=A+C=\left( \Phi ^{-1}+\Phi \right) \mu -2K\) (with Φ as defined before). The payoff for a one-time deviation for firm 1 is \(\pi ^{d}=B+C=\left( 1+\Phi \right) \mu -2K.\) After firm 2 observes that it is attacked in its best market by firm 1, next period it optimally repositions in market 1 from aℓ to ah. The payoff for both firms is now equal to π0 = B + B = 2μ − 2K forever. The following proposition holds:
Proposition 7
(multimarket contact)
1.
If both firms each have a market in which they lead, they both make more profits than if they share each market equally.
2.
The minimum discount factor, i.e., future valuation, that makes that firms do not deviate in the short term and sustain the local asymmetries, is equal to the ratio of each firm’s smaller and larger market share, i.e., \( \delta ^{\ast }=\frac{\pi ^{d}-\pi ^{\ast }}{\pi ^{d}-\pi ^{0}}=\Phi ^{-1}\)
3.
The minimum discount factor needed to sustain local asymmetries (δ ∗ ) increases monotonically from 0 in μ, the degree of product differentiation.
The first part of the proposition states that \(\pi _{i}^{\ast }>\pi _{i}^{0},\) i.e., that there is always a profit incentive to sustain the combination of a market with a quality advantage and a market with a quality disadvantage. This result is implied by Proposition 2. Going back to that proposition, with asymmetric positioning for both firms in both markets, the perceived quality gap in market 1 is ah − aℓ to firm 1, whereas in market 2 it is − ah + aℓ. The positioning difference when both competitors position at ah is equal to 0 in both markets. It follows from Proposition 2 that for both firms \(\pi (a_{h}-a_{\ell })+\pi (-a_{h}+a_{\ell })>2\pi \left( 0\right) \).
The second part of the proposition conveys that in order for the multimarket collusion to hold, the discount rate has to exceed Φ − 1. Recall that Φ is the ratio of the share of the high perceived quality player to that of the low perceived quality player. It was shown that this ratio is larger than 1, and, thus, it that 0 < δ ∗ < 1. As a matter of interpretation, the more asymmetric existing shares are, the less forward looking managers need to be to sustain them.
The third part of the proposition is based on the result that \(\partial \delta ^{\ast }/\partial \mu >0.\) This result implies that as markets are less and less differentiated, even myopic managers will resist the temptation to reposition to gain higher perceived quality in their “low perceived quality” market. This is for 2 reasons. First, the post-deviation drop in profits C − B in Fig. 2 from competing head-to-head will become larger with less product differentiation, i.e., the long term punishment increases. Second, the short term incentive to deviate B − A will go to zero as μ becomes smaller, i.e., the short term benefit of deviation decreases.
The interpretation of this result is that once a CPG industry has a geographic distribution of leading brands, for instance because order-of-entry was geographically distributed (Bronnenberg et al. 2006), these leading brands have an incentive not to compete too fiercely in the markets where they are lagging for fear of “commoditizing” the market, which would make all firms worse off in the future.
7 Discussion
7.1 Interpretation of different equilibria
To summarize the different cases considered in this paper, Fig. 3 outlines the equilibria that exist for alternative values of the three variables of our competitive analysis of the CPG industry: (i) the costs of creating local perceived quality \(K\left( a_{h}\right) ,\) (ii) the degree of objective horizontal differentiation μ, and (iii) the sequence of choosing quality.7 To visualize the results, we use a numerical example. The numerical scenario considered here uses ah = 1 and aℓ = 0.8
Fig. 3
Equilibria for product differentiation \(\protect\mu ,\) and cost \(K\left( a_{h}\right) \)
×
Zone I outlines the cases where the cost \(K\left( a_{h}\right) \) of positioning high is so large that both products position low in all markets. Because it does not pay to invest in a single market, there is no profit incentive to invest in a multimarket contact framework either (markets are assumed to be separated and independent).
Zone II represents the cases covered in Section 5 where a single-market asymmetric equilibrium exists. The graph illustrates Proposition 5 (part 5), i.e., that the range of \( K\left( a_{h}\right) \) over which asymmetric equilibria are obtained becomes smaller as μ increases. Per the same proposition, the range will eventually shrink from [0 ah − aℓ] (in the numerical example [0 1]) for small values of μ, to a single point \(\left( a_{h}-a_{\ell }\right) /3\) (in the numerical example 1/3) for large values of μ. Because asymmetric positioning is an equilibrium in a single market, when the two firms compete independently on more than one market, a particular firm may lead in all markets, in several, or in none, depending on local entry patterns. If order of entry across these markets is spatially dependent, regional dominance by firms across a set of local markets will emerge.
Zone III covers the cases where the cost \(K\left( a_{h}\right) \) of positioning at high perceived quality is so small that in a single market all products would position at ah. However, realizing that they are better off having monopoly power in at least a fraction of the markets, in a multi-market context firms maintain asymmetric positions if they share local leadership and value the future enough. The results of Proposition 7 are represented in this graph by the asymmetric positioning that occurs along the horizontal axis, i.e., when \(K\left( a_{h}\right) =0.\) In a single market setting this does not happen (i.e., there is no support of Zone II on the horizontal axis). For completeness, Fig. 3 was created with δ = 0.75. Thus even if firms only value next period’s profits at 75% of current profits, the area over which asymmetric positioning emerges (zone III) relative to a single market case, is very substantial.
Finally, zone IV contains all cases where firms position at ah in all markets. As the firm’s value for future profits increases, the importance of the fourth zone diminishes further.
Zones II and III combine to give all cases where asymmetric positioning equilibria may occur. One of the central results of the analysis is that the occurrence of asymmetric equilibria is strongly dependent on horizontal differentiation. Indeed, Fig. 3 illustrates once more that sustained asymmetric market shares as in Fig. 1 is more likely to happen with undifferentiated than with differentiated goods.
A few elaborations of these results exist, which I mention here without proof. First, it can be shown that the presence of an outside good does not affect Fig. 3 substantively, as long as the outside good is not too large. Second, the main results of the paper are not materially affected if we consider competition in more than 2 markets even when the markets in which firms lead are not divided equally across competitors. Third and finally, the base scenario in the multimarket case contained the assumption that improvements in perceived quality come at no costs. Relaxing this assumption makes that the multimarket argument holds stronger. That is to say, for multimarket competition with \(K\left( a_{h}\right) >0\), the same result as before is obtained, except that it holds with a lower threshold on the firm’s discount rate (i.e., it holds more generally).
7.2 An empirical example
Conversely, the study implies that incentives to create and sustain perceived quality differentiation are less strong when products are horizontally differentiated. For discussion purposes, I present one example of such a category: breakfast cereals. Breakfast cereals are a good example of a horizontally differentiated category (see also Nevo 2001) because consumers are capable of distinguishing the different products sold, say, Corn Flakes and Cheerios, and there is no common preference ordering.
The arguments presented here predict that there should be much variation in local shares in the Mexican salsa category but not in the cereal category. If, in addition, the main brands in both industries are roughly symmetric (e.g., if the national brand pairs are of similar objective quality and all cater to the mass market), then the local ratio between the leading brand’s share and the second brand’s share is predicted to be large in the case of Mexican salsas but close to unity for the breakfast cereals. Figures 1 and 4 show that this is indeed what happens.9
Fig. 4
Local market share of two leading manufacturers in cereals
×
Table 1 presents three measures of share asymmetry across and within markets for the Mexican salsa and breakfast cereal industries. The first and second measure quantify share asymmetries within markets. In the competition between Pace and Tostitos, the average size of the local leader is 2.65 that of the second brand. In the competition between Cornflakes and Cheerios, this ratio is 1.35 (1.22 in the competition between Kellogg and General Mills).10 In the case of Mexican salsa, the leading brand is twice as large as the lagging brand in almost half of the markets. In the case of breakfast cereals this occurs not even once. The third measure is the standard deviation across markets of the log share ratio. It quantifies whether market share leadership and dominance is constant across markets. A large value on this ratio is an indication that both brands have their own geographic territory of high-share markets in direct competition with each other.11 From Table 1, it is clear that the measure of spatial variability is much larger in the Mexican salsa than in the breakfast cereal industry.
In sum, the contrast between these industries presents an empirical example of one theoretical implication of the analysis. Future research could consider a more extensive empirical analysis of the relation between product similarity and local share asymmetry.
8 Conclusion
This paper has shown that local asymmetries can arise with little or no objective product differentiation and may be sustained under conditions commonly observed in CPG industries: the leading national brands sell objectively similar products, order of entry and investments in perceived quality are local, and firms compete on perceived quality and price in multiple markets.
There are many reasons why competing firms of undifferentiated goods face different initial conditions in a given market, e.g., order-of-entry effects on brand perceptions (e.g., Bronnenberg et al. 2006) or on shelf-space (Bowman and Gatignon 1996; Robinson and Fornell 1985). These phenomena can lead to initial differences in market shares and profitability. The analysis in this paper suggests that such “initial market conditions,” e.g., product launch strategies and early differences in perceived quality matter especially in undifferentiated categories. They are therefore strategically important in CPG industries, where consumer related arguments for asymmetric market shares are often relatively weak. If goods are the same, initial market conditions persist, whereas if products are differentiated, these initial market conditions will not be sustainable. In the latter case, all competitors tend to compete for a “fair share” in all local markets.
There are several areas for future research. First, in the present paper, I assumed the presence of only two brands. Whereas duopolies do of course duopolies exist, there is value in analyzing the case of more entrants. Second, in my model, consumer preferences are static. In this model, local brand advantages are sustained because firms have a long term incentive to maintain consumer perceptions of quality differentiation. That is, the persistence of the quality differences within a market is driven by firms. An alternative argument, beyond the scope of this paper, but worthwhile for future study, is that consumer perceptions or advertising effects are sticky (e.g., Doraszelski and Markovich 2007; Dubé et al. 2006). Although speculative, positive carry-over in consumer preferences and firms’ competition in multiple markets may interact to produce even more stable asymmetric outcomes than those found here.
Acknowledgements
I thank Ronald Cotterill from the Food Marketing Policy Center for the use of his data. I am also thankful for discussions with and comments from Pradeep Bhardwaj, Pradeep Chintagunta, Jean-Pierre Dubé, Vrinda Kadiyali, and Adam Rennhoff. The paper further benefited from comments made by seminars participants at Carnegie-Mellon University, Duke University, Emory University, Erasmus University Rotterdam, Northwestern University, the Wharton School, the University of California at Berkeley, the University of Michigan, and the University of Toronto. Errors are mine. A practitioner note based on an early version of this paper was written by Booz|Allen|Hamilton and is available from http://www.strategy-business.com/media/file/sb34_041-research_notes.pdf. This research was funded by NSF grant SES-0644761.
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (
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Some useful relations are \(\frac{ds_{1}}{dp_{1}}=-\frac{1}{\mu } s_{1}(1-s_{1}),\)\(\frac{ds_{1}}{dp_{2}}=\frac{1}{\mu }s_{1}s_{2},\)\(\frac{ ds_{1}}{da}=\frac{1}{\mu }s_{1}(1-s_{1}).\) Taking the first order condition for firm 1 gives,
This proofs Proposition 1. The result states further that changes in a are never priced by the firm to the market completely. Indeed, it may be noted from the definition of Φ that the sensitivity of p1 to changes in a is always between 0 and 1. □
Proof of Proposition 2
Once again, the subscript m is dropped from the notation. It needs to be shown that the profits of both firms are convex in a. Thus, the second order derivative of profits with respect to a needs to be evaluated at the equilibrium prices. It is sufficient that
where the last equality relation follows from Eq. 6. To simplify the derivation, I can use the expressions in Eq. 19 and take the derivative of both expressions with respect to a.
Recalling that \(\Phi =\exp \left[ \left( -p_{1}+p_{2}+a\right) /\mu \right] , \) the derivative dΦ/da of the ratio of shares at optimal prices with respect to a is
From Eq. 22, \(\dfrac{df_{i}(\Phi )}{d\Phi }>0,\) and therefore the sign of the LHS of Eq. 26 is equal to the sign of \(\dfrac{d\Phi }{d\mu }.\) Rearrange the definition of Φ at optimal prices to obtain the implicit equation that
with \(p_{1}^{\ast }-c=\mu /(1-s_{1})=\mu (1+\Phi ), p_{2}^{\ast }-c=\mu /(1-s_{2})=\mu (1+\Phi ^{-1}).\) Thus, at optimal prices \(\Phi =\exp \left( \dfrac{a}{\mu }-\Phi +\dfrac{1}{\Phi }\right) \). From this equation, take the derivative to obtain that
Thus, the smaller μ, the more (less) profits rise in quality for the quality leader (lagger). □
Proof of Proposition 4
This result is implied by Proposition 1. If both firms have high perceived quality they both set prices of c + 2μ. These prices stem from \( p_{i}^{\ast }=c_{i}+\mu /(1-s_{i}),\) and from the obvious result that if both have the same positioning si = 1/2. It is easily verified that there are no unilateral deviations from this proposed equilibrium. □
Proof of Proposition 5
1.
Proof is given in the text preceding Proposition 1
(a)
It needs to be shown that \(\mu \left( \Phi -1\right) -\mu \left( 1-\Phi ^{-1}\right) \) is decreasing in μ. First, from the text preceding the proposition, \(\mu \left( \Phi -1\right) \) and \(\mu \left( 1-\Phi ^{-1}\right) \) may be interpreted as the profit before quality investment for the high quality and low quality firm, respectively. Without loss in generality, firm 1 invests in local branding and firm 2 does not. For any positive quality gap a
Taking derivatives with respect to μ, and using Proposition 3 gives the final result, i.e., because both \(\dfrac{d^{2}\pi _{1}}{d\alpha d\mu }\) and \(\dfrac{d^{2}\pi _{2}}{d\alpha d\mu }\) are negative
It is obvious that \(\lim_{\mu \downarrow 0}\mu \left( 1-\Phi ^{-1}\right) =0\). Applying l’Hopital’s rule to \(\lim_{\mu \downarrow 0}\mu \left( \Phi -1\right) ,\) I get
Suppose that firms set quality sequentially, with firm 1 choosing first. Depending on the combination of firm 1’s and firm 2’s quality choices, firm 2 receives at optimal prices, payoffs π2(a1,a2) as follows:
Note that \(\left( 1-\Phi ^{-1}\right) \leq \left( \Phi -1\right) .\) Given that firm 1 moves first, it can use all this knowledge. To do so it has to consider three scenarios.
1.
Case I: \(K\left( a_{h}\right) <\mu \left( 1-\Phi ^{-1}\right) \) where firm 2 always plays ah. In this case, firm 1 also plays ah.
2.
Case II: \(\mu \left( 1-\Phi ^{-1}\right) <K\left( a_{h}\right) <\mu \left( \Phi -1\right) ,\) where firm 2 always plays the opposite of firm 1 . If firm 1 plays ah, then firm 2 plays aℓ, and firm 1’s profit is \(\mu \Phi -K\left( a_{h}\right) .\) If firm 1 plays aℓ then firm 2 plays ah and firm 1’s profits are \(\mu \Phi ^{-1}-K\left( a_{\ell }\right) .\) Hence firm 1 will play ah if profits are higher than when playing aℓ, i.e., \(\mu \Phi -K\left( a_{h}\right) >\mu \Phi ^{-1}-K\left( a_{\ell }\right) ,\) or:
Is this always true in case II? Case II implies that \(\mu \left( 1-\Phi ^{-1}\right) <K\left( a_{h}\right) <\mu \left( \Phi -1\right) .\) Because \( \mu \left( \Phi -1\right) <\mu \left( \Phi -\Phi ^{-1}\right) ,\)\(K\left( a_{h}\right) <\mu \left( \Phi -1\right) \) implies that \(K\left( a_{h}\right) <\mu \left( \Phi -\Phi ^{-1}\right) \). Hence, with asymmetric equilibria (case II), firm 1 will always position at ah.
3.
Case III: \(K\left( a_{h}\right) >\mu \left( \Phi -1\right) ,\) where firm 2 always plays aℓ. In this case, it is easy to see that firm 1 plays aℓ.□
Proof of Proposition 7
1.
Let firm 1 be positioned at ah in market 1 while firm 2 is positioned at aℓ. In market 2 the opposite happens. Denote the ratio of output of product 1 to that of product 2 at optimal prices in market 1 again by \(\Phi \equiv s_{11}^{\ast }/s_{21}^{\ast }.\) Further, denote the equilibrium profits of firm i by \(\pi _{i}^{\ast }\equiv \sum_{m}\pi _{im}^{\ast }=\pi _{i1}^{\ast }+\pi _{i2}^{\ast }.\) Given equal cost, the prices of products mirror each other across markets, i.e. \( p_{11}^{\ast }=p_{22}^{\ast }\), and \(p_{12}^{\ast }=p_{21}^{\ast }.\) From the definition of the ratio of outputs, it is therefore obvious that in market 2, \(s_{12}^{\ast }/s_{22}^{\ast }=\Phi ^{-1}.\) By Proposition 1, Φ > 1, i.e., in market 1, firm 1 is the product with the higher perceived quality, prices, and demand. Equations 5 and 6 give that
From this formulation it is clear that multimarket profit is lowest when Φ = 1. Therefore the following inequality always holds
$$ \mu \Phi +\mu \Phi ^{-1}-2K\geq 2\mu -2K. $$
(43)
2.
The second part of the proposition implies that existing reciprocal asymmetries are sustainable – even when breaking them is free – as long as firms value future profits sufficiently. Specifically, firm 1 resists the temptation to reposition from aℓ to ah if a periodic profit of \(\pi _{i}^{\ast },\) is valued higher than a one time profit of \(\pi _{i}^{d}\) followed by a periodic profit of \(\pi _{i}^{0}.\) This valuation is met for all discount rates δ that satisfy
Hence, when \(\delta >\delta ^{\ast }\equiv \frac{\pi _{i}^{d}-\pi _{i}^{\ast }}{\pi _{i}^{d}-\pi _{i}^{0}}=\frac{1}{\Phi }\) firm 1 does not reposition. By symmetry, the same holds for firm 2.
3.
I need to show that \(\frac{d\delta ^{\ast }}{d\mu }>0\) or equivalently that \(\frac{d\Phi }{d\mu }<0\) as long as Φ > 1. This was already shown in Eq. 29□
This fact is illustrated by the fact that Fig. 1 represents the annual averages of market shares for 1996, suggesting that the differences in share are not simply due to temporary local marketing programs.
In other words, it is generally too expensive for consumers to travel across advertising cells when buying supermarket products. Observationally, this is equivalent to the constraint that consumers are treated as immobile.
The result is not specific to the logit demand function. A linear demand function is obtained by replacing Eq. 2 with g(z) = 1, z = [ − 1/2,..,1/2]. Then, profits at optimal prices can be shown to equal \(\pi _{1}=\frac{1}{18}\frac{\left( 3\mu +a_{m}\right) ^{2}}{\mu } -K\left( a_{1m}\right) \) and \(\pi _{2}=\frac{1}{18}\frac{\left( 3\mu -a_{m}\right) ^{2}}{\mu }-K\left( a_{2m}\right) \), with am = a1m − a2m. From this formulation, it is clear that the proposition replicates. The convexity result may not hold for other demand systems.
Soberman (2002) shows however that in a single market, if consumers differ with respect to their awareness of products, the monotonicity of profits in differentiation may not hold.
This result holds also when Eq. 2 is replaced by g(z) = 1, z = [ − 1/2,..., + 1/2]. In that case demand is linear and the region over which asymmetric choices of quality hold is equal to, \(\frac{\Delta a}{3 }-\tfrac{\left( \Delta a\right) ^{2}}{18\mu }<K\left( a_{h}\right) <\tfrac{ \Delta a}{3}+\tfrac{\left( \Delta a\right) ^{2}}{18\mu }.\) Clearly, this region widens (monotonically) as μ becomes smaller.
Comparisons to the single period single market game in the previous section are thus not immediate. However, unless consumers accept the idea of each firm taking periodic turns at being the “high-quality” player, a single market repeated game will result in the same equilibrium as the single period game.
This measure can be redefined to reflect differences in the national shares of brands. That is, if the national brands are not symmetric, we use within market asymmetries adjusted for the national asymmetry in share. These adjustments do not materially change the example in the table.
It is noted that a low value is not evidence of the absence of local asymmetries, but rather of the absence of geographic differences in the asymmetries.
