Luxury brand licensing: Competition and reference group effects

INTRODUCTION

A brand is a name, term, sign, symbol, or design that contributes to the value of a product beyond its functional use (Farquhar, 1989). A great example is Louis Vuitton: a luxury brand that has US$ 33.6 billion in brand value (Forbes, 2018). Luxury brands usually build their initial brand image/reputation by designing, producing, and selling high‐quality products in certain categories for niche customers. For example, Giorgio Armani offers a high‐end designer clothing line, Gucci designs and manufactures handbags from fine leather, and Bang & Olufsen makes uniquely designed electronics.

In many instances, once the market for a luxury brand's primary (speciality) products matures, it faces pressure from investors to grow and capture aspirational consumers. To do so, many luxury brands use their strong brand image as a “platform” and license their brand names for quickly launching products in new categories for aspirational consumers.1 Specifically, many luxury brands license their brand names to firms (licensees) with the expertise to design, produce, and sell licensed products. For example, Burberry, Gucci, and Hugo Boss license their fragrance and/or cosmetics business to Coty—one of the world's largest beauty and fragrance companies (Sandle, 2017). In the same vein, Bulgari, Ferragamo, Prada, and Versace license their eyewear to Luxottica—the world's largest eyewear company (License Global, 2004). In 2017, retail sales of licensed goods reached $271.6 billion, and the bulk of this sales figure was generated from the sales of licensed goods that bear different luxury brand names (Greene, 2009; Licensing Industry Merchandisers' Association, 2018). In general, licensed products are significantly more affordable than the primary products (License Global, 2004). For example, many consumers cannot afford Gucci handbags, but they can show their aspiration by purchasing licensed products such as Gucci fragrance (Centre for Fashion Enterprise, 2012). Therefore, licensing creates an opportunity for luxury brands to build a presence for aspirational consumers in the mass market and to venture into new product categories with greater ease.

While appealing, licensing might come at a price and dilute the image of a luxury brand because, under brand licensing, the system is “decentralized” in the sense that the luxury brand loses its control of sales operations in the new product category to its licensee. When making their purchasing decisions, consumers of luxury brands' primary products (i.e., snobs) value exclusivity and are conscious about the composition (i.e., type and number) of consumers adopting the brand (Dubois & Laurent, 1995; J. Kapferer & Bastien, 2009; Stegemann, 2006). Due to these social effects, in the event that its licensee develops and sells too many licensed products, the image of the luxury brand can be tarnished (Colucci et al., 2008; License Global, 2004; Stegemann, 2006; The Economist, 2004). Therefore, brand licensing can hurt the sales of a brand's primary products, as experienced by Gucci, Yves Saint Laurent (YSL), and Burberry when their licensing attempts failed (License Global, 2004).2

Consequently, there are complex trade‐offs when luxury brands need to decide whether or not to license their brand names to licensees. On the one hand, they can use licensing to grow and reach out to their aspirational consumers in the mass market who value the brand popularity (i.e., followers). On the other hand, licensing reduces luxury brands' attractiveness for consumers purchasing their primary products in the niche market who care about brands' exclusivity (i.e., snobs). Surprisingly, to the best of our knowledge, there is no theoretical research on luxury brand licensing in the marketing literature despite its importance (especially, for luxury brands), and it is still not clear whether luxury brands should license their brand names in new product categories or not.

Theoretical research in marketing has traditionally focused on centralized brand‐extension strategies where the brand extends by controlling the design, production, marketing, and distribution of the new product “in‐house” (e.g., see Amaldoss & Jain, 2015; Cabral, 2000; Keller & Lehmann, 2006, and references therein). However, brlicensing is a decentralized brand‐extension strategy where, through a licensing contract, the brand licenses its name to an “external licensee,” who designs, produces, and sells the new product. For this reason, theoretical research in marketing literature remains silent about the strategic interactions between the brand and its licensee, and the issue of licensing contracts, especially, in luxury context. Therefore, our paper represents the first theoretical analysis that examines how social effects and competition can affect luxury brand licensing.

In this paper, we develop a game‐theoretic model to examine how competition and interactions between snobs and followers (i.e., “reference group” effects) impact on a luxury brand's licensing strategy. We consider two competing brands that produce their primary products in the same category (e.g., handbags) and sell them in the same niche market. At the same time, by using either fixed‐fee or royalty contracts, both brands consider licensing their brand names to two competing licensees which have expertise in producing affordable products in a different category (e.g., eyewear) and selling them in the same mass market. Under a fixed‐fee contract, the licensee pays the brand a lump‐sum fixed fee upfront, and the licensee has the right to produce and sell certain products that carry the brand name for an extended time frame (Centre for Fashion Enterprise, 2012; Chevalier & Mazzalovo, 2012). Under a royalty licensing contract, the brand charges the licensee a per‐unit royalty fee for each unit sold (Centre for Fashion Enterprise, 2012; License Global, 2004). On the consumer side, we model reference group effects by considering two segments, namely, “snobs” and “followers.” Snobs in the niche market value exclusivity, and they do not want to be associated with followers (i.e., negative popularity effect). However, followers in the mass market have a strong desire to assimilate the same brand adopted by snobs so that they value licensees' products more as more snobs purchase the brand (i.e., positive popularity effect). Only snobs can afford brands' expensive primary products; therefore, brands offer their primary products to snobs, while licensees offer their licensed products to followers.

As a benchmark, we study the monopoly case and find that the monopolist brand should not license when the snobs' negative popularity effect is too high. We also show that, when the snobs' negative popularity effect is intermediate (neither too high nor too low), a royalty licensing contract is preferred by the monopolist brand over a fixed‐fee licensing contract. This is because the royalty fee makes the licensee more inclined to raise its price and sell fewer licensed products. In doing so, the brand can manage the impact of the negative popularity effect on the snobs' demand for the primary product. In summary, we complement economics literature on patent licensing (e.g., see Beggs, 1992; Bousquet et al., 1998; Poddar & Sinha, 2002) and identify social effects (or conspicuous consumption) as another rationale behind royalty contracts that are frequently observed in practice (Centre for Fashion Enterprise, 2012; License Global, 2004).

We also examine the duopoly setting. To explicate our analysis, we first consider the case when brands can only use fixed‐fee contracts to license. Interestingly, in contrast to the monopoly setting, we find that licensing is always beneficial for both brands since fixed‐fee licensing creates an indirect (strategic) effect that “softens” price competition between brands so that both brands can afford to increase their selling price without losing market share. This is in contrast to Amaldoss & Jain (2015) who show that a centralized brand‐extension strategy (i.e., “umbrella branding”) “intensifies” price competition between brands and reduces brands' profits from their primary products. As a result, this result challenges a common belief among luxury brand experts (e.g., J. Kapferer & Bastien, 2009; J.‐N. Kapferer, 2015) and implies that, under competition, luxury brands can benefit from a decentralized brand extension via “brand licensing.” We also characterize brands' equilibrium licensing strategies under fixed‐fee contracts. We find that licensing is not always optimal for both brands and, in equilibrium, both brands license only when the negative popularity effect is sufficiently low. When the snobs' negative popularity effect is above a certain threshold, each brand would have earned more if they could both commit to licensing via fixed‐fee contracts; however, in the absence of such a commitment, we find that both brands would face a prisoner's dilemma and do not license in equilibrium.

Next, we incorporate royalty licensing contracts into our duopoly model and extend our analysis to the case where brands can use either royalty or fixed‐fee contracts when they license. We find that a royalty licensing contract can create a new royalty effect that “intensifies” the competition between brands so that both brands will lower their prices when they both license. This result is driven by the fact that, under a royalty licensing contract, both brands can earn more royalties by increasing the followers' demand for the licensed product. Because of the followers' positive popularity effect, both brands can increase the followers' demand in the mass market by increasing the snobs' demand in the niche market. As both brands compete for higher demand in the niche market, the price competition between them is intensified. As a result, when both brands license, prices of their primary products will be lower under a royalty contract than under a fixed‐fee contract. When the followers' positive popularity effect is sufficiently high, the competition between brands in the snob market is very intense and the royalty contract is dominated by the fixed‐fee contract.

Finally, we characterize licensing strategies of brands in equilibrium where each brand can use a fixed‐fee or royalty contract, and we identify cases where two brands use symmetric or asymmetric licensing strategies. We show that, in cases where positive and/or negative popularity effects are sufficiently high, the royalty contract will never dominate and, whenever a brand chooses to license in equilibrium, it will adopt the fixed‐fee contract. We find that, in the event when both brands choose to license, a royalty licensing contract is preferred in equilibrium by at least one brand, only when positive and negative popularity effects are both low and the licensing market is large enough. All aforementioned results have important managerial implications, which we shall discuss in Section 7.

This paper is organized as follows: In the following section, we review the related literature. In Section 3, we present our model and assumptions. We study the monopoly setting in Section 4. In Section 5, we present our analysis of the duopoly setting with fixed‐fee contracts. Section 6 extends our duopoly analysis in Section 5 by considering royalty licensing contracts. Finally, we discuss the managerial implications of our results in the context of luxury brand licensing and the future research in Section 7. Proofs of all results in the paper are presented in Appendix I.2 in the Supporting Information.

LITERATURE REVIEW

Our paper is related to three research streams: patent licensing, distribution channel, and conspicuous consumption. First, the economics literature on patent licensing dates back to Arrow (1962). Using different game‐theoretic frameworks, several economists analyzed different licensing strategies of an inventor (licensor). Kamien (1992) shows that, when there is perfect information, fixed‐fee licensing outperforms royalty licensing for the inventor when the inventor (licensor) is an outsider and does not compete with its licensees. However, royalty licensing dominates when the inventor is an insider and competes with its licensees, and/or when there is demand/cost uncertainty or information asymmetry; see Bousquet et al. (1998), Beggs (1992), Gallini & Wright (1990), and Choi (2001). Unlike the economic literature on patent licensing, we examine the issue of luxury brand licensing by considering reference group effects and are able to capture the impact of licensing on luxury brand dilution.

Second, there is extensive literature in marketing and operations management on the distribution channel (or the supply chain). By studying a bilateral monopoly (i.e., an upstream firm (manufacturer) selling its product through a downstream firm (retailer)), the literature identifies the decentralization as the main cause of channel inefficiency and focuses on the vertical integration (or coordination) between channel members through pricing schemes or formal contracts (e.g., see Cachon, 2003). By considering a monopolist manufacturer that produces and sells a durable good over two periods, Desai et al. (2004) are the first who show that the manufacturer is better off from selling through a retailer. and the decentralization can benefit the channel if the manufacturer can commit to specific wholesale prices for both periods in advance. Similarly, Su & Zhang (2008) show that a bilateral monopoly channel for a nondurable good can benefit from decentralization if consumers are forward looking and can strategically delay their purchases. Cachon and Kök (2010) study a channel with multiple competing upstream firms (manufacturers) that sell their products through a common downstream firm (retailer) by using a two‐part tariff or wholesale‐price and quantity‐discount contracts. By allowing upstream firms to compete for the business of the downstream firm, they show that a two‐part tariff or quantity discount contract intensifies price competition between upstream firms so that they are better off using wholesale price contracts. Ingene and Parry (2000) consider an upstream firm selling through two competing downstream firms and determine the conditions under which a channel‐coordinating wholesale‐price strategy is preferred by the upstream firm over a two‐part tariff. McGuire and Staelin (1983) study a distribution channel where two competing upstream firms (manufacturers) vertically integrate into the downstream (e.g., retailing) or sell their products through two dedicated downstream firms (retailers). They show that, when the products are highly substitutable, it is not optimal for upstream firms (or their channels) to vertically integrate and control the operations of their downstream firms. This is because, in such cases, decentralization within the channel softens price competition between upstream firms and increases their profits as well as the profit of their respective channels. Moorthy (1988) studies the same channel structure as in McGuire and Staelin (1983) and identifies general conditions under which decentralization within a channel is optimal in equilibrium. Unlike the literature on the distribution channel, our paper considers reference group effects and studies a more general channel structure with two upstream firms (brands) that already compete against each other in an existing market (or a product category) and consider expanding into a new market (or a product category) by licensing their brand names and selling through two dedicated competing downstream firms (licensees).

Third, the literature on conspicuous consumption dates back to Veblen (1899) who postulates that individuals consume conspicuous products to signal their wealth and social status. Becker (1991) and Corneo and Jeanne (1997) show that the demand for a product may increase in its price when consumers are followers (conformists) and value a product more when more people purchase it. Amaldoss and Jain (2005a, 2005b) develop a model of conspicuous consumption and analyze how demand and price of a firm are affected by snobs and followers in the monopoly and duopoly settings. Agrawal et al. (2015) analyze the product design and introduction strategies of a firm selling a conspicuous durable product over multiple periods and find that, with exclusivity‐seeking consumers or snobs, firms introduce products with high durability at low volume and high price. Arifoğlu et al. (2020) consider snobbish consumers with heterogeneous (high and low) valuations. They find that snobbish consumer behavior leads to buying frenzies and price markdowns. Unlike these papers, we model reference group effects and analyze luxury brands' licensing strategies. There are also several papers that study the impact of conspicuous consumption on pricing and the product management strategies of firms selling multiple products (e.g., Amaldoss & Jain, 2008; Balachander & Stock, 2009). Unlike these papers, we analyze the implications of reference group effects on brands' licensing strategies.

In this paper, we adopt the modeling framework developed by Amaldoss & Jain (2015) to capture: (1) the snobs' negative popularity effect and (2) the followers' positive popularity effect. However, our paper is fundamentally different in four aspects.

First, unlike Amaldoss & Jain (2015) who study the “product line extension” within the same category through umbrella or individual branding, we focus on the “product category extension” through brand licensing and aim to determine when a brand should license its brand name to extend in a new product category.

Overall, our paper is the first to examine different brand licensing strategies (i.e., fixed‐fee and royalty contracts) operating in a decentralized system in the presence of reference group effects and competition.

MODEL PRELIMINARIES

Consider two competing luxury brands A and B that produce and sell the same category of “speciality” and “more expensive” product(s) in a niche/exclusive market (e.g., Fendi and Gucci for leather goods). Each brand considers licensing its brand name to its corresponding (external) licensee (say, licensee a for brand A and licensee b for brand B) who has expertise in designing, producing, and selling a different category of “more affordable” product (e.g., cologne) in the mass market that carries the corresponding brand name. We use

I ∈ { A , B } $I\in \lbrace A,B\rbrace$

i ∈ { a , b } $i\in \lbrace a,b\rbrace$

Market structure. The “primary” products of both brands are sold in market s (i.e., snob market) comprised of high‐end, exclusivity‐seeking consumers (i.e., “snobs”) with market size equal to 1. The “licensed” products produced by the licensees are sold in a different market f (i.e., follower market) comprised of low‐end, aspirational consumers (i.e., “followers”) with market size β (that can be larger than market s). Followers cannot afford brands' primary products that are very expensive, but they can satisfy their aspirations by purchasing affordable licensed products (Amaldoss & Jain, 2015; Centre for Fashion Enterprise, 2012). For tractability and clear exposition, our base model assumes that snobs do not purchase the licensed products. However, in Appendix F in the Supporting Information, we extend our duopoly model under fixed‐fee contracts and consider cases where a fraction of snobs purchases licensed products.

Our model captures the “competition effect” within each market and “reference group effects” across markets as follows.

Within market competition effect. For both snobs and followers, a product's value is influenced by functional and social effects. Within each market s (or f), we use the Hotelling model to capture heterogeneous preferences for the functionality of the product so that all snobs are uniformly distributed over the line [0, 1], where brand A's product is located at 0 and B at 1. Hence, for a snob who is located at θ, his/her functional value for brand A's product is

( v s − t s θ ) $(v_s - t_s \theta )$

( v s − t s ( 1 − θ ) ) $(v_s - t_s(1-\theta ))$

v s $v_s$

t s $t_s$

Using a similar construct, we assume that licensed product a is located at 0 and b at 1, a follower located at θ values product a at

( v f − t f θ ) $(v_f - t_f \theta )$

( v f − t f ( 1 − θ ) ) $(v_f - t_f(1-\theta ))$

Cross market reference group effects. Through licensing, a brand's name is exposed to both snobs and followers in markets s and f, which can bring about reference group effects, namely, “positive” and “negative” popularity effects among snobs and followers. Snobs despise the popularity of licensed products sold in market f so that a snob's utility derived from purchasing brand I is decreasing in

D f i ( e ) $D_f^{i(e)}$

D f i ( e ) $D_f^{i(e)}$

U s A ( θ ) = ( v s − t s θ ) − λ s β D f a ( e ) − p A , $$\begin{equation} U_s^A{(\theta )} ={(v_s-t_s\theta )} -\lambda _s\beta D_f^{a(e)}-p^A, \end{equation}$$

1

λ s > 0 $\lambda _s>0$

β D f a ( e ) $\beta D_f^{a(e)}$

p A $p^A$

λ s $\lambda _s$

λ s $\lambda _s$

Followers in market f interpret the popularity of a brand in market s as a form of endorsement; hence, a follower's utility derived from purchasing licensed product i is “increasing” in

D s I ( e ) $D_s^{I(e)}$

D s I ( e ) $D_s^{I(e)}$

U f a ( θ ) = ( v f − t f θ ) + λ f D s A ( e ) − p a , $$\begin{equation} U_f^a{(\theta )} ={(v_f-t_f\theta )} +\lambda _{f}D_s^{A(e)}-p^a, \end{equation}$$

2

λ f > 0 $\lambda _f>0$

p a $p^a$

λ f $\lambda _f$

Remark 2 Within market social effects

Consumers' individual‐level desire for uniqueness within each market (e.g., snobs and followers might want to be different from everyone else in their own market) exists even when a brand does not license and has a second‐order impact on a luxury firm's brand licensing strategies compared to reference group effects across markets (segment‐specific desire for uniqueness). Because we aim to study luxury brands' licensing strategies, we focus on reference group effects and, for tractability, we ignore consumers' individual‐level desire for uniqueness in our base model. In Appendix D in the Supporting Information, we extend our duopoly model under fixed‐fee contracts by considering within market social effects and study the impact of consumers' individual‐level desire for uniqueness on brands' licensing decisions under fixed‐fee contracts.

Profit functions of a brand and its licensee. Each brand I licenses its name through a contract that specifies a transfer payment

T I $T^I$

D s I $D_s^I$

T I $T^I$

3

4

c s $c_s$

c f $c_f$

c s > c f $c_s>c_f$

c f = 0 $c_f=0$

c s = c $c_s=c$

Licensing contracts. In this paper, we study fixed‐fee and royalty contracts that are commonly used in the luxury goods industry (Centre for Fashion Enterprise, 2012; Chevalier & Mazzalovo, 2012). Under a fixed‐fee contract, the licensee i pays a fixed fee

k I $k^I$

T I = k I $T^I=k^I$

T I = r I β D f i $T^I = r^I \beta D_f^i$

r I $r^I$

Remark 3 Mixed contracts

To isolate the effect associated with the fixed fee

k I $k^I$

and royalty fee

r I $r^I$

, we consider fixed‐fee and royalty contracts separately instead of jointly as in a mixed contract with the transfer payment

T I = k I + r I β D f i $T^I=k^I+r^I \beta D_f^i$

. We tease out the impact of fixed lump‐sum payment

k I $k^I$

and per‐unit royalty fee

r I $r^I$

on luxury brand licensing and show that they have different implications on brands' prices and profits. Identifying the combined effect of a fixed fee and per‐unit royalty fee is beyond the scope of this paper.

Rational expectations equilibrium. We note that snobs' or followers' expectations, that is,

D f i ( e ) $D_f^{i(e)}$

D s I ( e ) $D_s^{I(e)}$

D f i $D_f^i$

D s I $D_s^I$

D s I = D s I ( e ) $D_s^I = D_s^{I(e)}$

I = A , B $I=A,B$

D f i = D f i ( e ) $D_f^i = D_f^{i(e)}$

i = a , b $i=a,b$

MONOPOLY

Consider the case when brand A operates as a monopoly located at 0 in market s. Brand A may license its brand name to licensee a located at 0 in market f. For ease of exposition, we shall restrict our analysis to the case when market s is fully covered (i.e., the resulting

D s A = 1 $D_s^A = 1$

v s $v_s$

We consider the following sequence of events. First, brand A decides whether to license or not, and if it licenses it determines and offers a (fixed‐fee or royalty) contract to licensee a. If licensee a agrees to the contract, then brand A sets its price

p A $p^A$

p a $p^a$

Next, we consider three cases: (i) brand A does not license, (ii) brand A licenses via fixed‐fee contract, and (iii) brand A licenses via royalty contract. Then, comparing brand A's optimal profits in these three cases, we determine its equilibrium licensing strategy in Section 4.4.

No licensing (NL)

As a benchmark, suppose brand A does not license to licensee a so that

D f a = 0 $D_f^a = 0$

and

T A = 0 $T^A = 0$

. It is optimal for brand A to set its price equal to

p A = v s − t s $p^A=v_s-t_s$

so that market s is covered. Thus, brand A's profit in the case of no licensing is given by

Π A N L = v s − t s − c . $$\begin{equation} \Pi ^A{\left(NL\right)} =v_s-t_s-c. \end{equation}$$

5

Fixed‐fee licensing contract (F)

We now consider the case when brand A licenses its brand name to its licensee a by charging a fixed‐fee

T A = k A $T^A=k^A$

. In Lemma 1, we characterize the fixed fee and prices of brand A and its licensee a when brand A uses a fixed‐fee contract to license. Lemma 1

When brand A licenses its brand name to licensee a by using a fixed‐fee contract, the fixed fee and prices are, respectively, given by

Through fixed lump‐sum payment

k A $k^A$

under the fixed‐fee contract, brand A extracts the entire surplus of licensee a (i.e.,

k A = p a β $k^A=p^a\beta$

) so that licensee a ends up with zero profit (and yet accepts the licensing contract). Lemma 1 shows that the fixed lump‐sum payment is strictly increasing in

λ f $\lambda _f$

. This implies that brand A can command a higher fixed licensing fee

k A $k^A$

as followers appreciate the brand's popularity in market s more (i.e., as

λ f $\lambda _f$

increases). Lemma 1 also reveals that licensing causes the monopoly luxury brand to lower its selling price compared to the case of no licensing, that is,

p A < v s − t s $p^A < v_s-t_s$

. This phenomenon is caused by the snobs' negative popularity effect

λ s $\lambda _s$

. When it licenses, brand A suffers from a lower margin for its luxury good, but it recovers this loss from the licensing fee

k A $k^A$

to be collected from licensee a.

Brand A's profit under the fixed‐fee contract is given by

6

Royalty contract

Next, we consider the case when brand A uses a royalty contract and charges

r A $r^A$

to licensee a for each unit sold in market f, that is,

T A = r A β D f a $T^A=r^A\beta D_f^a$

. Lemma 2 characterizes the royalty fee and prices when brand A licenses by using a royalty contract. Lemma 2

When brand A licenses its brand name to licensee a by using a royalty contract, the per‐unit royalty fee and prices are, respectively, given by

From Lemma 2, we observe that as snobs' “negative popularity effect”

λ s $\lambda _s$

increases, brand A charges a higher royalty fee

r A $r^A$

. With a higher royalty fee

r A $r^A$

, licensee a's marginal cost increases so that it charges a higher price

p a $p^a$

and sells to fewer followers. Therefore, unlike the fixed‐fee contract with which brand A extracts all licensing revenues, brand A can impact its licensee's price and sales via the royalty fee

r A $r^A$

. In return, because

r A < p a $r^A<p^a$

when

λ s < v f + λ f $\lambda _s < v_f + \lambda _f$

, brand A gives up some licensing revenues and licensee a can obtain a positive profit (i.e.,

Π a > 0 $\Pi ^a>0$

) under the royalty contract.

Moreover, by comparing Lemmata 1 and 2, we observe that brand A and its licensee charge (weakly) higher prices under the royalty contract in the monopoly setting. Compared to the fixed‐fee contract, the royalty contract increases licensee a's effective marginal cost. Therefore, licensee a charges a higher price and sells to fewer followers under the royalty contract (i.e., double marginalization effect of royalty licensing). This, due to the strategic complementarity between prices of the brand and its licensee, increases snobs' valuations more; therefore, brand A charges a higher price for its own primary product under the royalty contract compared to the fixed‐fee contract (i.e., strategic complementarity effect of royalty licensing).

Brand A's profit under the royalty contract is given by

Π A ( R ) = v s − t s − c + β 2 t f ( r A − λ s ) v f + λ f − r A . $$\begin{equation} \Pi ^A(R)=v_s-t_s-c+\frac{\beta }{2t_f}(r^A-\lambda _s){\left(v_f+\lambda _f-r^A\right)}. \end{equation}$$

7

Equilibrium licensing strategy of the monopoly brand

To characterize the equilibrium licensing strategy of brand A, we compare brand A's profit without licensing (i.e.,

Π A ( N L ) = v s − t s − c $\Pi ^A(NL) = v_s - t_s -c$

) and with fixed‐fee and royalty contracts (i.e.,

Π A ( F ) $\Pi ^A(F)$

in (6) and

Π A ( R ) $\Pi ^A(R)$

in (7)) and obtain the following result. Proposition 1

(i)

Brand A does not license, that is,

Π A ( N L ) ≥ max { Π A ( F ) , Π A ( R ) } $\Pi ^A(NL)\ge \max \lbrace \Pi ^A(F),\Pi ^A(R)\rbrace$

, if, and only if,

λ s ≥ v f + λ f $\lambda _s\ge v_f+\lambda _f$

.

(ii)

When brand A licenses (i.e.,

λ s < v f + λ f $\lambda _s<v_f+\lambda _f$

), the royalty contract dominates the fixed‐fee contract (i.e.,

Π A ( R ) > Π A ( F ) $\Pi ^A(R)>\Pi ^A(F)$

), if, and only if: (1)

λ s > ( 2 − 1 ) ( v f + λ f ) $\lambda _s > (\sqrt {2}-1) (v_f+\lambda _f)$

when

λ f < 2 t f − v f $\lambda _f<2t_f-v_f$

; or (2)

λ s > v f + λ f − 2 ( 2 − 2 ) t f $\lambda _s > v_f+\lambda _f-2(2-\sqrt {2}) t_f$

when

λ f ≥ 2 t f − v f $\lambda _f\ge 2t_f-v_f$

.

Proposition 1(i) implies that the licensing decision of a monopoly is driven by the interplay between snobs' negative popularity effect

λ s $\lambda _s$

and followers' positive popularity effect

λ f $\lambda _f$

. Specifically, when the snobs are sufficiently less sensitive towards the popularity of the brand in market f (i.e., when

λ s $\lambda _s$

is lower than a threshold that increases in followers' positive popularity effect

λ f $\lambda _f$

), brand A can afford to license its name to licensee a because the gain from licensing outweighs the loss caused by the lower profit margin in market s. Even though we consider luxury brand licensing as a decentralized brand extension strategy, this result is in line with Amaldoss & Jain (2015) who show that, when the monopoly brand extends via umbrella branding in a centralized manner by producing the new product in‐house, the price of its primary product decreases due to snobs' negative popularity effect; therefore, the monopoly brand extends only if followers' positive popularity effect is sufficiently larger than the snobs' negative popularity effect.5 Further, in the monopoly setting, umbrella branding can be interpreted as the first best solution in a decentralized setting since, under umbrella branding, the brand extends in a centralized manner and aims to maximize total profits from both market s and f. Hence, the monopoly brand prefers umbrella branding over any decentralized brand‐extension strategies such as fixed‐fee and royalty licensing. This implies that the decentralization hurts the monopoly brand when it extends via brand licensing.

Proposition 1(ii) shows that, when licensing, brand A prefers the fixed‐fee contract when snobs' negative popularity effect is sufficiently low, while it prefers the royalty contract when the negative popularity effect is neither too high nor too low. On the one hand, the double marginalization effect of royalty licensing creates channel inefficiency and reduces brand A's licensing revenues from market f; on the other hand, the strategic complementarity effect of royalty licensing curbs the negative impact of licensing on snobs and enhances brand A's profits from its primary product. When

λ s $\lambda _s$

is intermediate, the latter dominates the former and brand A prefers the royalty contract. This indicates that, in the presence of reference group effects, double marginalization in a decentralized channel can actually benefit the monopoly brand and increase its total profit. It also provides an alternate explanation for why royalty contracts are observed in conspicuous markets (Centre for Fashion Enterprise, 2012) and complements the literature by showing that reference group effects can be another rationale behind royalty contracts in addition to uncertain demand (Bousquet et al., 1998), asymmetric information (Beggs, 1992; Choi, 2001; Gallini & Wright, 1990), and competition (Poddar & Sinha, 2002).

DUOPOLY: FIXED‐FEE LICENSING CONTRACTS

To explicate our analysis and ease our exposition, we examine the case when competing brands can only use fixed‐fee contracts if they decide to license. (In Section 6, we expand our duopoly analysis by incorporating royalty contracts.) Because brand A and brand B are symmetric, it suffices to consider three cases: (i) both brands do not license, (ii) both brands license via fixed‐fee contracts, and (iii) only one brand licenses via a fixed‐fee contract and the other brand does not license. Below, we study each of these three cases, and then, by comparing brands' optimal profits associated with these three cases, we characterize the equilibrium licensing strategies of both brands under fixed‐fee contracts in Section 5.4.

For tractability, we restrict our analysis to cases where it is optimal for duopoly brands to cover both market s and f (i.e.,

D s A + D s B = 1 $D_s^A+D_s^B=1$

D f a + D f b = 1 $D_f^a+D_f^b=1$

v s $v_s$

v f $v_f$

Both brands do not license (NL, NL)

Suppose both luxury brands do not license (so that

D f a = D f b = 0 $D_f^a=D_f^b=0$

) and compete only in the snob market s. Then (1) reveals that a snob located at θ will obtain a net utility

U s A ( θ ) = v s − t s θ − p A $U_s^A(\theta ) =v_s-t_s\theta -p^A$

from purchasing A or

U s B ( θ ) = v s − t s ( 1 − θ ) − p B $U_s^B(\theta ) =v_s-t_s(1-\theta ) -p^B$

from purchasing B. Hence, the marginal snob

θ s $\theta _s$

is indifferent between A and B, where

θ s = 1 / 2 + ( p B − p A ) / 2 t s $\theta _s=1/2+(p^B - p^A )/2t_s$

. Because market s is fully covered, the proportion of snobs purchasing from brand A and B is

D s A = θ s $D_s^A=\theta _s$

and

D s B = 1 − θ s $D_s^B=1-\theta _s$

, respectively. Substituting

D s A $D_s^A$

,

D s B $D_s^B$

, and

T A = T B = 0 $T^A=T^B=0$

into (3), we obtain the profits of brands A and B. Then, by considering the first‐order conditions, the optimal prices for the case when both brands do not license are equal to

p A = p B = c + t s $p^A=p^B=c+t_s$

. Consequently, by (3), the brands' profits for the case when both do not license satisfy

Π I N L , N L = t s 2 for I = A , B . $$\begin{equation} \Pi ^I {\left(NL, NL\right)} =\frac{t_s}{2} \ \mbox{for} \ I = A, B. \end{equation}$$

8

Throughout this paper, we use “

( X , Y ) $(X,Y)$

” to denote the case when brand A chooses licensing strategy X and brand B chooses licensing strategy Y.

Both brands license via fixed‐fee contracts (F, F)

When brands A and B license their brand names to external licensees a and b by charging fixed fees

T A = k A $T^A = k^A$

and

T B = k B $T^B = k^B$

, respectively, we get: Lemma 3

When both brands license their brand names by using fixed‐fee contracts, the fixed fee and prices are, respectively, given by

for

I = A , B $I=A,B$

and

i = a , b $i=a,b$

.

Lemma 3 shows that, unlike in the monopoly case (F) where the brand licenses via a fixed‐fee contract (see

p A $p^A$

in Lemma 1), the brands' prices when they both use fixed‐fee contracts are increasing in the snobs' sensitivity to brand popularity

λ s $\lambda _s$

. When both brands use fixed‐fee contracts to license, their licensees adopt symmetric pricing strategies (i.e.,

p a = p b $p^a=p^b$

by Lemma 3) and share market f equally (i.e.,

D f i = 1 / 2 $D_f^i=1/2$

for

i = a , b $i=a,b$

). Consequently, when snobs compare two brands in terms of their exclusivity in market f, brands are identical and the “negative popularity effect” of each brand cancels each other out so that the net effect is absent.

In addition, Lemma 3 reveals that, relative to brands' equilibrium prices associated with the no‐licensing case

( N L , N L ) $(NL, NL)$

presented in Section 5.1, the prices of both brands are higher when they both license via fixed‐fee contracts. Notice that the term

β λ f λ s / t f $\beta \lambda _f\lambda _s/t_f$

in

p I $p^I$

as stated in Lemma 3 captures an “indirect effect” of licensing that can “soften competition” in markets s (see Cabral & Villas‐Boas, 2005). To examine how fixed‐fee licensing softens competition between brands, let us suppose that brand A increases its price by one unit. Then brand B's market share in market s will increase, and this increase in popularity of brand B will make licensee b's product (that carries brand B's name) more attractive to followers in market f (due to the followers' “positive” popularity effect). Consequently, licensee a's sales will decrease, but it will increase the snobs' valuation of brand A in market s (due to the snobs' “negative” popularity effect), which affords brand A to increase its price a little bit without affecting its demand. As competition between brands A and B in market s softens, both brands can afford to charge higher prices with licensing (than the case when no brand licenses). Furthermore, as the negative or positive popularity effect increases, a unit increase in brand A's price has more impact on licensee a's market share or snobs' valuations. Consequently, the competition between brands softens more, and brands' prices increase in

λ s $\lambda _s$

and

λ f $\lambda _f$

. Remark 5 Relaxing full‐market coverage of market s

By considering cases where market s is partially covered, Appendix C in the Supporting Information extends our duopoly model under fixed‐fee contracts and compares brands' prices in cases

( F , F ) $(F,F)$

and

( N L , N L ) $(NL,NL)$

. Since there is no competition between brands in this case, the negative popularity effect does not cancel out and leads to a decrease in brands' prices; moreover, the competition‐softening indirect (strategic) effect of fixed‐fee licensing no longer exists. Instead, fixed‐fee licensing creates strategic substitutability between brands' prices in market s (i.e., it is optimal for a brand to decrease its price if the other brand increases its price) and, combined with the negative popularity effect, leads to an increase in brands' prices. In cases with high

λ f $\lambda _f$

and low

λ s $\lambda _s$

, the price‐increasing effect due to strategic substitutability created by fixed‐fee licensing dominates the price‐decreasing negative popularity effect of fixed‐fee licensing; therefore, brands' prices increase.

When both brands use fixed‐fee contracts to license, their profits are given by

Π I F , F = t s 2 + β λ f λ s 2 t f + t f + β λ f λ s t s β 2 , $$\begin{equation} \Pi ^I{\left(F, F\right)}= \frac{t_s}{2}+\frac{\beta \lambda _f\lambda _s}{2t_f}+ {\left(t_f+\frac{\beta \lambda _f\lambda _s}{t_s}\right)}\frac{\beta }{2} ,\end{equation}$$

9

for

I = A , B $I=A,B$

. Notice by (9) and

Π I ( N L , N L ) = t s / 2 $\Pi ^I(NL, NL)=t_s/2$

that

Π I ( F , F ) > Π I ( N L , N L ) $\Pi ^I(F, F)>\Pi ^I(NL, NL)$

for

I = A , B $I=A,B$

. Thus, Lemma 4 follows. Lemma 4

Relative to the no‐licensing case, each brand earns more when they both license by using fixed‐fee contracts, that is,

Π I ( F , F ) > Π I ( N L , N L ) $\Pi ^I (F, F)>\Pi ^I (NL, NL)$

for

I = A , B $I=A,B$

.

Lemma 4 implies that both brands earn more by licensing their brands to their respective licensees by using fixed‐fee contract. This result is in contrast to the monopoly case (F) (see Proposition 1) and appears to be counterintuitive because licensing has a “negative popularity effect” on snobs' valuations. However, as discussed above, in a duopoly when both brands use fixed‐fee licensing, the negative popularity effect of licensing on each brand cancels each other out and the competition between brands is softened due to the “indirect effect” across markets s and f. Consequently, both brands can afford to charge higher prices for their primary product and obtain more profits from market s even without taking into account the licensing revenues.

This result is in contrast to Amaldoss & Jain (2015) who show that, when both brands use umbrella branding strategies and extend themselves by producing the new product in‐house, the price competition between brands intensifies and brands' profits from their primary products in market s decrease.8 Also, against the common opinion among luxury brand experts (e.g., J. Kapferer & Bastien, 2009; J.‐N. Kapferer, 2015), our result suggests that luxury brands might benefit from decentralization when extending their brands through licensing. As such, brand licensing can be preferred over umbrella branding.

Only one brand licenses by using a fixed‐fee contract (F, NL)

It remains to consider the case when exactly one brand licenses by using a fixed‐fee contract. Because both brands and both licensees are symmetric, it suffices to study the case

( F , N L ) $(F, NL)$

in which brand A licenses its name to licensee a via a fixed‐fee contract

T A = k A $T^A=k^A$

so that licensee a operates as a monopoly in market f. Lemma 5 characterizes the fixed fee and prices in this case. Lemma 5

When brand A licenses its brand name to licensee a by using a fixed‐fee contract and brand B does not license: (i)

if

λ s < 3 t s / β $\lambda _s<3t_s/\beta$

, both brands compete in market s, and the fixed fee and prices are, respectively, given by

(ii)

if

λ s ≥ 3 t s / β $\lambda _s\ge 3t_s/\beta$

, brand B becomes a monopoly in market s, and the fixed fee and prices are, respectively, given by

k A = v f − t f β , p B = v s − t s , and p a = v f − t f . $$\begin{equation*} k^A= {\left(v_f-t_f\right)} \beta , \mbox{ } p^B=v_s-t_s, \mbox{ and } p^a=v_f -t_f. \end{equation*}$$

Lemma 5(i) shows that, when the negative popularity effect is low (i.e.,

λ s < 3 t s / β $\lambda _s<3t_s/\beta$

), brand A that licenses charges a lower price than brand B that does not license. This is because licensing makes brand A less exclusive for snobs due to the negative popularity effect, and, to stay competitive in market s, it has to charge a lower price than brand B. Lemma 5(ii) shows that, when the negative popularity effect is high (i.e.,

λ s ≥ 3 t s / β $\lambda _s \ge 3t_s/\beta$

), no snob purchases from brand A once it licenses its brand name to licensee a. Thus, brand B operates as a monopoly in market s and licensee a operates as a monopoly in market f.

Both brands are symmetric so that the profit of each brand in the case when only brand B licenses is given by

Π B ( N L , F ) = Π A ( F , N L ) $\Pi ^B(NL , F ) = \Pi ^A(F, NL)$

and

Π A ( N L , F ) = Π B ( F , N L ) $\Pi ^A(NL , F ) = \Pi ^B(F, NL )$

. Then, the brands' profits when only one brand uses the fixed‐fee contract are given by

10

11

where

( x ) + = max ( x , 0 ) $(x) ^{+}=\max (x,0)$

.

Equilibrium licensing strategies of duopoly brands under fixed‐fee contracts

By comparing brands' profit functions (presented in the previous sections) under different licensing strategies as in a two‐player simultaneous‐move game, Proposition 2 characterizes the licensing strategy that each brand will adopt in equilibrium under fixed‐fee contracts. In preparation, we define the thresholds

λ s k ( 1 ) $\lambda _{sk}^{(1)}$

and

λ s k ( 2 ) $\lambda _{sk}^{(2)}$

as follows:

12

13

and we let

λ s k ( 3 ) = min ( 3 t s / β , λ s k ( 2 ) ) $\lambda _{sk}^{(3)}=\min (3t_s/\beta ,\lambda _{sk}^{(2)})$

. Also, we define

λ s k L = min ( λ s k ( 1 ) , λ s k ( 3 ) ) $\lambda _{sk}^L=\min (\lambda _{sk}^{(1)},\lambda _{sk}^{(3)})$

and

λ s k H = max ( λ s k ( 1 ) , λ s k ( 3 ) ) $\lambda _{sk}^H=\max (\lambda _{sk}^{(1)},\lambda _{sk}^{(3)})$

. Proposition 2

Under fixed‐fee licensing contracts, brands' equilibrium licensing strategies can be characterized as follows: I.

When the base valuation of the licensed product is low so that

v f ≤ t f + t s 2 β $v_f\le t_f+\frac{t_s}{2\beta }$

,

(a)

both brands do not license if

λ s ≥ λ s k H $\lambda _s\ge \lambda _{sk}^H$

;

(b)

both brands either license or do not license (i.e., two equilibria exist) if

λ s k ( 1 ) < λ s < λ s k ( 3 ) $\lambda _{sk}^{(1)}<\lambda _s<\lambda _{sk}^{(3)}$

;

(c)

only one brand licenses if

λ s k ( 3 ) < λ s < λ s k ( 1 ) $\lambda _{sk}^{(3)}<\lambda _s<\lambda _{sk}^{(1)}$

;

(d)

both brands license if

λ s ≤ λ s k L $\lambda _s\le \lambda _{sk}^L$

.

II.

When the base valuation of the licensed product is high so that

v f > t f + t s 2 β $v_f> t_f+\frac{t_s}{2\beta }$

, (a)

only one brand licenses if

λ s > λ s k ( 3 ) $\lambda _s>\lambda _{sk}^{(3)}$

;

(b)

both brands license if

λ s ≤ λ s k ( 3 ) $\lambda _s\le \lambda _{sk}^{(3)}$

.

Figure 1a illustrates Proposition 2(I) for the case when

v f ≤ t f + t s 2 β $v_f\le t_f+\frac{t_s}{2\beta }$

. Specifically, consistent with Proposition 1 for the monopoly case, Proposition 2(Ia) shows that both brands do not license for sufficiently high

λ s $\lambda _s$

values (

λ s ≥ λ s k H $\lambda _s\ge \lambda _{sk}^H$

, that is, region I(a)). However, recall from Lemma 4 that, due to the “indirect effect” of fixed‐fee licensing that can soften competition, fixed‐fee licensing is more profitable for the brands as the snobs' negative popularity effect

λ s $\lambda _s$

or the followers' positive popularity effect

λ f $\lambda _f$

increases. Even so, it is interesting to observe that no brand should license when

λ s $\lambda _s$

lies within region I(a). To understand why, recall from Lemma 4 that each brand would be better off if both brands could “commit” to licensing via fixed‐fee contracts. However, in the absence of such a commitment, brands face a prisoner's dilemma and do not license. To better understand the intuition behind this result, consider a scenario where both brands license. In region I(a), the negative popularity effect

λ s $\lambda _s$

is significantly high so that a brand is better off by making its brand more exclusive to please the snobs. In this case, at least one brand will want to deviate and not to license (e.g.,

Π B ( F , N L ) > Π B ( F , F ) $\Pi ^B(F,NL)>\Pi ^B(F,F)$

). Moreover, if one of the brands deviates and does not license, the profit of the other brand significantly decreases due to the negative popularity effect (e.g.,

Π A ( F , N L ) < Π A ( N L , N L ) $\Pi ^A(F,NL)<\Pi ^A(NL,NL)$

). Hence, both brands end up not licensing in equilibrium in region I(a), facing a prisoner's dilemma.

OPEN IN VIEWER

FIGURE 1

Brands' equilibrium licensing strategies under fixed‐fee contracts.

From Figure 1a, we observe that, given any

λ s < 3 t s / β $\lambda _s<3t_s/\beta$

, when the positive popularity effect

λ f $\lambda _f$

is sufficiently high (regions I(b) and I(d)), cases where both brands use fixed‐fee contracts also become an equilibrium. In region I(b), licensing revenues are significant (due to high

λ f $\lambda _f$

), but the direct negative impact is also significant (due to high

λ s $\lambda _s$

). The latter dominates the former and licensing decreases a brand's profits when the other brand does not license (i.e.,

Π A ( N L , N L ) > Π A ( F , N L ) $\Pi ^A(NL,NL)>\Pi ^A(F,NL)$

), whereas, since the indirect effect softens competition in both markets and improves profits when both brands license, the former dominates the latter and a brand benefits from licensing when the other brand also licenses (i.e.,

Π B ( F , F ) > Π B ( F , N L ) $\Pi ^B(F,F)>\Pi ^B(F,NL)$

). Thus, there are two equilibria in region I(b). On the other hand, in region I(d), licensing always benefits a brand independent from whether the other brand licenses or not (i.e.,

Π A ( F , F ) > Π A ( N L , F ) $\Pi ^A(F,F)>\Pi ^A(NL,F)$

and

Π A ( F , N L ) > Π A ( N L , N L ) $\Pi ^A(F,NL)>\Pi ^A(NL,NL)$

), and, thus, both brands license. This is because licensing softens competition in both markets (due to indirect effect) and/or provides significant additional revenues.

Figure 1a also shows that, for a given

λ s $\lambda _s$

in region I(c), only one brand licenses if followers' sensitivity to brand popularity is sufficiently low (region I(c)). A brand benefits from licensing in region I(c) only when the other brand does not license (i.e.,

Π A ( F , F ) < Π A ( F , N L ) $\Pi ^A(F,F)<\Pi ^A(F,NL)$

and

Π A ( F , N L ) > Π A ( N L , N L ) $\Pi ^A(F,NL)>\Pi ^A(NL,NL)$

). In such cases, licensing revenues are not high enough (due to low

λ f $\lambda _f$

) for both brands to license and licensing decreases their exclusivity. Instead, only one brand licenses and obtains lower profits from market s, yet its total profits increase as it receives all licensing revenues. However, when licensing revenues are sufficiently high (e.g., high β so that the size of market f is sufficiently large), it is never the case that only one brand licenses in equilibrium (i.e.,

λ s k ( 3 ) = 3 t s / β $\lambda _{sk}^{(3)}=3t_s/\beta$

) and region I(c) in Figure 1a disappears.

Figure 1b illustrates Proposition 2(II), which corresponds to the case when

v f > t f + t s 2 β $v_f > t_f+\frac{t_s}{2\beta }$

. When followers' base valuation is sufficiently high (i.e.,

v f > t f + t s 2 β $v_f > t_f+\frac{t_s}{2\beta }$

), (12) states that

λ s k ( 1 ) = ∞ $\lambda _{sk}^{(1)}=\infty$

. Hence, it is always beneficial for a brand to use a fixed‐fee contract when the other brand does not license, that is,

Π A ( F , N L ) > Π A ( N L , N L ) $\Pi ^A(F,NL)>\Pi ^A(NL,NL)$

. Therefore, as shown in Figure 1b, for

v f > t f + t s 2 β $v_f > t_f+\frac{t_s}{2\beta }$

, unlike in the monopoly case, licensing is always optimal and at least one brand uses a fixed‐fee contract in equilibrium. Specifically, both brands license by using fixed‐fee contracts when the snobs' negative popularity effect

λ s $\lambda _s$

is low (i.e.,

λ s < λ s k ( 3 ) $\lambda _s<\lambda _{sk}^{(3)}$

), and only one brand licenses via a fixed‐fee contract otherwise.

DUOPOLY: INCORPORATING ROYALTY CONTRACTS

We now expand our duopoly analysis in Section 5 by adding royalty contracts into the consideration set so that, when brands consider licensing, they can choose between fixed‐fee and royalty contracts. To characterize the brands' equilibrium licensing strategies in this case, we need to compare their profit functions under six different licensing strategies as in a simultaneous‐move game with two symmetric players (i.e., brand A and B) and three strategies (i.e.,

N L $NL$

Both brands license by using royalty contracts (R, R)

First, consider the case where brands A and B license their brand names to licensees a and b by charging (per‐unit) royalty fees

r A $r^A$

and

r B $r^B$

, respectively. To ensure that equilibrium royalty fees and prices exist in this case,9 we assume that the followers' positive popularity effect

λ f $\lambda _f$

is sufficiently high so that

λ f ≥ t f t s 2 β . $$\begin{equation} \lambda _f \ge \sqrt {\frac{t_{f}t_s}{2\beta }}. \end{equation}$$

14

Lemma 6 characterizes equilibrium royalty fees and prices when both brands license via royalty contracts Lemma 6

When both brands license by using royalty contracts, the royalty fee

r I $r^I$

satisfies

where

λ s r ( 1 ) $\lambda _{sr}^{(1)}$

is given by (G.5) in Appendix G in the Supporting Information. Also, the optimal prices of brand I and its licensee i satisfy

p I = c + t s + β λ f λ s t f − β λ f r I t f and p i = r I + t f + β λ f λ s t s . $$\begin{equation*} p^I=c+t_s+\frac{\beta \lambda _f\lambda _s}{t_f }-\frac{\beta \lambda _{f}r^I }{t_f } \mbox{ and } p^i=r^I+t_f+\frac{\beta \lambda _f\lambda _s}{t_s}. \end{equation*}$$

Relative to brand I's equilibrium prices in case both brands use fixed‐fee contracts to license (see Lemma 3), Lemma 6 reveals that, under royalty contracts, licensees charge higher prices in market f, while brands charge lower prices in market s. When both brands use royalty licensing, the effective marginal costs of licensees increase by their respective royalty fee; as a result, each licensee increases its price according to an extra term

r I $r^I$

, which is determined by brand I (i.e., the double marginalization effect of royalty licensing).10 Next, to understand why brands' prices are lower under royalty contracts, observe first that the “indirect effect” (i.e.,

β λ f λ s / t f $\beta \lambda _f\lambda _s/t_f$

) that softens the competition in market s continues to persist under royalty contracts. Moreover, strategic complementarity between prices of brands and their respective licensees plays no role in brands' price differences under fixed‐fee and royalty contracts, and the strategic complementarity effect of royalty licensing disappears under competition. This is because the double marginalization effect of royalty licensing does not change the number of followers purchasing licensed products as brands' licensees adopt symmetric pricing strategies and share market f equally (i.e.,

D f i = 1 / 2 $D_f^i=1/2$

for

i = a , b $i=a,b$

) when both brands use either fixed‐fee or royalty contracts. However, under the royalty contracts, the royalties to be collected by each brand depend on the demand of the respective licensed product in market f. At the same time, due to the followers' positive popularity effect

λ f $\lambda _f$

, one can boost the demand for the licensed product in market f by increasing the demand of the brand in market s. For these reasons, each brand has an incentive to lower its price

p I $p^I$

to increase its demand in market s (which causes the licensed product's demand in market f to increase). This price‐lowering strategy is caused by the royalties (that depend on the sales of the licensed product in market f), and we shall refer to this effect (i.e.,

r I β λ f / t f $r^I\beta \lambda _f/t_f$

) as the “royalty effect” that “intensifies price competition” between brands in market s so that each brand charges a lower price under royalty contracts. Together with note 8, this indicates that, in the duopoly setting, the royalty effect due to the royalty contract has a similar impact on brands' prices in market s and follows from a similar intuition as the indirect (strategic) effect due to umbrella branding as analyzed by Amaldoss & Jain (2015).

When both brands use royalty contracts to license, brands' profits satisfy

Π I R , R = t s 2 + β λ f λ s 2 t f + β 2 r I 1 − λ f t f $$\begin{equation} \Pi ^I{\left(R, R\right)}=\frac{t_s}{2}+\frac{\beta \lambda _f \lambda _s}{2t_f}+\frac{\beta }{2}r^I{\left(1-\frac{\lambda _f}{t_f}\right)} \end{equation}$$

15

for

I = A , B $I=A,B$

. By comparing brands' profits as stated in (15) against (8) (as in the no‐licensing case

( N L , N L ) $(NL,NL)$

) and against (9) (as in the case

( F , F ) $(F,F)$

under fixed‐fee contracts), we obtain Lemma 7 that involves different threshold values for

λ s $\lambda _s$

(namely,

λ s r ( 2 ) $\lambda _{sr}^{(2)}$

and

λ s r ( 3 ) $\lambda _{sr}^{(3)}$

that are given, respectively, by (G.6) and (G.7) in Appendix G in the Supporting Information) and threshold values for

λ f $\lambda _f$

(namely,

λ f r L = min ( λ f r ( 1 ) , λ f r ( 2 ) ) $\lambda _{fr}^L=\min (\lambda _{fr}^{(1)},\lambda _{fr}^{(2)} )$

and

λ f r H = max ( λ f r ( 1 ) , λ f r ( 2 ) ) $\lambda _{fr}^H=\max (\lambda _{fr}^{(1)},\lambda _{fr}^{(2)} )$

, where

λ f r ( 1 ) , λ f r ( 2 ) < t f $\lambda _{fr}^{(1)},\lambda _{fr}^{(2)}<t_f$

are given, respectively, by (G.9) and (G.10) in Appendix G in the Supporting Information). Lemma 7

(i)

Relative to the case when both brands license via royalty contracts, as in case

( R , R ) $(R, R)$

, each brand I is better off when both brands do not license (i.e.,

Π I ( N L , N L ) > Π I ( R , R ) $\Pi ^I(NL, NL)>\Pi ^I(R, R)$

for

I = A , B $I=A,B$

) if, and only if,

λ s < λ s r ( 2 ) $\lambda _s < \lambda _{sr}^{(2)}$

and

λ f ∈ ( t f , 3 t f ) $\lambda _f\in (t_f,3t_f)$

.

(ii)

Relative to the case that both brands license via royalty contracts, as in case

( R , R ) $(R, R)$

, each brand I earns more profits in the case that both brands license via fixed‐fee contracts (i.e.,

Π I ( F , F ) > Π I ( R , R ) $\Pi ^I(F, F)>\Pi ^I(R, R)$

for

I = A , B $I=A,B$

) if, and only if: (1)

λ s > λ s r ( 3 ) $\lambda _s > \lambda _{sr}^{(3)}$

when

λ f ∈ ( λ f r L , λ f r H ) $\lambda _f\in (\lambda _{fr}^L,\lambda _{fr}^H )$

and

λ f r ( 1 ) ≤ λ f r ( 2 ) $\lambda _{fr}^{(1)} \le \lambda _{fr}^{(2)}$

; or (2)

λ s < λ s r ( 3 ) $\lambda _s < \lambda _{sr}^{(3)}$

when

λ f ∈ ( λ f r L , λ f r H ) $\lambda _f\in (\lambda _{fr}^L,\lambda _{fr}^H )$

and

λ f r ( 1 ) > λ f r ( 2 ) $\lambda _{fr}^{(1)}>\lambda _{fr}^{(2)}$

; or (3)

λ f ≥ λ f r H $\lambda _f\ge \lambda _{fr}^H$

.

Lemma 7(i) asserts that, instead of licensing via royalty contracts, as in the case

( R , R ) $(R, R)$

, both brands are better off by not licensing when

λ f ∈ ( t f , 3 t f ) $\lambda _f \in (t_f, 3t_f)$

and

λ s < λ s r ( 2 ) $\lambda _s< \lambda _{sr}^{(2)}$

so that the royalty effect (

r I β λ f / t f $r^I\beta \lambda _f/t_f$

) dominates the indirect effect of licensing (

β λ f λ s / t f $\beta \lambda _f \lambda _s/t_f$

). Hence, licensing via royalty contracts is not beneficial. Clearly, both brands can eliminate the “royalty effect” by licensing for free (

r A = r B = 0 $r^A=r^B=0$

) so that they can benefit from the “indirect effect” of licensing. In fact, because

λ f > t f $\lambda _f>t_f$

, (15) reveals that each brand would be better off in equilibrium if both could “commit” to licensing its name for free by setting

r A = r B = 0 $r^A=r^B=0$

. Because such a commitment is absent, brands face a prisoner's dilemma and both charge a positive royalty fee (i.e.,

r A = r B > 0 $r^A=r^B>0$

by Lemma 6) and end up with significantly lower profits when they both use royalty contracts.

Lemma 7(ii) shows that, independent from the negative popularity effect

λ s $\lambda _s$

, when the positive popularity effect is sufficiently high (i.e.,

λ f ≥ λ f r H $\lambda _f\ge \lambda _{fr}^H$

), the fixed‐fee contracts perform better than the royalty contracts in cases where both brands license. This implies that, under competition, when the positive popularity effect is sufficiently high, luxury brands always benefit from using fixed‐fee contracts. This result is due to the fact that, when the followers' appreciation for the brand

λ f $\lambda _f$

is sufficiently high, royalty effect (

β λ f r I / t f $\beta \lambda _f r^I/t_f$

) is very high and the price competition between brands is intensified significantly under royalty contracts so that both brands have to lower their prices.

Only one brand licenses by using a royalty contract (R, NL)

Next, consider the case when only one brand (brand A) licenses via a royalty contract, while the other brand (brand B) does not license. Hence, brand A charges the royalty fee

r A $r^A$

for each unit that licensee a sells (as a monopoly) in market f. Before we present our analysis, let us make two observations. First, because licensee a operates as a monopoly in market f that is fully covered, it is always optimal for brand A to set the royalty fee

r A = p a $r^A=p^a$

to extract licensee a's entire profit. Second, because the market f is fully covered by licensee a's product, it is optimal for licensee a to set its price

p a $p^a$

so as to cover market f and sell to a follower located

θ = 1 $\theta =1$

. By noting that these two observations are the same as in Section 5.3, we can conclude that, when only one brand licenses and the other does not, fixed‐fee and royalty contracts are equivalent. Thus, the equilibrium prices when only one brand uses a royalty contract are identical to those in Lemma 5 of Section 5.3, and the brands' profits when only one firm licenses via a royalty contract are given by

16

17

for

I = A , B $I=A,B$

, where

Π I ( F , N L ) $\Pi ^I(F, NL)$

and

Π I ( N L , F ) $\Pi ^I(NL, F)$

are given, respectively, by (10) and (11).

One brand uses a royalty contract and the other brand uses a fixed‐fee contract (R, F)

Now, consider the case where both brands license and use different contracts. Without loss of generality, suppose that brand A uses a royalty contract and charges a per‐unit royalty fee

r A $r^A$

to its licensee a while brand B uses a fixed‐fee contract and charges a fixed lump‐sum payment

k B $k^B$

to its licensee b. To characterize the royalty fee

r A $r^A$

and ensure that brands and their licensees compete in market s and f, respectively, we assume that

λ f ≥ t f $\lambda _f\ge t_f$

and

β t f > t s $\beta t_f>t_s$

(i.e., followers have a sufficient level of aspiration for brand popularity in market s, and the size of market f (or follower market) is large enough) in this case.11

Lemma I.4 in Appendix I.1 in the Supporting Information characterizes brand A's royalty fee

r A $r^A$

, brand B's fixed lump‐sum payment

k B $k^B$

, and the prices in market s and f in case

( R , F ) $(R,F)$

. We observe from Lemma I.4 that brand A (that uses a royalty contract) can affect the prices of brand B (that uses a fixed‐fee contract) and both licensees by choosing its royalty fee

r A $r^A$

. Licensing via a royalty contract gives brand A extra leverage over brand B and enables it to determine the market shares of brands in market s and licensees in market f. Consequently, brand A always sells to more snobs (i.e., obtains more than half of the snob market) and its licensee (licensee a) attracts more (less) followers when the positive popularity effect is sufficiently higher (lower) than the negative popularity effect.

Brands' profits in this case are given by

18

19

where

r = r A $r=r^A$

in Lemma I.4 in Appendix I.1 in the Supporting Information, and first equalities in (18) and (19) follow from the symmetry of the brands.

Equilibrium licensing strategies of duopoly brands

We finally characterize brands' equilibrium licensing strategies when they can use either fixed‐fee or royalty contracts to license. Characterizing equilibrium for all

λ s $\lambda _s$

and

λ f $\lambda _f$

values in this case is analytically intractable as it requires comparing each brand's profits associated with six different cases (presented in this section and in Section 5). Proposition 3 characterizes equilibrium when the negative popularity effect is sufficiently high (i.e.,

λ s ≥ 3 t s / β $\lambda _s\ge 3t_s/\beta$

), and when the negative popularity effect is low and positive popularity effect is high (i.e.,

λ s < λ s r ( 1 ) $\lambda _s<\lambda _{sr}^{(1)}$

and

λ f ≥ 3 t f $\lambda _f\ge 3t_f$

). Proposition 3

Brands' equilibrium licensing strategies can be characterized as follows: (i)

If

λ s < λ s r ( 1 ) $\lambda _s<\lambda _{sr}^{(1)}$

and

λ f ≥ 3 t f $\lambda _f\ge 3t_f$

, both brands license by using fixed‐fee contracts.

(ii)

If

λ s ≥ 3 t s β $\lambda _s\ge \frac{3t_s}{\beta }$

, (a) both brands do not license when

v f ≤ t f + t s 2 β $v_f\le t_f+\frac{t_s}{2\beta }$

; and (b) only one brand licenses by using either a royalty or fixed‐fee contract when

v f > t f + t s 2 β $v_f> t_f+\frac{t_s}{2\beta }$

.

Proposition 3 resembles Proposition 2, and the equilibrium licensing strategies when brands can use fixed‐fee or royalty contracts have similar characteristics as under fixed‐fee contracts when the negative popularity effect is sufficiently high, and when the negative popularity effect is low and the positive popularity effect is high (i.e., as illustrated in Figure 1 for

λ s ≥ 3 t s / β $\lambda _s\ge 3t_s/\beta$

, and

λ s < λ s r ( 1 ) $\lambda _s<\lambda _{sr}^{(1)}$

and

λ f ≥ 3 t f $\lambda _f\ge 3t_f$

). Hence, Proposition 3 can be interpreted in the same manner as Proposition 2.

Proposition 3(i) shows that, when the negative popularity effect is low and the positive popularity effect is high enough (i.e.,

λ s < λ s r ( 1 ) $\lambda _s<\lambda _{sr}^{(1)}$

and

λ f ≥ 3 t f $\lambda _f\ge 3t_f$

), both brands license and prefer fixed‐fee contracts, even though either of them could use a royalty contract. The intuition behind this result is as follows. Since the negative popularity effect is low (i.e.,

λ s < λ s r ( 1 ) $\lambda _s<\lambda _{sr}^{(1)}$

), each brand is better off licensing (via a fixed‐fee or royalty contract) independent from the strategy of the other brand. Therefore, both brands license. Moreover, since the positive popularity effect is high (i.e.,

λ f ≥ 3 t f $\lambda _f\ge 3t_f$

), both royalty and indirect effects are high if a brand uses a royalty contract so that each brand is better off using a fixed‐fee contract, no matter what contract the other brand uses to license. Hence, both brands prefer licensing via fixed‐fee contracts for

λ s < λ s r ( 1 ) $\lambda _s<\lambda _{sr}^{(1)}$

and

λ f ≥ 3 t f $\lambda _f\ge 3t_f$

.

Proposition 3(ii) implies that, as in the monopoly case (see Proposition 1), when followers' base valuation is sufficiently low (i.e.,

v f ≤ t f + t s 2 β $v_f \le t_f+\frac{t_s}{2\beta }$

) and the snobs' negative popularity effect is very strong (i.e.,

λ s ≥ 3 t s / β $\lambda _s\ge 3t_s/\beta$

), both brands should not license, even when they can use fixed‐fee or royalty contracts, because both brands cannot afford to dilute their brands via licensing. Also, as in Section 5.4, Proposition 3(ii), coupled with Lemmata 4 and 7, implies that, in some cases, for sufficiently high

λ s $\lambda _s$

values (e.g.,

λ s ≥ 3 t s / β $\lambda _s\ge 3t_s/\beta$

), both brands would actually be better off if they were able to commit to licensing via fixed‐fee or royalty contracts; however, without such a commitment, they face a prisoner's dilemma under competition and end up not licensing.

Numerical examples. To obtain a more complete picture about the brands' equilibrium licensing strategies beyond the range of positive and negative effects that are considered in Proposition 3, we conduct an extensive numerical study.12 We observe from all numerical examples for sufficiently low negative popularity effect (i.e.,

λ s < 3 t s / β $\lambda _s<3t_s/\beta$

) that both brands license via fixed‐fee contracts in the equilibrium for all values of positive popularity effect when the follower market is small enough (i.e.,

λ f < t f $\lambda _f< t_f$

for low enough β), or for high values of the positive popularity effect when the follower market is large (i.e.,

λ f ≥ t f $\lambda _f\ge t_f$

for large β). (We omit these numerical examples for brevity.) This has two important implications for low values of negative popularity effect (i.e.,

λ s < 3 t s / β $\lambda _s<3t_s/\beta$

): (1) brands never use royalty licensing and always prefer fixed‐fee licensing if the follower market is small; and (2) Proposition 3(ii) is valid, and the same intuition applies for all

λ f ≥ t f $\lambda _f\ge t_f$

.

Figure 2 illustrates brands' equilibrium licensing strategies for low values of negative and positive popularity effects (i.e.,

λ f < t f $\lambda _f<t_f$

and

λ s < 3 t s / β $\lambda _s<3t_s/\beta$

) when the follower market is large enough (i.e.,

β ∈ { 6 , 10 } $\beta \in \lbrace 6,10\rbrace$

), and

t s = t f = 1 $t_s=t_f=1$

and

c = 0.5 $c=0.5$

$. In the figure, snobs' and followers' base valuations (

v s $v_s$

and

v f $v_f$

) are set very high so that markets s and f are fully covered (see conditions in Lemma H.2 in Appendix H in the Supporting Information). Figure 2 shows that, when the negative popularity effect is low, royalty licensing is preferred (by at least one brand) only when the positive popularity effect is low and the follower market is large enough, and it is used in equilibrium in more cases as the follower market becomes larger. This suggests that, under competition, royalty licensing is used by the brands to impact on their licensees' marginal costs and sales in large markets when the negative and positive popularity effects are low.

OPEN IN VIEWER

FIGURE 2

Brands' equilibrium licensing strategies under fixed‐fee and royalty contracts for

λ f < t f $\bm{\lambda} _{\bf f} < {\bf t}_{\bf f}$

and

λ s < 3 t s / β $\bm {\lambda}_{\bf s} < {\bf 3t}_{\bf s}/\bm{\beta }$

when

t s = t f = 1 $\bm {t_s=t_f=1}$

and

c = 0.5 ${\bf c}=0.5$

$. Note: For numerical examples considered in Figure 2a,b, we choose

v s $v_s$

and

v f $v_f$

large enough and satisfy conditions in Lemma H.2 in Appendix H in the Supporting Information so that markets s and f are covered; moreover, only one brand licenses by using either a fixed‐fee or royalty contract, as in cases

( F , N L ) $(F,NL)$

and

( R , N L ) $(R,NL)$

, for

λ s ≥ 3 t s / β $\lambda _s\ge 3t_s/\beta$

while both brands license by using fixed‐fee contracts, as in the case

( F , F ) $(F,F)$

, for

λ s < 3 t s / β $\lambda _s<3t_s/\beta$

and

λ f ≥ t f $\lambda _f\ge t_f$

.

Further, from Proposition 3, and Figure 2a,b, we observe that both brands prefer royalty licensing only when the follower market (i.e., β) is sufficiently large, the negative popularity effect is neither too high nor too low, and the positive popularity effect is sufficiently low. This is because, in such cases, royalty contracts enable brands to increase marginal costs of their licensees and prevent them to sell too much in market f; moreover, they soften price competition between brands so that they can charge higher prices in market s (i.e., a high indirect strategic effect and a low royalty effect). Lastly, together with Proposition 3, Figure 2 indicates that any combination of no licensing (NL), and fixed‐fee and royalty licensing (F and R) is possible so that each of the six cases analyzed in Sections 5 and 6 can be observed in equilibrium.

DISCUSSION AND CONCLUDING REMARKS

Over the last 30 years, many luxury brands have licensed their brand names to licensees so that they can extend their product offerings in new product categories in a cost‐effective and time‐efficient manner (License Global, 2004). While licensing can enable a luxury brand to capture additional revenues from aspirational consumers (or followers), it can lead the brand to lose the direct control over the sales of the licensed products to the licensee. Consequently, licensing can backfire and make the brand less attractive for the exclusivity‐seeking consumers (or snobs) who purchase brands' own primary products as it was evident when several luxury brands such as Gucci, YSL, and Burberry failed when they attempted to license in the 1980s and 1990s (License Global, 2004).

To examine these two countervailing forces associated with licensing, we have developed a game‐theoretic model to investigate how reference group effects and competition affect luxury brands' licensing strategies. Our analysis provides some useful insights on luxury brand licensing.

How do fixed‐fee and royalty licensing affect the price of a brand's primary product? Due to snobs' desire for uniqueness, it is intuitive to expect a decrease in the price of a brand's primary product when it licenses. While we have confirmed this intuition in the monopoly setting, we have shown that it is not true in most cases in the duopoly setting. Specifically, in cases where both brands license via fixed‐fee contracts, an indirect effect emerges and “softens price competition” between brands. Therefore, fixed‐fee licensing increases prices of brands' primary products in the duopoly setting. In cases where both brands use royalty contracts, in addition to the indirect effect that softens price competition between brands, a royalty effect arises and “intensifies price competition” between brands. The royalty effect dominates the indirect effect, and hence royalty licensing decreases brands' prices only when followers' desire to adopt the same brand as snobs (i.e., positive popularity effect) is sufficiently high. This is because, when followers have a strong desire to emulate snobs, both brands compete for the snobs' demand by lowering their prices so that they can attract more followers to purchase their licensed products and increase their overall royalties. These results indicate that the impact of licensing on brands' prices and profits depends critically on contracts being used, and luxury brands should be careful when they determine their licensing contracts.

Limitations and future research. When we developed our model, we have made simplification assumptions for tractability and to obtain clean insights. Consequently, our model has limitations and there are several avenues for future research. First, we have only considered brand licensing through fixed‐fee and royalty contracts in order to isolate the effect of fixed fee and per‐unit royalty fee. However, brands can also use mixed licensing contracts (i.e., a combination of fixed‐fee and royalty contracts) or umbrella branding strategy (i.e., producing in‐house) to extend in a new product category. Future work can study mixed licensing contracts and/or umbrella branding strategy. Second, we have assumed that brands have a single primary product and they consider extending only in a single (new) product category via licensing. In practice, luxury brands have multiple primary products and/or they can use brand licensing to extend in more than one product category. Future research can extend our paper by studying such cases. Third, we have assumed that followers value a brand's licensed product more as more snobs purchase its primary product (i.e., positive popularity effect). However, there can be cases where followers do not want to be associated with snobs (i.e., followers value a brand's licensed product less as more snobs purchase its primary product). Our paper can be extended by considering such cases. Lastly, we showed that, in the duopoly setting under competition, fixed‐fee licensing always leads to higher prices and profits for brands compared to no licensing when the snob market is fully covered (i.e., snobs' base valuation is sufficiently high). Our analysis in Appendix C in the Supporting Information indicates that, when the snob market is partially covered (i.e., snobs' base valuation is sufficiently low), this result holds true only for high and low values of positive and negative popularity effects, respectively. Future work can empirically test for what realistic parameter values this result is valid and thereby identify how likely it is to occur in practice.