Interaction between innovation choice and market-entry timing in a competitive fashion supply chain

We consider a duopoly in which a premium firm (Firm 1) competes with a regular firm (Firm 2). They launch a new fashion product, adopting one of two types of innovation, qualitative or non-qualitative, which offer different levels of market acceptance and uncertainty. We consider two groups of fashion consumers, snobs and conformists (defined by preference for exclusivity or conformity). We first examine the case in which the premium firm commits to entering the market first and chooses its type of innovation, and then the regular firm decides on market-entry timing and innovation type. The price game and the strategy interaction between the two firms are examined. We show that consumers' exclusivity and conformity positively impact the optimal decisions of the two firms when the initial market share of snobs is large. When the market-share loss due to late entry is sufficiently high, Firm 1 may prefer a non-qualitative innovation under certain identified conditions; otherwise, it always prefers a qualitative innovation. Firm 2 always benefits from Firm 1's choice of qualitative rather than non-qualitative innovation. We further discuss the strategy interaction when the premium firm commits to entering the market late.


Introduction
Competition between fashion supply chains is intense, and fashion trends change rapidly. Firms in the fashion market may have strong market power (premium firms) or relatively weak market power (regular firms). Both types of firm frequently introduce new fashion products in the competitive market, to attract consumers by adopting innovations, either qualitative or non-qualitative. Qualitative innovation relies on new technologies to improve product quality, while non-qualitative innovation makes changes in appearance, such as cut, colour, or shape. For example, UNIQLO, a Japanese fashion brand, pays attention to qualitative innovation in its basic product lines instead of offering the newest fashion trends. The UNIQLO Heattech product line uses innovative materials that can absorb the moisture generated by the human body before converting it into heat (Schulz-Müllensiefen and Stöckmann 2016). Other brands, such as H&M and ZARA, are more inclined to focus on responding to consumer trends as quickly as possible by adopting non-qualitative innovation to introduce fashionable elements in product appearance. Nike and Adidas, two competing fashion sports brands, introduce either technical (qualitative) or design (nonqualitative) innovation into their new products every year. These companies commonly choose only one of the two types of innovation in launching a new product, due to limited capacity, even though they could work on both technology and style elements. It is well known that launching a new product can be risky at the outset, even though the firm that enters the market first has the potential to capture more consumer demand. Conversely, a firm may postpone its marketentry timing until uncertainty about consumer preference is resolved, but this delay may lead to a loss of market share. Therefore, market-entry timing, along with the innovation choice, is a critical strategy choice for a firm to be competitive in the market.
In a fashion supply chain, the premium firm with more market power usually commits to entering the market early and makes its innovation choice. A regular firm generally reacts to the premium firm's innovation, setting its strategy of market-entry timing and innovation choice. For instance, to connect with the LGBTQ community, Nike started the BETRUE collection in 2012 by adding a few symbols of pride into its products (Nike News 2019). After Nike's successful initiative, Adidas developed its PRIDE collection in 2015 to attract this community, embellishing the shoe upper with the iconic rainbow symbol (Adidas News 2021). Nike and Adidas, in this example, successively entered this new market by adopting design (non-qualitative) innovation. On the other hand, Nike dominated the running shoe market for a long time with the Air Max 360 that is a cushioning technology (qualitative innovation) developed in 2006, aiming to improving the comfort of running shoes (Nike News 2015). In 2013, the advent of Adidas Boost, Adidas's cushioning technology set off a global upsurge (Stonebrook 2016). Both Nike and Adidas successively adopted this technical (qualitative) innovation strategy, and this strategy is widely considered by fashion firms in launching a new product. In this paper, we are interested in investigating competing firms' price strategy and competition interaction.
Fashion consumers are inclined to pay more attention to psychological benefits than functional benefits. Driven by exclusivity and conformity, fashion consumers can be categorised into two consumer groups: snobs and conformists. When a product is widely consumed in the market, the snob perceives it with a low valuation (exclusivity), while the conformist perceives it with a high valuation (conformity) (Amaldoss and Jain 2015;Zheng, Chiu, and Choi 2012). These two consumer groups are deemed to be interdependent, and the motivating social influences (exclusivity and conformity) are very important. Specifically, conformists are more willing to buy the fashion product if more snobs buy it, whereas snobs are unwilling to buy the product when more conformists buy it (Shen, Qian, and Choi 2017). For example, Lacoste, a fashion sports brand, aims to target high-end customers; in France, however, after it was adopted by young North Africans from a lower social class, the brand's original high-end customers moved away from it (Chevalier and Mazzalovo 2008).
The interaction of these two consumer groups, which affects firms' price competition and pricing strategies, has attracted much attention. The two groups' impacts on market entry and innovation strategies, however, are understudied. Here, we use our duopoly model to address the following research questions: (1) What are the impacts of consumer behaviours on competing firms' price decisions and profits? (2) Given the premium firm's market-entry strategy, what is the optimal strategy profile (including market-entry strategy and innovation choice) for the regular firm? (3) What is the optimal innovation choice for the premium firm under early or late market-entry strategy?
(4) What are the impacts of market share and market acceptance on the premium firm's innovation choice?
To address these research questions, we consider two interdependent groups of consumers in the market (snobs and conformists) and two firms (premium and regular). The firms make innovations (qualitative or non-qualitative) and act in two periods (early and late). Each firm can choose one of the two types of innovation, under different levels of market acceptance and uncertainty. Consumer preference for the product is uncertain at the outset but it is resolved in the later period.
A firm's strategy profile consists of a choice of market entry time and an innovation type. We first consider the case in which Firm 1 commits to entering the market early and needs to choose its innovation strategy. Then Firm 2 decides its optimal strategy profile including market-entry timing and innovation choice. The two firms engage in price competition to maximise their individual profit. The corresponding optimal strategy profile for Firm 2 and the optimal innovation choice for Firm 1 are obtained. The impacts of market-share and market-acceptance parameters on Firm 1's innovation choice are also discussed. We find that, first, consumers' exclusivity and conformist effects positively impact the equilibrium prices and profits of the two firms when the initial market share of snobs is relatively large, while they have no impact on a firm's innovation choice and market-entry strategy. Second, when Firm 1 adopts a qualitative innovation and the market-share discount is larger than 2/3, Firm 2 tends to give up the qualitative innovation and first-to-market strategy profile; when Firm 1 adopts a non-qualitative innovation, Firm 2 does so only for a larger market-share discount. Third, when the market-share discount is less than 0.7, Firm 1 may prefer a non-qualitative innovation under certain conditions; otherwise, it always prefers a qualitative innovation. In addition, its preference for a non-qualitative innovation shrinks with the market-share discount and the level of market acceptance of qualitative innovation. We extend our discussion to consider the case where Firm 1 commits to entering the market late. We show that a region always exists where Firm 1 prefers a nonqualitative innovation, independent of the market-share discount. In addition, Firm 2 is always better off from Firm 1's choice of qualitative innovation as opposed to non-qualitative.
The contributions of this paper are as follows. First, we consider both qualitative and non-qualitative innovations in launching a new fashion product and qualitatively capture their different levels of market acceptance and risk. Although these two types are useful ways of thinking about innovation in retail fashion, only limited studies in the literature consider them theoretically. We enrich the literature on innovation by filling the gap. Second, this study is the first to discuss analytically the interaction of innovation type and market-entry timing between two competing firms; we capture the practice in a competing fashion supply chain and offer new insights into the fashion supply chain. Third, social influence and its impacts on operations and marketing decisions are important for the fashion industry. The research on social influence, however, has hitherto been largely ignored. Our study complements the existing research and offers implications for fashion supply chain management.
The remainder of this paper is organised as follows: Section 2 reviews the related literature and Section 3 describes the model. Section 4 presents the equilibrium solutions when Firm 1 commits to entering the market early. Section 5 extends the discussion to the case when Firm 1 enters the market late. Section 6 briefly concludes and proposes extensions for future work. All proofs are presented in the online Appendix.

Literature review
Our research is related to the studies on innovation. Innovation has recently been defined as 'an activity of creating a new product or service, new technology, new organisation, or enhancement of existing product or service using existing technologic processes and organisations' (Ramadani and Gërguri 2011). With this broad scope, two significant types of innovation can be defined in relation to product innovation: technical innovation and design innovation. Technical innovation, or qualitative innovation, usually contributes to improving product quality or increasing product functionality (Ramadani and Gërguri 2011;Xie, Huo, and Zou 2019). Design innovation refers to product appearance, aesthetics, features, and emotional or symbolic aspects (Homburg, Schwemmle, and Kuehnl 2015;Kim, Kim, and Choi 2019), and can be regarded as nonqualitative or non-technical innovation. Most researchers focus on technical innovation (Aydin and Parker 2018;2019;Pan and Li 2016), but a growing number of studies have realised the importance of product design innovation (Liu et al. 2020;Micheli and Gemser 2016;Tabeau et al. 2017), because it can influence consumer purchasing behaviour by forming more positive consumer attitudes to the products. In this paper, we consider two categories of widely adopted innovation (qualitative and non-qualitative) to classify new fashion products.
In this stream of research, some studies have examined innovation from the perspective of modelling. For example, Ülkü, Toktay, and Yücesan (2005) investigate the optimal timing of technical innovation in a supply chain with one original equipment manufacturer and one contract manufacturer. Li and Zhao (2021) discuss why and how cooperation occurs in supply chains with the presence of process innovation in upstream component production. Wang and Shin (2015) consider a supply chain with one supplier and one manufacturer, in which the supplier invests in technical innovation, and explore the impacts of contracts on supply chain coordination. Hao et al. (2019) develop a framework where a high-tech firm sequentially introduces new products with incremental innovation over two selling seasons, and investigate how innovation features impact the firm's operational strategy and profit. Taking both technical and non-technical innovations into account, Hu, Mai, and Pekeč (2020) suppose that technical innovation can only spill over from the innovator to the contract manufacturer (CM) in a coopetitive supply chain, while non-technical innovation can spill over in the market. They find that in both cases an innovator may strategically outsource to a competitor CM. Shen et al. (2016) examine the impacts on the supply chain of outsourcing design innovation, and compare supply chain performance under an Original Equipment Manufacturer (OEM) strategy and an Original Design Manufacturer (ODM) strategy. Unlike the studies above, we consider two types of innovation (qualitative and nonqualitative) in a fashion supply chain. With consideration of market-entry timing and consumer psychology, we look at how competing firms balance the values of market share and information in their choice of innovation type.
Our study is also related to the literature on marketentry timing. Market-entry timing is a critical issue in developing a new product, because the risks of premature entry and the problems of missed opportunities should be balanced (Lilien and Yoon 1990). It is well known that the pioneer sees the advantages of market share, but also the high risks associated with product and market development (Kalish and Lilien 1986;Lilien and Yoon 1990;Zachary et al. 2015). Empirical studies support these findings. For example, Biggadike (1976) studied 40 industrial product entries and found that pioneering entrants generally maintained their market share advantage. In a cross-sectional study of 129 products, Urban et al. (1986) report that the second entrant obtains only about three quarters of the market share of the pioneer, and later entrants capture smaller shares. Evidence also shows that market pioneers typically face the greatest market uncertainty due to the difficulty in forecasting sales for a pioneering product (Robinson and Min 2002). Taking both benefits and risks into account, our paper discusses firms' market-entry timing decision in balancing the values of market share and information.
In a competitive environment, a firm should pay more attention to market-entry timing to obtain a competitive edge. Several game theoretic models have addressed this problem. For example, Swinney, Cachon, and Netessine (2011) consider both established firms and startups who invest in capacity to enter a new market, and investigate the relationship of capacity investment (for market-entry) timing and uncertainty. Wang, Thomas, and Rudi (2014) explore production (for market-entry) timing decisions for competing firms, and find that the responsive production strategy (late entry) tends to be favourable when uncertainty is high or production competition is not too strong. Niu et al. (2019) also discuss firms' decisions on production timing in a coopetitive supply chain and show that the firms' production timing decisions depend significantly on the degree of acceptance of market uncertainty and competition intensity. See Demirag, Xue, and Wang (2021), Wu and Zhang (2014), and Yang et al. (2017) for related studies. All of these models, however, focus on the value of information and quantity (price) competition, ignoring the value of market share. Unlike these studies, our paper focuses on the competing fashion supply chain with consideration of consumer behaviour, and considers both information and market-share values for two (price) competing firms. In addition, two innovation choices (qualitative and non-qualitative) are considered, and interaction of innovation choice and market-entry timing for the two competing firms is discussed.
Another related research stream is the studies on pricing strategy affected by social influence. Social influence is the degree to which an individual's purchasing decision is affected by social network members (Asian, Wang, and Dickson 2020;Maldonado et al. 2018;Molinero, Riquelme, and Serna 2015), and mainly includes exclusivity and conformity effects. Exclusivity means that the consumers are unwilling to buy a product when it is popular in the market, and conformity means that the consumers tend to buy a popular product. Driven by exclusivity and conformist effects, fashion consumers can be classified into snobs and conformists (Shen, Qian, and Choi 2017;Zheng, Chiu, and Choi 2012). Snobs are less likely to buy a product as the number of its purchasers increases (Gao, Lim, and Tang 2016), while conformists have the opposite preference (Zhen et al. 2019). The two consumer groups coexist in the fashion supply chain, and the resulting social influence has significant impacts on firms' pricing strategies Jain 2005a, 2005b). For further studies related to the impacts of social influence on pricing decisions, see Amaldoss and Jain (2015), Shen, Qian, and Choi (2017), and Zhang, Chen, and Zaccour (2020). Unlike these works, we focus on the innovation choice and marketentry timing interaction between two competing firms in a fashion supply chain and examine the impacts of social influence on the pricing and strategy interactions.

Model
Consider one premium firm (Firm 1) that competes with one regular firm (Firm 2) in a new market selling substitutable fashion products. Facing uncertain demand, Firm 1 commits to entering the market at the outset (first-to-market strategy), while Firm 2 can choose either a first-to-market strategy with uncertain demand or a late-entry strategy with the demand uncertainty resolved.
We define δ as the market-share discount, and i reflects the fact that the first entrant is more likely to obtain a higher market share than the later entrant (Feng et al. 2020;Lilien and Yoon 1990;Zachary et al. 2015). A high δ means less market-share loss if the late-entry strategy is chosen. Note that 1 = 1, as Firm 1 adopts the first-to-market strategy in our basic model; and 2 = 1 if Firm 2 also chooses the first-to-market strategy while 2 = δ if Firm 2 chooses the late-entry strategy (Jakopin and Klein 2012;Feng et al. 2020).
In the fashion market, consumers experience two types of social influences, exclusivity and conformist effects. The two effects divide the consumers in the market into two groups, snobs (s) and conformists (c), and each consumer group affects the other. That is, fashion conformists are willing to buy a fashion product if more snobs buy it; fashion snobs, however, are not willing to buy the product if more conformists buy it (Chiu et al. 2018;Zhang, Chen, and Zaccour 2020).
where A reflects the uncertain level of market acceptance that characterises the risk of launching a new fashion product, α is the initial market share of snobs and 1 − α is that of conformists, and b and β reflect consumers' exclusivity and conformity effects, respectively.
The duopoly price competition in the fashion industry is widely adopted (e.g. Guo, Choi, and Shen 2020). In addition to price competition, the two firms also compete in innovation strategy. Two innovation strategies can be classified (k = {T, N}), as qualitative innovation (T) and non-qualitative innovation (N). The former (T) refers to innovation that applies new technologies to new products to improve product quality (e.g. UNIQLO Heattech, Nike Air Max 360, and Adidas Boost in our introductory examples), while the latter (N) refers to innovation appearance design (such as the cut, colour, or shape that defines new fashion trends; ZARA and H&M in our example).
Innovations of either type, however, may lead to uncertain market acceptance (Hu, Mai, and Pekeč 2020;Li and Xu 2015;Yu, Lan, and Zhao 2021). We capture market uncertainty with the random variable A with a mean of μ k and a variance of σ 2 k , where k ∈ {T, N}. Two assumptions related to our two innovation strategies are presented as follows.
Assumption 3.1 reflects the fact that a qualitative innovation enjoys a high level of market acceptance with low uncertainty (the new product is obviously improved), while a non-qualitative innovation suffers from a low level of market acceptance with high uncertainty (the new product is just different). Intuitively, a qualitative innovation ensures high quality for the new product, which will attract more consumers as they seek out better quality, or even look to buy a better version of something they already own. Non-qualitative (design) innovation is assumed to have higher uncertainty, as preference for design varies from person to person. UNIQLO's technical (qualitative) innovations, for example, like Heatech and AIRism have been widely praised by consumers. While H&M has had popular designs (non-qualitative innovation), on the other hand, it has also received poor reviews on major design effort. For instance, the exaggerated colours and patterns of the collaborative collections designed by Kenzo in 2016 were not well accepted.
These examples lend support to the assumption that the non-qualitative innovation is riskier.

Assumption 3.2: Qualitative and non-qualitative innovations incur the same cost.
Assumption 3.2 helps us focus on the strategy interaction between the two competing firms. We relax this assumption by considering cost difference in the online Appendix B and show that our main results still hold.
To address this duopoly problem, we develop a fourstage game model. The sequence of events is as follows (illustrated in Figure 1). In Stage 1, Firm 1 enters the market and makes its innovation choice. In Stage 2, Firm 2 chooses the optimal strategy profile including marketentry timing and innovation choice. In Stage 3, Firm 1 sets the retail price p 1 if Firm 2 chooses to adopt a late-entry strategy, or both firms set retail prices p 1 and p 2 simultaneously if Firm 2 chooses to adopt a first-tomarket strategy. In Stage 4, the uncertainty in the market acceptance (A) is realised, and Firm 2 sets the retail price p 2 if it adopts a late-entry strategy.

Equilibrium
In this section, we first solve Firm 2's optimal strategy profile for a given innovation strategy of Firm 1 (either qualitative or non-qualitative), and then derive Firm 1's optimal innovation strategy. We start with optimal pricing decisions of both firms in Stages 3 and 4.

Firm 1 adopts a qualitative innovation
Given that Firm 1 adopts a qualitative innovation (T), Firm 2 has two innovation choices (k = {T, N}), either a qualitative innovation (T), or a non-qualitative innovation (N); it also has two market-entry-timing strategies (w = {F, L}), either a first-to-market strategy (F), or a late-entry strategy (L). As such, Firm 2 has four strategy profiles: (T, F), (T, L), (N, F), and (N, L). Let r = {TF, TL, NF, NL} denote these four possible strategy profiles. In this paper, we focus on the situation in which both firms have demands from both consumer groups to discuss the competition interaction between the two firms. Define The equilibrium solutions for these strategy profiles are presented in Proposition 4.1.
Proposition 4.1: When Firm 1 adopts a qualitative innovation, the expected equilibrium outcomes for Firm 2's four strategy profiles r = {TF, TL, NF, NL} are summarised in Table 1.
With Table 1, when the initial market share of snobs (α) is in the range of α r 1 < α < α r 2 , where r = {TF, TL, NF, NL}, both consumer groups are captured by each firm (i.e. D is > 0 and D ic > 0 for i = 1, 2), and α r 1 and α r 2 are given in Table A1 in the online Appendix A. This suggests that a moderate level of α can ensure that the two consumer groups are captured by both firms, where the two thresholds (α r 1 and α r 2 ) are significantly impacted by consumers' exclusivity effect (b) and conformity effect (β). Let Then we have α < 1 2 <ᾱ. With the equilibrium solutions in Proposition 4.1, the impacts of β, b, and δ on the equilibrium price (p r i ) and profit ( r i ) of Firm i = 1, 2 are summarised as follows.
Corollary 4.1 shows that the firms' pricing decisions and profits are significantly affected by the proportion of each consumer group in the market. When snobs are dominant (α > 1 2 ), the relatively high portion of snobs can also attract more conformists. Both firms can charge a higher retail price with an increase either in β or b, and this ensures a high-profit margin for each firm. Charging a higher price results in lower conformist demand, however, which avoids a loss of snob demand with an increase of b. This is very common for luxury fashion brands who tend to charge a high price for their limited-edition products, aiming to attracting more snobs.
When conformists are dominant in the market (α < 1 2 ), to capture more conformists with an increase of β, the firms should reduce the retail prices to attract more snobs. Here the conformist market is more attractive for the two firms, so they charge a low retail price and the competition in the conformist market is intensified. Some fast fashion brands (such as UNIQLO and H&M), which target mainly conformists, tend to charge a low price to attract more consumers, which inevitably leads to intense competition. In addition, both firms are motivated to increase retail prices with a high market-share discount (δ). Intuitively, a high market share allows Firm 2 to charge a high retail price, which also induces Firm 1 to charge a high price.
Corollary 4.1 shows that both firms benefit from a high conformity/exclusivity effect when the market share of snobs is sufficiently large. Recall that the decrease in the retail price (negative price effect) as β increases results in an increase in the demand (positive demand effect) when α < α < 1 2 . The positive demand effect can offset the negative price effect, resulting in more profit for the two firms. Inversely, when 1 2 < α <ᾱ, the increase in the retail price (positive price effect) results in the decrease in the demand (negative demand effect), as b increases. The positive price effect cannot be offset by the negative demand effect, and thus both firms are worse off.
Next, we use the first-to-market value (M k ), information value (I k ), and innovation value (V w ) of Firm 2 to evaluate the effectiveness of Firm 2 in choosing strategies based on the timing of entering the market and innovation, respectively. We define these three values as follows.
Definition 4.1: For k = {T, N}, the first-to-market value of Firm 2 (M k ) is defined as the difference of the riskless profits of adopting the first-to-market and late-entry strategies, based on innovation choice. Then Definition 4.2: For k = {T, N}, the information value of Firm 2 (I k ) is defined as the difference of the risk profits between adopting the late-entry and first-to-market strategies, based on its innovation choice. Then I k = δ 2 σ 2 k B 2 1 4B 2 (1+bβ) .
We also denote I = I T − I N as the difference of information values between two forms of innovations.

Definition 4.3:
For w = {F, L}, the innovation value of Firm 2 (V w ) is defined as the difference of the riskless profits between adopting a qualitative innovation and adopting a non-qualitative innovation, based on its market-entry strategy. Then . Corollary 4.2 presents the properties of Firm 2's three values. (2) I N > I T > 0, and thus, I < 0; Unlike the results in Wang, Thomas, and Rudi (2014), in which the first-to-market value is always positive under a quantity competition, even if δ = 1 (no marketshare loss), we show that the first-to-market value of Firm 2 depends on its innovation choice and δ. It can be negative if δ is sufficiently high. The reason is that as compared to the situation in a simultaneous game, the first-mover's quantity decision will negatively impact the second-mover's quantity decision in a sequential game, under quantity competition. Thus, when Firm 2 chooses a late-entry strategy, it allows Firm 1 (which has the firstmover advantage) to set a high quantity, which pushes Firm 2 to set a low quantity. Firm 2, therefore, is more willing to enter the market early to generate a relatively high quantity. Although it has to face intense competition, the profit loss due to the competition can be offset by the first-mover advantage.
In contrast, under price competition, the first-mover's price decision will positively affect the second-mover's price decision in a sequential game. When Firm 2 chooses the late-entry strategy, Firm 1 will set a higher price, in comparison with a simultaneous game, resulting in a higher price for Firm 2. This implies that Firm 2 has second-mover advantage under price competition, while the first mover can have advantage under the quantity competition. Under price competition, the first-tomarket strategy is unattractive to Firm 2 because the intense competition and the first-mover disadvantage will dominate the market-share value, leading to a negative first-to-market value. Given that Firm 1 enters the market early, the first-to-market value can measure the market-share advantage, the first-mover disadvantage, and competition disadvantage, for δ ∈ (0, 1).
Specifically, when Firm 2 adopts a qualitative innovation, it enjoys a positive first-to-market value only if δ < 2 3 , implying that a large market-share advantage dominates the first-mover and competitive disadvantages. However, when Firm 2 adopts a non-qualitative innovation, in addition to the market-share discount (which requires δ < 8 9 ), the ratio of the market-acceptance level of innovation should satisfy 1 < μ T μ N < (8−9δ) 2 to ensure a positive first-to-market value. This is because, when the difference of the market-acceptance level for the two innovations is relatively low, Firm 2's innovation competition and the first-mover disadvantage can be offset by the market-share advantage.
Obviously, the information value of adopting a nonqualitative innovation is larger than that of the qualitative innovation, because the non-qualitative innovation is riskier.
Firm 2 always benefits from adopting a qualitative innovation for a given market-entry strategy. Furthermore, the qualitative innovation advantage when adopting a late-entry strategy is larger than that when adopting a first-to-market strategy, if δ is sufficiently large. Intuitively, a high market-share discount means a smaller market-share loss with the late-entry strategy, which enables Firm 2 to benefit more from adopting a qualitative innovation when it chooses the late-entry strategy.
The impacts of the discount (δ) on the three values are summarised in Corollary 4.3.
Intuitively, the first-to-market value (M k ) decreases with δ as the market-share loss decreases. The information value (I k ) increases with δ because the information will be more valuable with a large market share. Similarly, the innovation value will be enlarged by the high market size. When the market-share loss is low (δ is large), firms are more likely to choose to obtain more accurate market information by waiting to enter the market late. Furthermore, low market-share loss means a large market base, which motivates firms to try to attract larger demand by choosing a qualitative innovation, with a high level of market acceptance.
Comparing Firm 2's profit under four strategy profiles, we have the following results.

Proposition 4.2: Firm 2 will never choose the NF strategy profile, since it is always dominated by the TF strategy profile.
Proposition 4.2 shows that for Firm 2, NF will never be an optimal strategy profile, which means that Firm 2 will never adopt a non-qualitative innovation with the first-to-market strategy. Firm 2 always prefers the TF over the NF strategy profile because when Firm 2 chooses the first-to-market strategy, it is always better off choosing a qualitative innovation for its high level of market acceptance. It is intuitive that a firm is more likely to adopt qualitative innovation when it enters the market early to compete with the other firms, as the qualitative innovation is more competitive than the nonqualitative innovation due to its high market-acceptance level. We . Given that Firm 1 adopts a qualitative innovation, Firm 2's optimal strategy profile is presented in Proposition 4.3 (illustrated in Figure 2).

Proposition 4.3: When Firm 1 adopts the qualitative innovation strategy, Firm 2's optimal strategy profile is:
( Figure 2 illustrates Firm 2's optimal strategy profile on the two-dimensional σ 2 T − σ 2 N plane, when Firm 1 adopts a qualitative innovation. The solid lines divide Figure 2(a,b) into three (two) regions, corresponding to the first and second results in Proposition 4.3, respectively. The results show that Firm 2's optimal strategy profile is greatly influenced by the uncertainties of these two innovations as well as the market-share discount.
When the market-share discount is relatively low (δ < 2 3 ), Firm 2 is willing to enter the market earlier when facing low uncertainties, given the large benefits of high first-to-market value. However, facing high uncertainty when a (non-) qualitative innovation is adopted, Firm 2 prefers to enter the market late and chooses the (non-) qualitative innovation, to take advantage of the information value. Specifically, when the uncertainty of a nonqualitative innovation is sufficiently large (σ 2 N > η N 1 ), Firm 2 benefits from high information value by adopting non-qualitative innovation. Obviously, when facing a low risk of launching an innovation and a high market-share loss, the firms always want to enter the market earlier to occupy the dominant position. On the contrary, when the development of an innovation is highly risky, the firms will delay entering the market to avoid loss due to high risk.
When the market share discount is large enough (δ > 2 3 ), Firm 2 cannot generate any positive first-to-market value from entering the market early (Corollary 4.2) and will not choose the first-to-market strategy (TF). Firm 2 chooses between strategy profiles TL and NL. Intuitively, a firm will inevitably give up entering the market early when the first-to-market advantage is risky or otherwise unattractive.

Firm 1 adopts a non-qualitative innovation
Given that Firm 1 adopts a non-qualitative innovation, the equilibrium solutions for the four possible strategy profiles for Firm 2 are presented in Proposition 4.4. Here we use the bar (¯) notation to differentiate the results in Section 4.1.

Proposition 4.4:
When Firm 1 adopts a non-qualitative innovation, the equilibrium outcomes for Firm 2's four strategy profiles r = {TF, TL, NF, NL} are summarised in Table 2.
For r = {TF, TL, NF, NL}, Table 2 shows that when the initial market share of snobs (α) satisfiesᾱ r 1 < α <ᾱ r 2 , both consumer groups can be captured by each firm (i.e. D is > 0 and D ic > 0 for i = 1, 2), whereᾱ r 1 andᾱ r 2 are given in Table A1 in the online Appendix A. The impacts of social influences and market-share discount on the equilibrium solutions are consistent with those where Firm 1 adopts a qualitative innovation (Corollary 4.1).
Accordingly, the first-to-market advantage value (M k ), information value (Ī k ), and innovation value (V w ) are given as follows, and their properties are presented in , and

Corollary 4.4: When Firm 1 adopts a non-qualitative innovation, then
(2)Ī N >Ī T , and thus Ī < 0; ( In comparison with the case where Firm 1 adopts a qualitative innovation (Corollary 4.2), Firm 2 is able to enjoy a positive first-to-market valueM T under a high market-share discount threshold ( 8 9 > 2 3 ), when Firm 1 adopts a non-qualitative innovation. In addition, Firm 2 can still obtain a positive first-to-market value with a relatively low δ (δ < 2 3 ) even if it adopts a non-qualitative innovation, implying that Firm 1's non-qualitative innovation can induce Firm 2 to take advantage of the firstto-market value. This is because Firm 2 will enjoy a more competitive advantage (first-to-market value) when it adopts a qualitative innovation that competes with Firm 1's non-qualitative innovation.
We also find that the information value is equal to that of the case in which Firm 1 adopts qualitative innovation, i.e.Ī T = I T , andĪ N = I N . This suggests that Firm 2's information value is independent of Firm 1's innovation choice.
In addition, it can be inferred that δ N > δ T , suggesting that a higher market-share discount is needed to ensure the innovation advantage of the late-entry strategy. This is because when Firm 1 adopts a non-qualitative innovation, Firm 2's innovation advantage of the first-to-market strategy will significantly increase; a high market-share discount would be required to give the late-entry strategy a high innovation value. We Comparing the equilibrium profits under Firm 2's four strategy profiles, we can summarise Firm 2's optimal strategy profile when Firm 1 adopts a nonqualitative innovation in Proposition 4.5 (illustrated in Figure 3).

Proposition 4.5:
When Firm 1 adopts the non-qualitative innovation strategy, Firm 2's optimal strategy profile is: Similar to Propositions 4.3, 4.5 also shows that Firm 2's strategy choice is significantly impacted by the uncertainties of the two types of innovation and the market-share discount. The difference is that the threshold of giving up the TF strategy profile increases from 2 3 to δ 1 , implying that Firm 2 will switch from the first-to-market strategy to a late-entry strategy with a higher market-share discount. The interpretation is that when Firm 1 adopts a non-qualitative innovation, Firm 2 has competitive advantage if it chooses a qualitative innovation and first-to-market strategy. In this case, only a large market share in the later period (δ) can induce Firm 2 to give up the first-to-market strategy. The implication for Firm 2 is that, when Firm 1 adopts nonqualitative innovation, even if the market-share advantage decreases, Firm 2 can be still profitable from adopting qualitative innovation and entering the market early.

Firm 1's optimal innovation choice
We have obtained Firm 2's optimal strategy profile. Now we analyse Firm 1's optimal innovation choice. Lemma 4.1 implies that Firm 1 always prefers a qualitative innovation. Intuitively, for a given strategy profile of Firm 2, Firm 1 always prefers a qualitative innovation over a non-qualitative innovation because it benefits from the high level of market acceptance of qualitative innovation without incurring an extra cost (Assumptions 3.1 and 3.2). We With Firm 2's optimal strategy profile in Propositions 4.3 and 4.5, and comparing Firm 1's profits under the two innovation options, its optimal innovation choice is summarised in Proposition 4.6. Proposition 4.6: Firm 1's optimal innovation strategy depends on δ, η N l , and η T z , where l = 1-4, z = 1, 2. Specifically, Firm 1 adopts non-qualitative innovation if conditions in Table A2 in the online Appendix A are satisfied, while it adopts qualitative innovation otherwise. Figure 3 depicts Firm 2's optimal strategy profiles when Firm 1 adopts (non-) qualitative innovation within different ranges of market-share discount (δ). In Region r-r, the first (second) r refers to Firm 2's optimal strategy profile when Firm 1 adopts a qualitative (non-qualitative) innovation. In Region r, Firm 2 always chooses strategy profile r, independent of Firm 1's innovation choice, with r ∈ {TF, TL, NL}.
Proposition 4.6 shows that Firm 1 is willing to choose a non-qualitative innovation under some conditions (the coloured regions in Figure 3), depending on the uncertainties of the two types of innovation and the marketshare discount. Specifically, Firm 1 may prefer a nonqualitative innovation only in Regions TF-NL (green), TF-TL (red), TL-TF (orange), and NL-TF (bule). In these regions, a non-qualitative innovation is preferred if the market-share discount (δ) is above (or below) a threshold (given in Table A2). Specifically, in Region TF-NL (TF-TL), Firm 2 switches from strategy profile TF to NL (TL) when Firm 1 switches from a qualitative innovation to a non-qualitative innovation. This switch can not only avoid head-to-head competition, it also allows Firm 2 to charge a high retail price due to a high marketshare discount, resulting in an increase in Firm 1's retail price. Thus, Firm 1 prefers a non-qualitative innovation. In Region TL-TF (NL-TF), Firm 2 chooses the TL (NL) strategy profile when Firm 1 adopts a qualitative innovation to avoid fierce competition. However, the loss in profit cannot be offset by the advantage due to the weakened competition for a low market-share discount. Therefore, Firm 1 switches to a non-qualitative innovation.
Firm 1 will never choose non-qualitative innovation when the market-share discount is sufficiently large (δ 1 < δ < 1, where 2 3 < δ 1 < 8 9 ). The implication is that the premium firm should adopt a qualitative innovation to retain competitive advantages when the market-share loss of late entry is relatively low. Figure 4 numerically illustrates the impact of μ T and δ on Firm 1's innovation choice. R 1 , R 2 and R 3 correspond to Firm 1's preference regions for non-qualitative innovation in Region TL-TF (orange) in Figure 3(b)-(d), respectively. R 4 and R 5 correspond to Firm 1's preference regions in Region NL-TF (blue) in Figure 3(c ,d), respectively. Figure 4 reveals the following important insights. First, with the increase of δ and μ T , Firm 1's preference region for non-qualitative innovation shrinks. The reasons are: first, in Region TL-TF, Firm 2 chooses the TL (TF) strategy profile when Firm 1 adopts a qualitative (non-qualitative) innovation, leading to softened (intensified) competition. The advantages of the weakened competition further generate the expansion of market share with an increase of δ, which induces Firm 1 to choose a qualitative innovation. Likewise, in Region NL-TF, Firm 1's qualitative innovation choice results in Firm 2 delaying market entry, avoiding head-to-head competition. With the increase of δ, Firm 1 benefits more from weakened competition. In addition, it is intuitive that Firm 1 is willing to adopt a qualitative innovation when its market-acceptance level (μ T ) is high. Second, Firm 1 will never choose a non-qualitative innovation when δ is sufficiently large (> 0.7). As the first-to-market player, Firm 1 does not need to be concerned about market-share loss in the later period. However, its innovation strategy will significantly impact Firm 2's price decisions and the competition between the two firms. Therefore, Firm 1 prefers a qualitative innovation due to its competitive advantage when the market-share loss (1 − δ) is less than 0.3.

Firm 2's preference on Firm 1's innovation choice
We have discussed Firm 1's innovation strategy (qualitative or non-qualitative), which depends on market conditions. Now we examine whether or not Firm 1's optimal innovation choice will benefit Firm 2. The result is summarised in Proposition 4.7 as follows.
Proposition 4.7 shows that Firm 2 prefers Firm 1's qualitative innovation. The reason is that, under price competition, adopting a qualitative innovation allows Firm 1 to charge a high retail price, leading to a high retail price for Firm 2. The price competition is softened and generates a positive market-acceptance spillover from the first-mover (Firm 1) to the second-mover (Firm 2).
Proposition 4.7 implies that the two firms' preferences are consistent in some regions after Firm 1's innovation choice. Notice that their preferences may conflict in some regions.

Extension: Firm 1 commits to a late-entry strategy
In our main model, Firm 1 is assumed to commit to entering the market early. In this section, we relax this assumption by extending the discussion to the case in which Firm 1 commits to entering the market late, waiting until market-acceptance uncertainty is realised 1 .
In this section, we examine the impact of Firm 1's marketing entrance time on the decisions of the duopoly. The timeline of the game for this case is illustrated in Figure 5. The major difference from the game sequence in Figure 1 is that Firm 1 delays announcement of its retail price to Stage 4 instead of announcing in Stage 3.
We can show that NF is not an optimal strategy profile for Firm 2 since NF can be dominated by strategy profile TF. The equilibrium outcomes for the three strategy profiles r = {TF, TL, NL} are given in Table A3 in the online Appendix A. Here, we use the hat (ˆ) and the tilde (˜) to denote the results when Firm 1 adopts a qualitative innovation and a non-qualitative innovation, respectively, in this section.
To ensure that both consumer groups can be captured by the two firms, α should satisfy b 1+b < α < 1 for r = {TL, NL} regardless of Firm 1's innovation choice. For r = TF, α TL 1 < α < α TL 2 (α NL 1 < α < α NL 2 ) is the condition if Firm 1 adopts a qualitative (non-qualitative) innovation, where α TL i and α NL i , i = 1, 2 are presented in Table A1 in the online Appendix A.
Comparing the profits under these three strategy profiles, we obtain Firm 2's optimal strategy profile when Firm 1 adopts a qualitative innovation in Proposition 5.1.
, and Proposition 5.1: If Firm 1 chooses a qualitative innovation, Firm 2's optimal strategy profile is: In comparison with Proposition 4.3, a parameter space always exists where Firm 2 chooses the TF strategy profile, regardless of the value of δ. This is because Firm 2 can not only avoid head-to-head competition, but can also obtain market-share advantage. These two advantages dominate the first-mover disadvantage, allowing Firm 2 always to enjoy a positive first-to-market value.
, and . When Firm 1 adopts a non-qualitative innovation, Firm 2's optimal strategy profile is summarised as follows.
Proposition 5.2: If Firm 1 chooses a non-qualitative innovation, Firm 2's optimal strategy profile is: Different from Proposition 5.1, a region exists in which Firm 2 will never choose the TF strategy profile.
and δ 2 < 1 otherwise. It suggests that when the market-acceptance-level ratio of the two innovations 2 ), and the market-share discount is relatively large (δ > δ 2 ), Firm 2 will not choose the TF strategy profile. This is because, under the TL strategy profile, Firm 2 enjoys the second-mover advantage and competitive advantage in a large market-acceptance-level difference on innovation, and these two advantages together dominate the market-share disadvantage.
Lemma 5.1 presents the impact of Firm 2's strategy profile on the profit of Firm 1, based on Firm 1's innovation strategy.
Lemma 5.1 shows that independent of Firm 1's innovation choice, Firm 2's strategy profile (either TL or NL) has no impact on Firm 1's profit. Intuitively, whether Firm 2 chooses the TL or NL strategy profile, it always engages in a simultaneous price competition with Firm 1, and this implies that Firm 1's price decision is not influenced, and Firm 2's strategy has no impact on Firm 1's profit (see Table A3 in the online Appendix A).
(2) for min{δ 2 , 1} < δ < 1, Firm 1 adopts nonqualitative innovation if (i)η N 1 < σ 2 N < max{min{η N 2 , η N 5 },η N 1 }, or (ii) σ 2 N < min{η N 1 ,η N 5 } and σ 2 T <η T 1 ; otherwise, a qualitative innovation is adopted. Figure 6 depicts Firm 2's optimal strategy profile when Firm 1 enters the market late and adopts a (non-) qualitative innovation. Specifically, Figure 6(a,b) is divided into five (four) regions. Firm 1 may prefer a non-qualitative innovation (k = N) in Regions TF-NL (green), TF (grey), TF-TL (yellow), and NL (stars). In comparison with the results in Figure 3, all coloured regions become larger, implying that Firm 1 is more likely to adopt a nonqualitative innovation for the parameter space. The reason is that Firm 1 can always obtain a higher information value from the non-qualitative innovation than from the qualitative innovation, when it enters the market late. The implication is that Firm 1 has more incentive to choose the non-qualitative innovation when it adopts the  late-entry strategy, than when it adopts a first-to-market strategy. Now we focus on the NL and TF-NL Regions to investigate the impacts of δ and μ T on Firm 1's innovation strategy. Figure 7 illustrates the change in the NL Region when δ varies. As δ increases, Firm 1's preference on the non-qualitative innovation first increases and then stays unchanged, depending on the relations ofη N 1 andη N 2 (σ 2 N > max{η N 1 ,η N 2 } in the NL Region). For η N 2 >η N 1 , when σ 2 N >η N 2 , Firm 2 always prefers NL over TF strategy profile. The intuition is that with the increase of δ, the advantage of NL increases. Firm 2 will choose it even for a lower σ 2 N (notice thatη N 2 decreases with δ). Thus, we can conclude that Firm 1's preference for non-qualitative innovation increases with δ, as Firm 1 always benefits from non-qualitative innovation in this region. Forη N 1 >η N 2 , Firm 1 is better off with non-qualitative innovation when σ 2 N >η N 1 . It is noted thatη N 1 is unchanged with δ, implying that Firm 1's preference on the non-qualitative innovation does not change. Figure 8 reveals that the NL Region shrinks with an increase in μ T , suggesting that Firm 1's preference over non-qualitative innovation decreases. Intuitively, a firm is more likely to choose a qualitative innovation when its market-acceptance level increases.  Table 3 numerically summarises the impacts of δ and μ T on Firm 1's non-qualitative innovation choice in TF-NL Region. Similarly, with an increase in δ, the area where Firm 1 prefers the non-qualitative innovation shrinks. In addition, for a low δ (δ = 0.4), with an increase in μ T , Firm 1 tends to choose a non-qualitative innovation in a larger parameter space of σ 2 T and σ 2 N . When δ is relatively large, this non-qualitative innovation area disappears, independent of μ T . In other coloured regions (TF and TF-TL), we also find that Firm 1 will never choose a non-qualitative innovation when the market-share loss is small enough.
The above discussion shows that when Firm 1 commits to entering the market early, and its market-share loss is sufficiently small (or equivalently, δ is sufficiently large), it will never choose a non-qualitative innovation. Interestingly, when Firm 1 enters the market late, a region always exists (NL) where Firm 1 prefers a non-qualitative innovation even for a small market-share loss. Specifically, its preference on a non-qualitative innovation may increase with lower market-share loss.
In addition, we show that Firm 2 always benefits from Firm 1's qualitative-innovation strategy when Firm 1 commits to entering the market late, except in the NL region where Firm 2 has the same preference towards the two innovations.

Conclusion
Firms in fashion supply chains introduce new products to attract more consumers in response to rapidly changing fashion trends. It is common in practice that two types of innovation can be used to distinguish a product as new: either a qualitative innovation (such as material) or a non-qualitative innovation (such as colour). Firms usually face uncertain demand at the launch of a product in the market, but this uncertainty can be resolved later. In this paper, we consider two market-entry strategies, first-to-market and late-entry. Fashion consumers can be seen as belonging to two categories (snobs and conformists), with their taste driven by the social influences of exclusivity and conformist effects. With consideration of consumer behaviour, we model two firms, one premium and one regular, that engage in price competition in introducing a new fashion product. The premium firm (Firm 1) commits to entering the market early and N ∈ (max{1/4σ 2 T + 5.76, 6.0312}, 6.605) δ = 0.4 and μ T = 1.1 in this simulation. makes its innovation strategy choice first. The regular firm (Firm 2) decides on its strategy profile, including innovation choice and market-entry timing later. The equilibrium prices and strategy interaction of the two firms are examined. We then extend the main model to the situation where the premium firm commits to entering the market late, to examine the impact of the premium firm's entry timing on the decisions of the duopoly.
The main results are summarised as follows. First, consumers' exclusivity and conformist effects have a positive impact on the equilibrium prices and profits of the two firms when the initial market share of snobs is relatively large, but have no impact on a firm's innovation choice and market-entry strategy. Second, independent of Firm 1's innovation and market-entry strategy, Firm 2 will never choose a non-qualitative innovation and first-to-market strategy profile. Third, when Firm 1 commits to entering the market early and adopts a qualitative innovation, Firm 2 will give up the qualitative innovation and first-to-market strategy profile when the market-share discount is larger than 2/3; when Firm 1 adopts non-qualitative innovation, Firm 2 does so only for a larger market-share discount. This suggests that Firm 1's non-qualitative innovation choice increases Firm 2's preference for the qualitative innovation and first-to-market strategy profile. Moreover, when the market-share discount is less than 0.7, Firm 1 may prefer non-qualitative innovation under certain conditions, and its preference on nonqualitative innovation shrinks with the market-share discount and the market-acceptance level of qualitative innovation. However, when the market-share discount is larger, Firm 1 always prefers a qualitative innovation.
If Firm 1 commits to entering the market late, a region always exists where Firm 1 prefers a non-qualitative innovation, independent of the market-share discount. This region may increase with the market-share discount, while it decreases with the market-acceptance level of qualitative innovation. In addition, Firm 2 always benefits from Firm 1's qualitative innovation choice.
We have considered two asymmetric competing firms, in which the premium firm first makes its innovation decision for a given market-entry timing commitment, and then the regular firm decides on the innovation choice and market-entry timing strategy. In some cases, the two firms may be symmetric and compete in the market. Both firms may make their individual innovation and market-entry strategy choices simultaneously. This extension would offer interesting results and insights. Note 1. Sections 4 and 5 examine the exogenous entry strategy for Firm 1. The endogenous entry strategy is discussed in the online Appendix B.

Disclosure statement
No potential conflict of interest was reported by the author(s).