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Quantitative Marketing and Economics

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01-09-2012

Linking reputations through umbrella branding

Author: Jeanine Miklós-Thal

Published in: Quantitative Marketing and Economics | Issue 3/2012

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Abstract

This paper develops a theory of umbrella branding as a way to link the reputations of otherwise unrelated products. The analysis predicts that umbrella branding can credibly signal positive correlation between the qualities of the included products to consumers, but cannot certify high quality or signal negative quality correlation. Moreover, whenever umbrella branding signals perfect positive quality correlation, firms that already sell a high (low) quality product have stronger (weaker) incentives to invest in developing another high quality product than new entrants.

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Other terms include brand extensions and brand stretching.

Using the same dataset, Erdem and Winer (1999) find further evidence of inter-category correlation of (multiple) attribute-perceptions for umbrella brands, while Erdem and Sun (2002) show that advertising has an uncertainty-reducing role across categories for umbrella brands.

Short of being manufactured by different firms, some umbrella branded products are manufactured in different factories located in different countries. Many piano brands for instance manufacture their cheaper models in China, while their higher-end models are manufactured in Japan.

As is standard in signaling games, babbling equilibria in which umbrella branding happens but is meaningless exist for all parameter values.

Milgrom and Roberts (1982) and Kreps and Wilson (1982) are seminal articles on the adverse selection approach. The basic framework of the moral hazard approach goes back to Klein and Leffler (1981) and Shapiro (1983). Mailath and Samuelson (2006) as well as Bar-Isaac and Tadelis (2008) present a variety of recent reputation models, some of which combine aspects of moral hazard and adverse selection.

Name trading between firms has been modelled by Kreps (1990) in a moral hazard context, and by Tadelis (1999) in an adverse selection model that shares several key features with my approach.

Another adverse selection model in which umbrella branding guarantees high quality is Hakenes and Peitz (2009), which compares umbrella branding with external quality certification. Moorthy (2010) discusses the robustness of Wernerfelt’s (1988) results, in particular with respect to the assumption that umbrella branding is more costly than separate branding, and proposes alternative off-equilibrium beliefs.

In fact, his model features both adverse selection and moral hazard aspects; the branding problem itself, however, is subject to a moral hazard problem.

In my model, there are feedback effects in both directions. This is necessary to derive endogenous quality correlation.

In Andersson (2002), Cabral (2009), and Rasmusen (2010), the basic mechanism ressembles that in Bernheim and Whinston (1990)’s analysis of collusion under multimarket contact. Hakenes and Peitz (2008), using the assumption that high quality products never fail, rely on pessimistic out-of-equilibrium beliefs following the failure of one or both umbrella branded products.

The analysis would be unchanged if instead of just one incumbent, a countable (i.e., measure zero) set of incumbents were endowed with a second product. The results would also continue to hold if each incumbent firm were endowed with a new product with a strictly positive but sufficiently small probability.

The analysis would be the same if instead of being endowed with a second product, an incumbent got randomly matched with an entrant to negotiate a brand licensing agreement (assuming the firms can observe each other’s qualities).

The reputations of other old products at the beginning of period t = 1 can be different from r ^o. Since past performances determine the beliefs about old products, it would be inapproriate to impose that consumers hold the same beliefs about all old products.

This way of modeling demand and prices is common in the theoretical literature on brands (see Tadelis 1999; Cabral 2000, 2009; Hakenes and Peitz 2007, 2008, 2009). It allows me to set aside prices as quality signals, an issue dealt with extensively elsewhere in the literature (Wolinsky 1983; Milgrom and Roberts 1986; Bagwell and Riordan 1991).

Pooling equilibria in which $x_{q_{o}q_{n}}=0$ for all (q _o, q _n) obviously always exist if the off-equilibrium beliefs following a deviation to umbrella branding are sufficiently pessimistic. A more interesting question is to establish conditions for the existence of equilibria in which umbrella branding happens.

The probabilities consumers assign to the quality profiles other than (g, g) are

$$ \begin{array}{rll} \mu _{gb} &=&\frac{r^{o}(1-r^{n})x_{gb}}{ r^{o}r^{n}x_{gg}+r^{o}(1-r^{n})x_{gb}+(1-r^{o})r^{n}x_{bg}+(1-r^{o})(1-r^{n})x_{bb} }, \\ \mu _{bg} &=&\frac{(1-r^{o})r^{n}x_{bg}}{ r^{o}r^{n}x_{gg}+r^{o}(1-r^{n})x_{gb}+(1-r^{o})r^{n}x_{bg}+(1-r^{o})(1-r^{n})x_{bb} },\text{ and} \\ \mu _{bb} &=&\frac{(1-r^{o})(1-r^{n})x_{bb}}{ r^{o}r^{n}x_{gg}+r^{o}(1-r^{n})x_{gb}+(1-r^{o})r^{n}x_{bg}+(1-r^{o})(1-r^{n})x_{bb} }. \end{array}$$

Statistical correlation is only defined for random variables, which in the present context means that umbrella branding must not fully reveal the quality of one or both products to consumers (0 < μ ^o, μ ⁿ < 1). Hence, the correlation coefficient ϕ derived in Eq. 5 below is not well-defined in an equilibrium with $\mu _{gg}=\mu ^{o}=\mu ^{n}=1$ as in Wernerfelt (1988). Note also that a priori an equilibrium with μ _gg = 1 can be the limit of a sequence of equilibria with either a positive, a zero, or a negative correlation coefficient ϕ. Proposition 1 in Section 5.1 shows that no equilibrium with μ _gg = 1 exists.

In the cases ignored so far, the beliefs after the first step of the revision are

$$ \begin{array}{rll} \mu _{F}^{o} &=&\frac{\mu _{gg}(1-g)+\mu _{gb}(1-b)}{\left( \mu _{gg}+\mu _{bg}\right) (1-g)+(\mu _{gb}+\mu _{bb})(1-b)}, \\ \mu _{S}^{n} &=&\frac{\mu _{gg}g+\mu _{bg}b}{\left( \mu _{gg}+\mu _{gb}\right) g+(\mu _{bg}+\mu _{bb})b},\text{ and} \\ \mu _{F}^{n} &=&\frac{\mu _{gg}(1-g)+\mu _{bg}(1-b)}{\left( \mu _{gg}+\mu _{gb}\right) (1-g)+(\mu _{bg}+\mu _{bb})(1-b)}. \end{array} $$

John et al. (1998) provide experimental evidence that extreme beliefs and beliefs about flagship products, which can be expected to be more precise than beliefs about other products, are resistant to negative feedback effects from extension products that do not share the core product’s quality attributes.

Smith and Park (1992) also find that “the brand extension-new brand differential in the revenue component of cash flow widens as brand strength increases”. Interpreting brand strength as the initial reputation r ^o of the core product, this finding is consistent with positive quality correlation: as can be easily checked, the signaling effect on the new product, μ ⁿ − r ⁿ, increases in r ^o in any equilibrium with ϕ > 0.

Any success (failure) also has a positive (negative) direct effect on the product concerned itself. The branding decision can have an impact on the size, but not the sign, of this effect. My discussion in the main text focuses on feedback effects instead, since these are key to understanding endogenous quality correlation.

An alternative way to express Δ₁ > 0 as a condition on the model parameters would be $r^{n}>\underline{r}^{n}\left( r^{o},\beta \right) \in \left( 0,1\right)$.

Some readers may feel a tension between condition (i) of Proposition 3 and condition (ii) of Proposition 2, which states that r ^o cannot be too close to 1. However, for any r ^o that satisfies condition (i) of Proposition 3, there exists a set of the other parameter values, including some g sufficiently close to 1, such that perfect positive quality correlation is an equilibrium. At the same time, keeping all other parameters fixed a perfect quality correlation equilibrium can only exist if r ^o is not too close to 1.

There are numerous examples of firms that after experiencing some initial success with one product (high enough r ^o in my model) pursued brand extensions but eventually failed in all markets. For instance, Excite@Home, once a leading cable internet provider, fell behind the competition and eventually went bankrupt after extending its brand to several online media properties (Haig 2003).

In this example, the first period profit difference Δ₁ is increasing in r ^o, but this need not always be the case.

To be more precise, the proof of Proposition 4 rules out all (pure or mixed strategy) equilibria with ϕ = − 1 and pure strategy equilibria with ϕ ∈ ( − 1, 0) .

The relative importance β of the different products determines whether Δ(b, b) > Δ(g, b) or Δ(b, b) > Δ(b, g) or both. For $\beta =\frac{1}{2}$, both inequalities hold.

Nothing would change if the firm made the investment decision prior to the branding decision.

Note that each firm’s profit-maximizing investment strategy depends on consumers’ beliefs but not on the other firms’ investment decisions.

If, given the investment decision, firms had an incentive to opt for a different branding decision ex post, then their (joint investment and branding) strategy would clearly not be optimal.

For these parameter values, there are no other pure strategy equilibria with feedback effects.

The other main dimensions of fit used in the literature are demand subsitutability and demand complementarity.

The strict inclusion in the set (b, g) follows from the fact that ϕ ≠ 0 is incompatible with umbrella branding fully revealing the quality of one (or both) of the products to consumers.

Whenever Δ₁ ≠ 0 , the umbrella branding incentives of the different firm types are completely aligned for all δ below some strictly positive threshold. There may not exist any such strictly positive threshold of δ if Δ₁ = 0 and one signaling effect is strictly positive, however. This case is neglected here because generically it does not occur.

The functional form of the willingness to pay function w implies that for any μ ₁ and μ ₂

$$ w\left( \mu _{1}\right) -w\left( \mu _{2}\right) =\left( g-b\right) \left( \mu _{1}-\mu _{2}\right) , $$

which explains why the term (g − b) appears in the denominator of Eq. 32. The results of this paper would be the same for any other linear and increasing function w(μ), e.g., w(μ) = μ.

It is obvious that the range of δ for which an equilibrium exists is always included in (0, 1) since δ is the share of profits accruing to the second period, lim_g→1Δ(q _o,q _n) can achieve any value between lim_g→1Δ₂(q _o,q _n) and Δ₁ by letting δ vary between 1 and 0.

If r ^o were equal to 1, for example, then beliefs may not be smooth: While for g = 1, it would not be clear what beliefs consumers should hold following a failure (of either one of the products), for g almost equal to 1, they would always continue to believe that both products are good (even after observing two failures). The statement in the proposition then directly follows from the results established in steps 1 to 3.

A strictly positive solution of Eq. 47 indeed exists if $\delta \left( {g-b}\right) ^{{2}}>\left( {1-b}\right) b$, which is hence a necessary condition for an equilibrium with perfect quality correlation here.

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Title: Linking reputations through umbrella branding
Author: Jeanine Miklós-Thal
Publication date: 01-09-2012
Publisher: Springer US
Published in: Quantitative Marketing and Economics / Issue 3/2012
Print ISSN: 1570-7156
Electronic ISSN: 1573-711X
DOI: https://doi.org/10.1007/s11129-012-9118-7