Promoting a Sustainability Culture in the Liquor Industry: Competition or Cooperation?

Abstract

As sustainability becomes a vital concern for consumers, liquor firms are increasingly integrating sustainable culture into their brand promotion campaigns. This study examines two liquor firms’ competitive and cooperative promotion strategies of a sustainability culture via a game theoretical model. The analytical results are obtained as follows: (1) The correlation coefficient between sustainability culture and liquor products negatively affects the promotion level of sustainability culture under the cooperative promotion strategy, whereas its impact is non-monotonic under the competitive promotion strategy. (2) Under the cooperative promotion strategy, the initial disparity in sustainability cultures always positively affects the promotion level of the common sustainability culture. However, under the competitive promotion strategy, its impact is the opposite for a liquor firm with a weak sustainability culture and a liquor firm with a strong sustainability culture. (3) The necessary conditions for adopting a cooperative strategy for promoting a common sustainability culture are that the initial disparity in sustainability cultures between the two liquor firms is in a moderate range. Therefore, for managers in the liquor industry, careful assessment of the initial disparity in sustainability cultures is essential when formulating cooperative or competitive strategies. It is also crucial to recognize the nuanced role played by the correlation between sustainability culture and liquor products. Moreover, these findings offer a robust theoretical foundation for future research into the influence of sustainability culture on liquor supply chain ecosystems.

1. Introduction

Given that more and more consumers are concerned with sustainability, the liquor industry has started proactively adapting to such a change in the alcohol consumption market. Because some consumers now prioritize sustainability-certified purchases, the diversified development of alcohol categories such as spirits, wine, and beer has established its unique competitive advantage under certain sustainability cultures [1,2,3]. For example, in the Chinese liquor industry, sauce-flavored and strong-flavored liquor segments hold 35% and 48% market shares, respectively [4]. In particular, Moutai’s Feitian series, holding a 19.3% share in the sauce-flavored liquor segment, exemplifies heritage-based cultural capital accumulation. Wuliangye’s eighth generation, capturing a 10% share in the strong-flavored liquor market, demonstrates harmony culture [5]. These two prominent Chinese liquor enterprises not only create product barriers through technological differences but also compete for consumers’ minds by emphasizing a “sustainability culture” (e.g., historical heritage, regional characteristics, and health concepts) behind them. This phenomenon reflects a shift in the competitive paradigm of the liquor industry: Product differentiation has evolved from a simple taste competition to a systematic shaping of sustainable cultural values [6]. More specifically, Moutai strengthens high-end cultural symbols through “Feitian Moutai” and began collaborating with Ruixing Coffee to launch soy sauce lattes, integrating traditional liquor culture into youthful consumption scenes. Wuliangye on the other hand, explores historical connotations through the “classic Wuliangye” series and implements digital marketing on platforms such as TikTok to build its brand image with sustainability culture. These examples suggest that although embedding a sustainability culture in liquor products is a growing consensus of liquor firms, how to link sustainability culture with liquor products is still a challenging problem.

While prior research has examined sustainability strategies [7,8,9], the interplay between firms through cooperation or competition remains underexplored in the liquor industry’s sustainability transition. Specifically, the existing literature reveals cooperation’s positive influence on liquor corporations [8], local economy [9,10], and government policy [11]. Yet the explanation of liquor’s institutionalized collaborations remains unclear [12,13]. Moreover, existing research predominantly analyzes wine or liquor industry competition through pricing [14,15,16] and geographic location selection [17]. Until recently, in China, sustainability is emerging as a new competition field, particularly in premium segments where Moutai’s cultural narrative commands 9.3% price premiums over its industrial peers [5]. This reflects that ESG-aligned brands may capture higher customer loyalty in the liquor market [18], and thus, Chinese liquor enterprises could leverages sustainable credentials such as historical legacy to increase their profitability [19].

However, current sustainability efforts in the liquor industry mainly focus on environmental technologies and supply chain management. The cultural dimensions of sustainability and their impact on market strategies receive little attention. Moreover, despite the advancements in information technology [20] (e.g., social media, big data analysis, etc.) allowing companies to more precisely target their audiences, deploying cutting-edge technology tends to be costly for sustainability culture promotions. Thus, when a liquor firm promotes its sustainable culture, sharing sustainability culture promotion costs with other liquor firms is rational. For instance, despite competing for premium market share, Moutai and Wuliangye jointly fund the “China Sustainable Distillery Alliance” [21]. Moreover, some small liquor brands have also built similar alliances [22], revealing a tiered coopetition pattern where sustainability acts as both a collaborative platform and competitive differentiator. However, there are also side effects of collaboration in promoting a common sustainability culture, such as increasing the risk of cultural homogenization. In this context, liquor firms face a dilemma: Should they intensify competition by emphasizing the uniqueness of their own sustainable culture or collaborate with other firms to promote common cultural values and share the costs? This decision not only affects short-term market share but also has significant impacts on the long-term ecological balance of the liquor industry.

Although the existing literature has extensively explored horizontal differentiation and coopetition strategies, there are several limitations: (i) Absence of cultural elements: The classic Hotelling model primarily focuses on product attributes such as quality and taste, neglecting the impact of cultural added value on consumer utility [3,4]. (ii) Unclear mechanism of cultural differences: While scholars have pointed out that cultural similarity promotes cooperation [5,6], there is a lack of quantitative analysis on how the degree of cultural differences between firms (e.g., the cultural distance between sauce-flavored and strong-flavored liquor) affects strategic choices [7]. Therefore, when liquor firms can achieve differentiation by investing in the shaping of sustainable culture [23,24,25], how do cultural promotion costs and the degree of cultural differences influence their choices between competition and cooperation strategies? To answer this question, this study raises the following research questions:

(i)

How would the correlation coefficient of a sustainability culture and liquor product affect the promotion level of a sustainability culture?

(ii)

How would the initial disparity in sustainability cultures between the two firms affect the promotion level of a sustainability culture?

(iii)

Under what conditions should liquor firms adopt a cooperative promotion strategy of a sustainability culture?

Accordingly, to answer the above questions, three research hypotheses are proposed as follows.

Liquor as a cultural product represents symbols and corresponding lifestyles. For example, French Bordeaux wine is inextricably linked to British elite culture [26]. Furthermore, based on the consumer culture theory, consumers can use the cultural attributes of liquor products to show their personality, identity, social status, and life goals [27]. On the other hand, correlating culture to wine brand is an important measure to affect wine consumption [28]. Thus, when sustainability culture begins to prevail in the liquor market, liquor firms would benefit from building a tight correlation between a sustainability culture and liquor product (i.e., a bigger correlation coefficient of a sustainability culture and liquor product). This is because a stronger tie within a sustainability culture and a liquor product is more likely to induce consumers to purchase this liquor product. Moreover, when a liquor firm intends to promote the level of a sustainability culture embedded in its liquor products, it is natural to think that the correlation coefficient of a sustainability culture and liquor product may negatively affect the promotion level of a sustainability culture because of the substitutability between them. Thus, the following hypothesis is proposed:

H1: 

The correlation coefficient of a sustainability culture and liquor product negatively affect the promotion level of a sustainability culture.

Butler and Fehr [29] point out that cultural differences affect cooperation efficiency through preferences and beliefs. In cooperation, a moderate level of cultural differences provides complementary resources and enhances the joint promotion effect (positive effect). In a competitive environment, a big cultural difference further strengthens promotion due to its resource endowment advantages (positive effect), while small cultural differences reduce investment due to resource limitations (negative effect), leading to polarization. Similarly, Gunnthorsdottir et al. [30] found an asymmetric impact of cultural diversity on cooperation. The feature of "fixed process + cultural plasticity" (Wang et al. [6]) in the liquor industry (such as the Chinese liquor industry) requires taking into account the cultural differences between liquor firms when considering promoting a sustainability culture in a cooperative or competitive environment. Hence, the following hypothesis is proposed:

H2: 

Initial sustainable culture disparity differently affects the promotion levels of sustainability culture for liquor firms with different levels of sustainability culture in a competitive environment but consistently affects their promotion level of a sustainability culture in a cooperative environment.

Farazi et al. [23] propose an inverted U-shaped relationship between cooperation intensity and competitive pressure. This finding suggests the existence of necessary market conditions—specifically, a range of parameter values—under which inter-firm cooperation can be achieved. As for the initial disparity in sustainability cultures in liquor firms, if the initial disparity in sustainability cultures is too small (big), it may lead to cooperation failure because the collaboration willingness of the liquor firm with a strong (weak) sustainability culture will decrease. Thus, when liquor firms consider achieving a cooperative promotion strategy of a sustainability culture, a moderate difference in sustainability cultures is an appropriately necessary condition. This argument is supported by Spadaro et al. [31], who quantified the specific range of cultural diversity thresholds in an industrial context. Therefore, the following hypothesis is proposed:

H3: 

A cooperative strategy is viable only when the initial cultural disparity in sustainability culture falls within a moderate range.

To examine the aforesaid hypotheses, a game theoretical model is developed. The following analytical results were obtained: First, the correlation coefficient between sustainability culture and liquor products has a negative impact on the optimal promotion level of sustainability culture under a cooperative promotion strategy, whereas its effect is non-monotonic under a competitive promotion strategy. Second, under a competitive promotion strategy, the initial disparity in sustainability cultures negatively influences the optimal promotion level for the liquor firm with a weaker sustainability culture but positively influences that of the firm with a stronger sustainability culture. In contrast, under a cooperative promotion strategy, the initial disparity in sustainability cultures consistently exerts a positive effect on the optimal promotion level of a common sustainability culture. Third, a cooperative strategy for promoting a sustainability culture should be adopted by liquor firms only when the initial disparity in sustainability cultures between the two firms falls within a moderate range.

The novelty of this study is as follows: First, this paper introduces a sustainability culture perspective as a lens through which to analyze competitive and cooperative promotion strategies in the liquor industry. This novel sustainability perspective offers valuable insights for managers in the liquor industry, particularly as they strive to meet the evolving preferences of emerging consumer generations. Second, this paper identifies the necessary conditions under which liquor firms can collaborate to promote a common sustainability culture. This finding reminds liquor firms’ managers to consider the initial cultural disparity in sustainability culture when reaching a collaboration in promoting a common sustainability culture. Finally, this study reveals the impacts of several key factors on the profitability of liquor firms. These factors include the correlation between sustainability culture and product, the initial disparity in sustainability cultures between the two firms, the mismatch cost between product sustainability cultures and consumer preferences, and differences in conversion rates toward a common sustainability culture. Thus, for managers in the liquor industry, this article provides an actionable tool for selecting cultural promotion strategies by combining the internal and external environmental factors faced by liquor firms as well as assisting managers in optimizing resource allocation. For policymakers related to the liquor industry, this research offers a method for them to formulate policies to select competitive or cooperative cultural strategies by comparing the total profits of the industry.

The rest of the paper proceeds as follows. Section 2 reviews the related literature. Section 3 and Section 4 develop and solve the game theoretical model, followed by sensitivity analyses in Section 5. Section 6 presents the numerical study, and Section 7 presents the main conclusions of this article.

2. Literature Review

This article is closely related to three streams of literature: (i) horizontal differentiation in competition, (ii) sustainable culture’s impact on cooperation, and (iii) competition and cooperation strategies.

The first stream of related literature focuses on horizontal differentiation or product design that meets the needs and preferences of different consumers to stand out in market competition. Although it is obvious that horizontal differentiation benefits a monopolistic firm by allowing it to attract more consumers [32,33], the case is more complicated under a competition scenario. Hydock and Wathieu [34] showed that consumers who focus on horizontal differentiation will prefer EDLP stores (infrequent discounters) compared to the Hi-Lo stores (frequent discounters). Blazy and Blum [35] found that horizontal differentiation has a substantial impact on both the sales and auction prices of auctioned artworks. Furthermore, Sánchez-Pérez et al. [36] show that the positive impact of horizontal differentiation on hotel prices is lower when competition is intense, and Liu et al. [37] and Liu et al. [38] considered a market in which two firms choose the endogenous horizontal product differentiation. Unlike the above literature, this paper shows that when two liquor firms have horizontal differentiation, a coopetition strategy is a practical method to support competing firms under certain conditions.

In the aspect of sustainability culture, the particularity of the liquor industry provides a unique scenario for the theory of horizontal culture differentiation. Taking Chinese Baijiu as an example, Maotai flavor liquor and Luzhou flavor liquor not only have different tastes but also have deep differences in brewing technology, historical inheritance, and regional culture [21]. Although Podstawski et al. [39] found that consumers’ choices of alcoholic products are highly dependent on cultural identity, the existing literature has not quantitatively analyzed the endogenous impact of cultural differences on corporate strategies. Therefore, this article innovatively embeds sustainable cultural differences into the Hotelling model, depicting consumers’ choice mechanisms through a two-dimensional preference space (function and culture attributes) and enriching the research on the traditional differentiation of the liquor industry.

The second stream of related literature is correlated to the literature about culture’s impact on cooperation. Liquor has been used to enhance cooperation through strengthening group culture [22]. Butler and Fehr [29] divided sustainable culture into preferences and beliefs, and they found that both preferences and beliefs play a prominent role in facilitating cooperation. Gunnthorsdottir et al. [30] examined efficiency-boosting cooperation and its underlying motivations in Iceland and the United States, and their results show that diverse cultures can attain comparable economic and societal outcomes through distinct sustainable cultural norms. In addition, cooperation can be categorized into individual and group levels. On the individual level, Nguyen and Kim [40] uncovered that a manager’s leading by example would reshape firm culture and finally promote the cooperation between employees in a company. On the group level, Spadaro et al. [31] indicate that impersonal cooperation between strangers allows societies to generate valuable public goods. The research in [41] presents an overview of the current research on cooperation within a cross-national context and found that sustainable cultural similarity plays a vital role in cooperation between groups. The above studies concentrate on whether culture has an impact on cooperation and how it works but ignore the degree of impact. Hence, this paper complements this stream of literature by investigating the degree of sustainable culture’s impact on cooperation.

The third stream of related literature investigates the strategies for balancing between competition and cooperation [42]. For instance, Hou et al. [43] analyzed how traditional ride-sharing platforms navigate between competitive and cooperative approaches when interacting with emerging platforms. Lai et al. [44] investigated how modular design affects a manufacturer’s recovery strategies across centralized, cooperative, and competitive models. Liu et al. [37] explored the dynamics of technological cooperation and competition between incumbent and entrant firms in the Information and Communications Technology (ICT) markets. Ouyang et al. [45] delved into the interplay between intragroup cooperation and competition, examining their impact on individual creativity. Additionally, some studies integrate both competition and cooperation into a unified framework. Farazi et al. [23], for instance, introduced the concept of a coopetition strategy, revealing an inverted U-shaped relationship between competition intensity and cooperation levels. While these studies primarily focus on the tradeoff between competition and cooperation—and, in some cases, their combination—they do not account for the influence of sustainable culture.

In summary, despite the above literature obtaining important results, it still has the following limitations: (i) Lack of cultural dynamism: Most studies treat culture as a static background, failing to model the process through which companies actively shape differentiation through cultural investment. (ii) Insufficient industry specificity: General models are inadequate for explaining the unique competitive landscape of the liquor industry, which combines ‘fixed processes’ with ‘culturally malleable’ aspects. (iii) Neglect of strategic endogeneity: Existing coopetition research often assumes exogenous strategies for firms, overlooking the two-way feedback between cultural differences and strategy selection. Therefore, using a game theoretical model, this work contributes to the extant literature in three aspects: characterizing the dynamics of sustainability, focusing on a specific industry, and examining the endogeneity of sustainable culture promotion strategies.

3. Model Description

Although the game theoretical model relies on certain assumptions and lacks direct empirical validation, it remains a powerful tool for capturing the strategic interactions between liquor firms, particularly in the presence of horizontal differentiation. Accordingly, a stylized game theoretical model is developed in this paper to examine the research problem.

Consider a model setting in which two competitive liquor firms, named firm 0 and firm 1, produce liquor products 0 and 1 with selling prices $p_0$ and $p_1$, respectively [46]. Due to the different brewing processes adopted by the two liquor firms, products 0 and 1 exhibit horizontal differences [47,48], and such differentiation also leads to differences in the liquor sustainable culture associated with each product (e.g., sauce-flavored liquor and its associated sauce sustainable culture and strong-flavored liquor and its strong-flavored sustainable culture). Without loss of generality, the production costs of both products are normalized to zero [49].

Consumers are not only affected by the horizontal differences in liquor products (e.g., different tastes) [50] but also influenced by the differentiated liquor sustainable cultures [51]. It is assumed that liquor product $i$ ($i=\mathrm{0,1}$) inherently provides each consumer with a positive basic utility $v_i>0$ [52], and its sustainable culture brings about an initial sustainable cultural utility ${ϵ}_i\ge 0$ [53]. To focus on the impact of liquor sustainable culture on firms’ strategic decisions, it is assumed that $v_0=v_1=v$. Meanwhile, without loss of generality, it is also assumed that the sustainable cultural effect of liquor product 1 is stronger than that of product 0 [54]. Thus, a stronger sustainable culture provides consumers with greater sustainable cultural utility, i.e., ${ϵ}_1\ge {ϵ}_0$. ${ϵ}_{\mathsf{\Delta }}={ϵ}_1-{ϵ}_0$ is used to characterize the initial disparity of sustainable culture between products 1 and 0.

Furthermore, considering the influence of liquor product $i$ and its associated sustainable culture on consumers, a two-dimensional ($1\times 1$) Hotelling model is adopted to capture consumers’ preferences for different liquor products and sustainable cultures [55,56,57]. Specifically, firm 0 is located at $\left(\mathrm{0,0}\right)$, while firm 1 is at $\left(\mathrm{1,1}\right)$. This spatial configuration mirrors real-world observations for liquor firms, such as Moutai and Wuliangye. Consumers are uniformly distributed within a $1\times 1$ square, with a total number of $N$, which is normalized to one. Each consumer’s preference is characterized by ($x,y$), where $x\in \left[\mathrm{0,1}\right]$ represents the consumer’s preference for products (e.g., a preference for strong-flavor sustainable culture or sauce-flavor sustainable culture), and $y\in \left[\mathrm{0,1}\right]$ indicates consumer’s preference for liquor sustainable cultures. If a consumer’s preference does not match the product type, there exists a negative matching utility $-t_{v}x$, where $t_v\ge 0$ characterizes the mismatch cost that the product purchased by the consumer does not match his/her preference and is also used to represent the degree of product differentiation [58]. Likewise, if consumer preferences mismatch liquor sustainable cultures, consumers will incur a negative utility $-t_{ϵ}y$, where $t_{ϵ}\ge 0$ is the mismatch cost between preference and liquor product sustainable culture [59,60]. A high (low) level of $t_{ϵ}$ indicates a large (small) degree of sustainable culture disparity. Note that since the sustainable culture promotion can be observed by consumers for free through different dissemination media such as television, media, and the internet, it is assumed that consumers obtain sustainable cultures of two liquor products without any additional costs, and the sustainable cultures between products 0 and 1 are incompatible. Namely, consumers who buy liquor product 0 cannot experience the sustainable culture from product 1 and vice versa.

In the liquor industry, a sustainability culture is one of the key factors influencing market competition. Liquor firms can strengthen their competitive advantage by cultivating and promoting a sustainable culture, thereby enhancing consumer appeal [61,62]. This study examines two strategies to foster sustainable culture within the liquor industry: the competitive promotion strategy, in which firms independently implement sustainability initiatives to differentiate themselves in the market, and the cooperative promotion strategy, which involves collaborative efforts among firms to collectively advance a common sustainability culture for mutual benefit. Additionally, empirical evidence suggests that the marginal utility gained from incremental advertising expenditure follows a diminishing returns pattern [63]. Based on this, it is assumed that for liquor firm $i$, the sustainable culture would add additional utility $a_i{e}_i$($\ge 0$) to consumers with costs $k_i{\left(e_i\right)}^2/2$ [64], where $a_i$ and $k_i$ respectively represent the utility conversion rate of a unique sustainable culture and the cost coefficient of promoting a unique sustainable culture. For simplicity, $a_i$ is normalized to 1.

As for the cooperative strategy of sustainable culture, firms 0 and 1 jointly promote a common sustainability culture based on the commonality of their products. For example, both sauce-flavored liquor and strong-flavored liquor belong to liquor, so firms can choose to enhance a universal sustainability culture as an entity instead of respectively cultivating their own unique sustainable culture [65]. Similarly, the costs of enhancing a common $e(>0)$ utility is $k{\left(e\right)}^2/2$, where $k$ represents the cost coefficient of promoting a common sustainability culture. Moreover, the promotion costs are shared by both firms in this case, and the cost-sharing proportion of promoting a common sustainability culture is $\lambda \in \left(\mathrm{0,1}\right)$ for firm 0 and $1-\lambda$ for firm 1. $\lambda =0$ represents that firm 0 affords all costs of promoting a common sustainability culture, while $\lambda =1$ represents that firm 0 affords no costs of promoting a common sustainability culture.

Moreover, for a given additional sustainability culture $e$ brought by the sustainability culture promotion, consumers’ utility values obtained by purchasing firms 0 and 1 are ${\gamma }_{0}e$ and ${\gamma }_{1}e$, respectively, where ${\gamma }_0\in \left[\mathrm{0,1}\right]$ and ${\gamma }_1\in \left[\mathrm{0,1}\right]$ are the conversion rates of a common sustainability culture. ${\gamma }_i=0$ represents that a common sustainability culture cannot be converted for the utility of consuming firm$i’$s product at all, while ${\gamma }_i=1$ represents that a common sustainability culture can be completely converted for the utility of consuming firm $i’$s product. This setting is consistent with the empirical findings in the case of Moutai and Wuliangye [12,20]. Because the initial sustainable culture utility of product 1 is assumed to be stronger than that of product 0 (i.e., ${ϵ}_1\ge {ϵ}_0$), following a similar spirit, the conversion rate of product 1 is assumed to be higher than that of product 0, i.e., ${\gamma }_1>{\gamma }_0$. Similarly, ${\gamma }_{∆}={\gamma }_1-{\gamma }_0$ represents the difference in the conversion rates of a common sustainability culture.

Additionally, it is assumed that consumers’ preference for sustainability culture is dominated by their preference for liquor products. In addition, to ensure the existence of interior solutions in the game model and to simplify the analysis, the following parameter restrictions are imposed:

$$k_0>k_0^{max }=\max \left\{\begin{array}{c}0,k_0^{\prime },{\displaystyle \frac{t_v+t_{ϵ}-\beta t_{ϵ}}{9t_v^2+9t_v{t}_{ϵ}}},{\displaystyle \frac{\left(1-\beta \right)k_1{t}_{ϵ}}{9k_1{t}_v^2-\left(1-\beta \right)t_{ϵ}-t_v\left(2-k_1\left(9t_{ϵ}-3{ϵ}_{\Delta }\right)\right)}},{\displaystyle \frac{2t_v^2+\left(1-\beta \right)t_v{t}_{ϵ}-\left(1-\beta \right)t_{ϵ}^2}{3t_v\left(t_v+t_{ϵ}\right)\left(3t_v-3t_{ϵ}+{ϵ}_{\Delta }\right)}},\\ {\displaystyle \frac{k_1(t_v+(1-\beta \left)t_{ϵ}\right)}{9k_1{t}_v^2+(-1+\beta )t_{ϵ}+t_v(-1+9k_1{t}_{ϵ})}},{\displaystyle \frac{2(t_v+(1-\beta \left)t_{ϵ}\right)}{9t_v^2-3(-1+\beta )t_{ϵ}{ϵ}_{\Delta }+3t_v(3t_{ϵ}+{ϵ}_{\Delta })}}\end{array}\right\}.$$

$$k_1>k_1^{max }=\max \left\{\begin{array}{c}0,{\displaystyle \frac{2\left(t_v+\left(1-\beta \right)t_{ϵ}\right)}{9t_v^2+9t_v{t}_{ϵ}}},{\displaystyle \frac{t_v+t_{ϵ}-\beta t_{ϵ}}{9t_v^2+9t_v{t}_{ϵ}}},{\displaystyle \frac{2t_v+t_{ϵ}-\beta t_{ϵ}}{9t_v^2+9t_v{t}_{ϵ}-3t_v{ϵ}_{\Delta }}},{\displaystyle \frac{2\left(t_v-\left(-1+\beta \right)t_{ϵ}\right)}{9t_v^2+t_v\left(9t_{ϵ}-3{ϵ}_{\Delta }\right)+3\left(-1+\beta \right)t_{ϵ}{ϵ}_{\Delta }}},\\ {\displaystyle \frac{t_v^3-(-2+\beta )t_v^2{t}_{ϵ}-(-1+\beta )t_v{t}_{ϵ}^2+\sqrt{2}\sqrt{t_v^2{(t_v+t_{ϵ})}^2{(t_v+t_{ϵ}-\beta t_{ϵ})}^2}}{9t_v^2{(t_v+t_{ϵ})}^2}}\end{array}\right\}.$$

$$k>k^{max}=\max \{0,{\displaystyle \frac{2\left(t_v+\left(1-\beta \right)t_{ϵ}\right){\gamma }_{\Delta }^2}{9t_v\left(t_v+t_{ϵ}\right)}},{\displaystyle \frac{2\left(t_v+\left(1-\beta \right)t_{ϵ}\right){\gamma }_{\Delta }^2}{3t_v\left(3t_v+3t_{ϵ}-{ϵ}_{\Delta }\right)}},{\displaystyle \frac{2(t_v-t_{ϵ})(t_v+(1-\beta \left)t_{ϵ}\right){\gamma }_{\Delta }^2}{3t_v(t_v+t_{ϵ})(3t_v-3t_{ϵ}+{ϵ}_{\Delta })}}\}.$$

$$t_v>t_v^{max }=\max \{0,{\displaystyle \frac{{ϵ}_{\Delta }}{3}}-t_{ϵ},t_{ϵ}-{\displaystyle \frac{{ϵ}_{\Delta }}{3}},{\displaystyle \frac{1}{6}}\left(-3t_{ϵ}+{ϵ}_{\Delta }+\sqrt{9t_{ϵ}^2+6\left(1-2\beta \right)t_{ϵ}{ϵ}_{\Delta }+{ϵ}_{\Delta }^2}\right),{\displaystyle \frac{1}{6}}(-3t_{ϵ}-{ϵ}_{\Delta }+\sqrt{9t_{ϵ}^2+6(-1+2\beta )t_{ϵ}{ϵ}_{\Delta }+{ϵ}_{\Delta }^2}\left)\right\}.$$

The main notations used in this paper are presented in

Table 1. List of notations.

Symbol	Description
$x$	Consumers’ preference for different liquor products, where $x\in \left[\mathrm{0,1}\right]$
$y$	Consumers’ preference for different liquor sustainability cultures, where $y\in \left[\mathrm{0,1}\right]$
$t_v$	The mismatch cost between the products purchased by consumers and their preferences.
$t_{ϵ}$	The mismatch cost between liquor sustainable cultures and consumer preferences.
$v_i$	The basic utility that a consumer obtained from liquor product $i$.
$\beta$	The correlation coefficient of liquor product and sustainability culture.
${ϵ}_i$	The initial sustainable cultural utility of consuming liquor product $i$.
${ϵ}_{\Delta }$	The initial disparity in sustainability cultures between the two firms.
$e_i/e$	The promotion level of a sustainability culture.
$k_i/k$	The cost coefficient of a sustainability culture promotion.
$p_i$	The selling price of liquor product $i$.
$D_i$	The demand of liquor product $i$.
$\lambda$	The cost-sharing proportion for a sustainability culture promotion.
${\pi }_i$	The firm $i$’s profit.
$\mathsf{\Pi }$	$\mathsf{\Pi }={\pi }_0+{\pi }_1$, the total profit of two firms.
${\gamma }_i$	The conversion rates of a common sustainability culture.
${\gamma }_{\Delta }$	The disparity in conversion rates of a common sustainability culture.
$U_i$	Consumer’s utility.

.

4. Model Analysis and Results

In this section, the equilibrium outcomes of the competitive promotion strategy are derived in Section 4.1, and the equilibrium outcomes of the cooperative promotion strategy are derived in Section 4.2.

4.1. The Competitive Promotion Strategy of a Sustainability Culture

This subsection analyzes the case where the competitive promotion strategy of a sustainability culture is adopted. In this circumstance, the decision sequence is depicted as follows. Stage 1: Firm $i$ chooses its promotion level of a sustainability culture $e_i$. Stage 2: Firm $i$ chooses its selling price $p_i$. Stage 3: Consumers decide to buy a product from firm 0 or firm 1. This game theoretical model is solved by backward induction. In this case, the decision sequence is presented in Figure 1.

First, given the firm $i$’s sustainability culture promotion level $e_i$ and selling price $p_i$, when a consumer chooses to buy product $i$, his/her utility is

$$U_i=\left\{\begin{array}{ll}v+{ϵ}_0+e_0-t_{v}x-t_{ϵ}y-p_0,& i=0\\ v+{ϵ}_1+e_1-t_v\left(1-x\right)-t_{ϵ}\left(1-y\right)-p_1,& i=1\end{array}\right.$$

(1)

Then, according to $U_0>(\le )U_1$, the demand function of firm $i$ is characterized as

$$D_i(e_i,p_i)=\left\{\begin{array}{c}\begin{array}{ll}\beta {\displaystyle \frac{e_0-e_1-p_0+p_1+t_v+t_{ϵ}-{ϵ}_{\Delta }}{2\left(t_v+t_{ϵ}\right)}}+\left(1-\beta \right){\int }_0^1{\int }_0^{x\left(y\right)}1dxdy,& i=0\\ 1-\beta {\displaystyle \frac{e_0-e_1-p_0+p_1+t_v+t_{ϵ}-{ϵ}_{\Delta }}{2\left(t_v+t_{ϵ}\right)}}-\left(1-\beta \right){\int }_0^1{\int }_0^{x\left(y\right)}1dxdy,& i=1\end{array}\end{array}\right.$$

(2)

where $x\left(y\right)={\displaystyle \frac{e_0-e_1-p_0+p_1+t_v+t_{ϵ}-2y{t}_{ϵ}-{ϵ}_{∆}}{2t_v}}\in \left[\mathrm{0,1}\right]$ represents the indifference point where consumers experience equivalent utility from purchasing products 0 and 1.

Finally, based on Equation (2), one can write the optimization problem for firm $i$ as follows:

$$\begin{array}{c}\underset{e_i}{\mathrm{m}\mathrm{a}\mathrm{x}}{\pi }_i=p_i\left(e_i\right)D_i\left(e_i,p_i\left(e_i\right)\right)-{\displaystyle \frac{1}{2}}{k}_i{\left(e_i\right)}^2\to \underset{p_i}{\mathrm{m}\mathrm{a}\mathrm{x}}{\pi }_i=p_i{D}_i\left(e_i,p_i\right)\end{array}$$

(3)

Because the objective functions in Equation (3) are concave in $p_i$ and $e_i$, by the first-order conditions, the equilibrium results are presented in Lemma 1. Note that the superscript “$\ast C$” is used to indicate the equilibrium outcomes in this case.

Lemma 1. 

Under the competitive promotion strategy of a sustainable culture, the equilibrium outcomes are

$$e_0^{\ast C}={\displaystyle \frac{t_v\left[2-k_1\left(9t_{ϵ}-3{ϵ}_{\Delta }\right)\right]+\left(1-\beta \right)t_{ϵ}\left(2+3k_1{ϵ}_{\Delta }\right)-9k_1{t}_v^2}{3k_1\left[t_v+\left(1-\beta \right)t_{ϵ}\right]-3k_0\left[9k_1{t}_v^2-\left(1-\beta \right)t_{ϵ}-t_v\left(1-9k_1{t}_{ϵ}\right)\right]}},$$

$$e_1^{\ast C}={\displaystyle \frac{\left(1-\beta \right)t_{ϵ}\left(2-3k_0{ϵ}_{\Delta }\right)+t_v\left[2-3k_0\left(3t_{ϵ}+{ϵ}_{\Delta }\right)\right]-9k_0{t}_v^2}{3k_1\left[t_v+\left(1-\beta \right)t_{ϵ}\right]-3k_0\left[9k_1{t}_v^2-\left(1-\beta \right)t_{ϵ}-t_v\left(1-9k_1{t}_{ϵ}\right)\right]}},$$

$$e_1^{\ast C}={\displaystyle \frac{\left(1-\beta \right)t_{ϵ}\left(2-3k_0{ϵ}_{\Delta }\right)+t_v\left[2-3k_0\left(3t_{ϵ}+{ϵ}_{\Delta }\right)\right]-9k_0{t}_v^2}{3k_1\left[t_v+\left(1-\beta \right)t_{ϵ}\right]-3k_0\left[9k_1{t}_v^2-\left(1-\beta \right)t_{ϵ}-t_v\left(1-9k_1{t}_{ϵ}\right)\right]}},$$

$$p_0^{\ast C}={\displaystyle \frac{k_0{t}_v\left(t_v+t_{ϵ}\right)\left\{9k_1{t}_v^2-t_v\left[2-k_1\left(9t_{ϵ}-3{ϵ}_{\Delta }\right)\right]-\left(1-\beta \right)t_{ϵ}\left(2+3k_1{ϵ}_{\Delta }\right)\right\}}{\left[t_v+\left(1-\beta \right)t_{ϵ}\right]\left\{k_0\left[9k_1{t}_v^2-\left(1-\beta \right)t_{ϵ}-t_v\left(1-9k_1{t}_{ϵ}\right)\right]-k_1\left(t_v+\left(1-\beta \right)t_{ϵ}\right)\right\}}},$$

$$p_1^{\ast C}={\displaystyle \frac{k_1{t}_v\left(t_v+t_{ϵ}\right)\left\{9k_0{t}_v^2-\left(1-\beta \right)t_{ϵ}\left(2-3k_0{ϵ}_{\Delta }\right)-t_v\left[2-3k_0\left(3t_{ϵ}+{ϵ}_{\Delta }\right)\right]\right\}}{\left[t_v+\left(1-\beta \right)t_{ϵ}\right]\left\{k_0\left[9k_1{t}_v^2-\left(1-\beta \right)t_{ϵ}-t_v\left(1-9k_1{t}_{ϵ}\right)\right]-k_1\left(t_v+\left(1-\beta \right)t_{ϵ}\right)\right\}}},$$

$${\pi }_0^{\ast C}={\displaystyle \frac{k_0\left[9k_0{t}_v^2-\left(1-\beta \right)t_{ϵ}-t_v\left(1-9k_0{t}_{ϵ}\right)\right]{\left\{9k_1{t}_v^2-t_v\left[2-k_1\left(9t_{ϵ}-3{ϵ}_{\Delta }\right)\right]-\left(1-\beta \right)t_{ϵ}\left(2+3k_1{ϵ}_{\Delta }\right)\right\}}^2}{18(t_v+(1-\beta \left)t_{ϵ}\right){\left\{k_1\left(t_v+\left(1-\beta \right)t_{ϵ}\right)-k_0\left[9k_1{t}_v^2-\left(1-\beta \right)t_{ϵ}-t_v\left(1-9k_1{t}_{ϵ}\right)\right]\right\}}^2}},$$

$${\pi }_1^{\ast C}={\displaystyle \frac{k_1\left[9k_1{t}_v^2-\left(1-\beta \right)t_{ϵ}-t_v\left(1-9k_1{t}_{ϵ}\right)\right]{\left\{9k_0{t}_v^2-\left(1-\beta \right)t_{ϵ}\left(2-3k_0{ϵ}_{\Delta }\right)-t_v\left[2-3k_0\left(3t_{ϵ}+{ϵ}_{\Delta }\right)\right]\right\}}^2}{18(t_v+(1-\beta \left)t_{ϵ}\right){\left\{k_1\left(t_v+\left(1-\beta \right)t_{ϵ}\right)-k_0\left[9k_1{t}_v^2-\left(1-\beta \right)t_{ϵ}-t_v\left(1-9k_1{t}_{ϵ}\right)\right]\right\}}^2}}.$$

4.2. The Cooperative Promotion Strategy of a Sustainability Culture

This subsection analyzes the case where the cooperative promotion strategy of a sustainability culture is adopted. In this circumstance, the decision sequence is depicted as follows. Stage 0: Firms 0 and 1 decide their cost-sharing proportion $\lambda \in \left(\mathrm{0,1}\right)$ for promoting a common sustainability culture. Stage 1: Firms 0 and 1 jointly determine the promotion level of a common sustainability culture $e$. Stage 2: Firm $i$ chooses its selling price $p_i$. Stage 3: Consumers decide to buy a product from firm 0 or firm 1. In this case, the decision sequence is presented in Figure 2.

In this case, for a given promotion level of a common sustainability culture $e$, if a consumer buys product $i$, his/her utility is depicted below as

$$U_i=\left\{\begin{array}{cc}v+{ϵ}_0+{\gamma }_{0}e-t_{v}x-t_{ϵ}y-p_0,& i=0\\ v+{ϵ}_1+{\gamma }_{1}e-t_v\left(1-x\right)-t_{ϵ}\left(1-y\right)-p_1,& i=1\end{array}\right.$$

(4)

In a similar manner, as per $U_0>\left(\le \right)U_1$, the demand function for firm $i$ is

$$D_i(e,p_i)=\left\{\begin{array}{cc}\beta {\displaystyle \frac{-p_0+p_1+t_v+t_{ϵ}-e{\gamma }_{\Delta }-{ϵ}_{\Delta }}{2(t_v+t_{ϵ})}}+\left(1-\beta \right){\int }_0^1{\int }_0^{x\left(y\right)}1dxdy,& i=0\\ 1-\beta {\displaystyle \frac{p_1-p_0+t_v+t_{ϵ}-e{\gamma }_{\Delta }-{ϵ}_{\Delta }}{2\left(t_v+t_{ϵ}\right)}}-\left(1-\beta \right){\int }_0^1{\int }_0^{x\left(y\right)}1dxdy,& i=1\end{array}\right.$$

(5)

where $x(y)={\displaystyle \frac{p_1-p_0+t_v+t_{ϵ}-2y{t}_{ϵ}+e{\gamma }_0-e{\gamma }_1+{ϵ}_0-{ϵ}_1}{2t_v}}\in \left[\mathrm{0,1}\right]$ is the indifference point where consumers experience equivalent utility from purchasing products 0 and 1.

Then, based on Equation (5), firm $i$ chooses a selling price $p_i$ to maximize its profit

$$\underset{p_i}{\max }{\pi }_i=p_i{D}_i(e,p_i)$$

(6)

Thus, according to the first-order conditions, one can derive firm $i$’s best price response to the level of sustainability culture promotion, i.e., $p_i\left(e\right)$. Furthermore, by substituting $p_i\left(e\right)$ into firm $i$’s respective profit function, firms 0 and 1 jointly choose a promotion level of a common sustainability culture $e$ to maximize their total profit:

$$\max \mathsf{\Pi }={\sum }_{i=\mathrm{0,1}}{\pi }_i\left(e,p_i\left(e\right)\right)-{\displaystyle \frac{1}{2}}k{e}^2$$

(7)

Because the objective function in Equation (7) is concave in $e$, by the first-order conditions, the equilibrium results are provided in Lemma 2. Note that the superscript “$\ast CO$” is used to indicate the equilibrium outcomes in this case.

Lemma 2. 

Under the cooperative promotion strategy of a sustainability culture, the equilibrium outcomes are

$$e^{\ast CO}={\displaystyle \frac{2(t_v+(1-\beta \left)t_{ϵ}\right){\gamma }_{\Delta }{ϵ}_{\Delta }}{9k{t}_v(t_v+t_{ϵ})-2(t_v+(1-\beta \left)t_{ϵ}\right){\gamma }_{\Delta }^2}},$$

$$p_0^{\ast CO}=t_v(t_v+t_{ϵ})({\displaystyle \frac{1}{t_v+(1-\beta )t_{ϵ}}}-{\displaystyle \frac{3k{ϵ}_{\Delta }}{9k{t}_v(t_v+t_{ϵ})-2(t_v+t_{ϵ}-\beta t_{ϵ}){\gamma }_{\Delta }^2}}),$$

$$p_1^{\ast CO}=t_v(t_v+t_{ϵ})({\displaystyle \frac{1}{t_v+(1-\beta )t_{ϵ}}}+{\displaystyle \frac{3k{ϵ}_{\Delta }}{9k{t}_v(t_v+t_{ϵ})-2(t_v+t_{ϵ}-\beta t_{ϵ}){\gamma }_{\Delta }^2}}),$$

$$D_0^{\ast CO}={\displaystyle \frac{1}{2}}-{\displaystyle \frac{3k(t_v+(1-\beta \left)t_{ϵ}\right){ϵ}_{\Delta }}{18k{t}_v(t_v+t_{ϵ})-4(t_v+t_{ϵ}-\beta t_{ϵ}){\gamma }_{\Delta }^2}},$$

$$D_1^{\ast CO}={\displaystyle \frac{1}{2}}+{\displaystyle \frac{3k(t_v+(1-\beta \left)t_{ϵ}\right){ϵ}_{\Delta }}{18k{t}_v(t_v+t_{ϵ})-4(t_v+t_{ϵ}-\beta t_{ϵ}){\gamma }_{\Delta }^2}},$$

$${\pi }_0^{\ast CO}={\displaystyle \frac{t_v(t_v+t_{ϵ}){\left\{2\left(t_v+\left(1-\beta \right)t_{ϵ}\right){\gamma }_{\Delta }^2-3k_c\left[3t_v^2+t_v\left(3t_{ϵ}-{ϵ}_{\Delta }\right)-\left(1-\beta \right)t_{ϵ}{ϵ}_{\Delta }\right]\right\}}^2}{2\left[t_v+\left(1-\beta \right)t_{ϵ}\right]{\left\{9k_c{t}_v\left(t_v+t_{ϵ}\right)-2\left[t_v+\left(1-\beta \right)t_{ϵ}\right]{\gamma }_{\Delta }^2\right\}}^2}}-{\displaystyle \frac{1}{2}}k\lambda {\left(e^{\ast CO}\right)}^2,$$

$${\pi }_0^{\ast CO}={\displaystyle \frac{t_v(t_v+t_{ϵ}){\left\{2\left(t_v+\left(1-\beta \right)t_{ϵ}\right){\gamma }_{\Delta }^2-3k_c\left[3t_v^2+t_v\left(3t_{ϵ}-{ϵ}_{\Delta }\right)-\left(1-\beta \right)t_{ϵ}{ϵ}_{\Delta }\right]\right\}}^2}{2\left[t_v+\left(1-\beta \right)t_{ϵ}\right]{\left\{9k_c{t}_v\left(t_v+t_{ϵ}\right)-2\left[t_v+\left(1-\beta \right)t_{ϵ}\right]{\gamma }_{\Delta }^2\right\}}^2}}-{\displaystyle \frac{1}{2}}k\lambda {\left(e^{\ast CO}\right)}^2,$$

$${\pi }_1^{\ast CO}={\displaystyle \frac{t_v(t_v+t_{ϵ}){\left(2\right(t_v+(1-\beta )t_{ϵ}){\gamma }_{\Delta }^2-3k_c(3t_v^2+(1-\beta )t_{ϵ}{ϵ}_{\Delta }+t_v(3t_{ϵ}+{ϵ}_{\Delta })\left)\right)}^2}{2\left[t_v+\left(1-\beta \right)t_{ϵ}\right]{\left\{9k_c{t}_v\left(t_v+t_{ϵ}\right)-2\left[t_v+\left(1-\beta \right)t_{ϵ}\right]{\gamma }_{\Delta }^2\right\}}^2}}-{\displaystyle \frac{1}{2}}k(1-\lambda ){\left(e^{\ast CO}\right)}^2.$$

Finally, based on the equilibrium operating profits presented in Lemma 2, the Nash bargaining method is adopted to determine the cost-sharing proportion between firm 0 and firm 1, which is depicted below:

$$\begin{array}{c}{\underset{\lambda \in \left[\mathrm{0,1}\right]}{\max }\left({\pi }_0^{\ast CO}-{\pi }_0^{\ast C}\right)}^{\theta }{\left({\pi }_1^{\ast CO}-{\pi }_1^{\ast C}\right)}^{1-\theta }\\ s.t. {\pi }_0^{\ast CO}\ge {\pi }_0^{\ast C}, {\pi }_1^{\ast CO}\ge {\pi }_1^{\ast C}\end{array}$$

(8)

where $\theta \in \left[\mathrm{0,1}\right]$ represents the relative bargaining power of firm 0, and $1-\theta$ indicates the relative bargaining power of firm 1. ${\pi }_0^{\ast C}$ and ${\pi }_1^{\ast C}$ define the disagreement point of the two participants (i.e., the equilibrium operating profits of firms 0 and 1 presented in Lemma 1). The constraints ${\pi }_0^{\ast CO}\ge {\pi }_0^{\ast C}$ and ${\pi }_1^{\ast CO}\ge {\pi }_1^{\ast C}$ indicate that firms 0 and 1 are willing to choose the cooperative promotion strategy of a sustainability culture only if their operating profits under the cooperative promotion strategy of a sustainability culture are not lower than their respective operating profits under the competitive promotion strategy of a sustainable culture. Otherwise, both firms do not choose the cooperative promotion strategy of a sustainable culture, leading to the failure of cooperation in promoting a common sustainability culture.

Define the following notations: ${\lambda }^{\#}=\theta +{\displaystyle \frac{\left(1-\theta \right)\left(p_0^{\ast CO}{D}_0^{\ast CO}-{\pi }_0^{\ast C}\right)-\theta \left(p_1^{\ast CO}{D}_1^{\ast CO}-{\pi }_1^{\ast C}\right)}{\frac{1}{2}k{\left(e^{\ast CO}\right)}^2}}$; $\overline{\theta }$ is the unique root of the function $\theta +{\displaystyle \frac{\left(1-\theta \right)\left(p_0^{\ast CO}{D}_0^{\ast CO}-{\pi }_0^{\ast C}\right)-\theta \left(p_1^{\ast CO}{D}_1^{\ast CO}-{\pi }_1^{\ast C}\right)}{\frac{1}{2}k{\left(e^{\ast CO}\right)}^2}}=0$, and $\underset{\_}{\theta }$ is the unique root of the function $\theta +{\displaystyle \frac{\left(1-\theta \right)\left(p_0^{\ast CO}{D}_0^{\ast CO}-{\pi }_0^{\ast C}\right)-\theta \left(p_1^{\ast CO}{D}_1^{\ast CO}-{\pi }_1^{\ast C}\right)}{\frac{1}{2}k{\left(e^{\ast CO}\right)}^2}}=1$.

Proposition 1. 

Under the cooperative promotion strategy of a sustainability culture, the equilibrium cost-sharing proportion is

$${\lambda }^{\ast }=\left\{\begin{array}{c}0, if \theta \ge \overline{\theta }\\ {\lambda }^{\#}, if \underset{\_}{\theta }<\theta <\overline{\theta }\\ 1, if \theta \le \underset{\_}{\theta }\end{array}\right.$$

Proposition 1 reveals that there exist two critical thresholds of relative bargaining power $\theta$ that determine the cost-sharing proportion for enhancing a common sustainability culture, which is also shown in Figure 3. More specifically, when the relative bargaining power of firm 0 is below the lower threshold ($\theta \le \underset{\_}{\theta }$), firm 0 will undertake all the costs of a common sustainability culture promotion, i.e., ${\lambda }^{\ast }=1$. In contrast, when the relative bargaining power of firm 0 is above the higher threshold ($\theta \ge \overline{\theta }$), firm 1 will bear all the costs of a common sustainability culture promotion, i.e., ${\lambda }^{\ast }=0$. When the relative bargaining power of firm 0 falls in between the two crucial thresholds ($\underset{\_}{\theta }<\theta <\overline{\theta }$), firms 0 and 1 will share the costs of a common sustainability culture promotion as per the cost-sharing proportions ${\lambda }^{\#}\in \left(\mathrm{0,1}\right)$ and $1-{\lambda }^{\#}$ correspondingly. Additionally, Proposition 1 implies a negative (positive) impact of the relative bargaining power of firm 0 on the cost-sharing proportions of firm 0 (firm 1). Moreover, the bigger the initial disparity of the sustainable culture, the smaller the cost-sharing proportions for firm 0.

Additionally, Proposition 1 also reveals a coopetition dynamic in the liquor firms’ sustainability promotion efforts. As the optimal cost-sharing proportion relies on the bargaining power ($\theta$) and cultural disparity (${\epsilon }_{\Delta }$), it aligns with the findings of Spadaro et al. [36] on cultural diversity’s cooperative benefits. Thus, the managers in the liquor industry can incentivize collaboration in promoting a common sustainability culture by appropriately affecting these crucial factors.

5. Sensitivity Analyses of $\mathsf{\beta },{\mathsf{ϵ}}_{\mathsf{\Delta }},{\mathbf{t}}_{\mathsf{ϵ}},\mathbf{a}\mathbf{n}\mathbf{d} {\mathsf{\gamma }}_{\mathsf{\Delta }}$

This section respectively conducts sensitivity analysis with respect to $\beta ,{ϵ}_{\Delta },t_{ϵ},$ and ${\gamma }_{\Delta }$. Note that the definition of ${ϵ}_{\Delta }^{\#}$ is provided in the proof of Proposition 2 in Appendix A.

Proposition 2. 

(i) Under the competitive promotion strategy of a sustainability culture,

$$\left\{\begin{array}{c}{\displaystyle \frac{\mathsf{\partial }{e}_0^{\ast C}}{\mathsf{\partial }\beta }}<0,{\displaystyle \frac{\mathsf{\partial }{D}_0^{\ast C}}{\mathsf{\partial }\beta }}<0,{\displaystyle \frac{\mathsf{\partial }{e}_1^{\ast C}}{\mathsf{\partial }\beta }}>0,{\displaystyle \frac{\mathsf{\partial }{D}_1^{\ast C}}{\mathsf{\partial }\beta }}>0, if {ϵ}_{\Delta }<{\displaystyle \frac{1}{3}}\left({\displaystyle \frac{1}{k_0}}-{\displaystyle \frac{1}{k_1}}\right) and k_0<k_1, \\ {\displaystyle \frac{\mathsf{\partial }{e}_0^{\ast C}}{\mathsf{\partial }\beta }}\ge 0,{\displaystyle \frac{\mathsf{\partial }{D}_0^{\ast C}}{\mathsf{\partial }\beta }}\ge 0,{\displaystyle \frac{\mathsf{\partial }{e}_1^{\ast C}}{\mathsf{\partial }\beta }}\le 0,{\displaystyle \frac{\mathsf{\partial }{D}_1^{\ast C}}{\mathsf{\partial }\beta }}\le 0, otherwise,\hfill \end{array}\right.\left\{\begin{array}{c}{\displaystyle \frac{\mathsf{\partial }{p}_1^{\ast C}}{\mathsf{\partial }\beta }}>0, if {ϵ}_{\Delta }<{ϵ}_{\Delta }^{\#},\\ {\displaystyle \frac{\mathsf{\partial }{p}_1^{\ast C}}{\mathsf{\partial }\beta }}\le 0, otherwise,\end{array}\right.\mathrm{and}{\displaystyle \frac{\mathsf{\partial }{p}_0^{\ast C}}{\mathsf{\partial }\beta }}>0.$$

(ii) Under the cooperative promotion strategy of a sustainability culture,

$$\left\{\begin{array}{c}{\displaystyle \frac{\mathsf{\partial }{p}_1^{\ast CO}}{\mathsf{\partial }\beta }}>0, if {ϵ}_{\Delta }<{\displaystyle \frac{{\left(9k{t}_v\left(t_v+t_{ϵ}\right)-2\left(t_v+\left(1-\beta \right)t_{ϵ}\right){\gamma }_{\Delta }^2\right)}^2}{6k{\left(t_v+\left(1-\beta \right)t_{ϵ}\right)}^2{\gamma }_{\Delta }^2}},\\ {\displaystyle \frac{\mathsf{\partial }{p}_1^{\ast CO}}{\mathsf{\partial }\beta }}\le 0, otherwise.\hfill \end{array}.\right.{\displaystyle \frac{\mathsf{\partial }{e}^{\ast CO}}{\mathsf{\partial }\beta }}<0,{\displaystyle \frac{\mathsf{\partial }{p}_0^{\ast CO}}{\mathsf{\partial }\beta }}>0,{\displaystyle \frac{\mathsf{\partial }{D}_0^{\ast CO}}{\mathsf{\partial }\beta }}>0,\mathrm{and}{\displaystyle \frac{\mathsf{\partial }{D}_1^{\ast CO}}{\mathsf{\partial }\beta }}<0.$$

Proposition 2 shows the impact of the correlation coefficient of a sustainability culture and product ($\beta$) on the equilibrium level of promoting a sustainability culture, selling prices, and demands for the two firms. When both firms adopt the competitive promotion strategy of a sustainability culture, the correlation coefficient consistently exerts a positive effect on the price of firm 0. However, the correlation coefficient of a sustainability culture and product affects firm 1’s price differently: When the initial disparity in sustainability cultures between the two firms is small, the correlation coefficient positively influences firm 1’s price; otherwise, it exerts a negative effect. Similarly, when the initial disparity of sustainability cultures between the two firms is small and the cost coefficient of firm 0 is less than that of firm 1, the impact of the correlation coefficient of a sustainability culture and product on the optimal promotion level of a sustainability culture and demand is negative for firm 0 but is positive for firm 1. Nevertheless, when the two conditions cannot be met simultaneously, $\beta$’s impacts on these equilibrium outcomes will reverse.

When the two firms adopt the cooperative promotion strategy of a sustainability culture, the correlation coefficient of a sustainability culture and product ($\beta$) always has a positive influence on the selling price and demand of firm 0 but a negative impact on the optimal promotion level of a common sustainability culture and the demand of firm 1. As for the selling price of firm 1, the impact of the correlation coefficient of a sustainability culture and product ($\beta$) is mixed depending on the initial disparity of the sustainability cultures between the two firms. Specifically, when the initial disparity of sustainability cultures between the two firms is small enough, the correlation coefficient of a sustainability culture and product positively affects the selling price of firm 1 but negatively affects it otherwise.

Finally, Proposition 2 reveals an important managerial insight: When a liquor firm with a weak sustainability culture and a liquor firm with a strong sustainability culture compete in promoting their own sustainability culture, the initial disparity in sustainability cultures between the two firms (i.e., ${ϵ}_{\Delta }$) and the relative cost advantage in promoting sustainability culture are two critical factors that determine the impact of the correlation coefficient of a sustainability culture and product ($\beta$) on the promotion level of a sustainability culture, as shown in

Table 2. The impact of $\beta$on the promotion level of a sustainability culture $e_i^{\ast C}$.

		$${\mathit{k}}_{\mathsf{\Delta }}$$
		Positive	Non-Positive
εΔ	Small	−(+)	+(−)
	Big	+(−)	+(−)

Note: $k_{\mathsf{\Delta }}=k_1-k_0$; “$+$” represents a positive impact of $\beta$ on the promotion level of a sustainability culture $e_0^{\ast C}$, while “$-$” represents a negative one. Moreover, for the promotion level of a sustainability culture $e_1^{\ast C}$, β’s impact is shown in the brackets.

. Specifically, for a liquor firm with a weak sustainability culture, if the initial disparity in sustainability cultures between the two firms is small and it has a cost advantage relative to the liquor firm with a strong sustainability culture ($k_{\mathsf{\Delta }}>0$), its promotion level of a sustainability culture should be reduced as the correlation coefficient of a sustainability culture, and its products becomes more intense. However, in this case, for the liquor firm with a strong sustainability culture, its optimal promotion level of a sustainability culture should be raised.

Proposition 3. 

(i) Under the competitive promotion strategy of a sustainability culture,${\displaystyle \frac{\mathsf{\partial }{e}_0^{\ast C}}{\mathsf{\partial }{ϵ}_{\Delta }}}<0,{\displaystyle \frac{\mathsf{\partial }{e}_1^{\ast C}}{\mathsf{\partial }{ϵ}_{\Delta }}}>0,{\displaystyle \frac{\mathsf{\partial }{p}_0^{\ast C}}{\mathsf{\partial }{ϵ}_{\Delta }}}<0$

,${\displaystyle \frac{\mathsf{\partial }{p}_1^{\ast C}}{\mathsf{\partial }{ϵ}_{\Delta }}}>0$,${\displaystyle \frac{\mathsf{\partial }{D}_0^{\ast C}}{\mathsf{\partial }{ϵ}_{\Delta }}}<0$, and${\displaystyle \frac{\mathsf{\partial }{D}_1^{\ast C}}{\mathsf{\partial }{ϵ}_{\Delta }}}>0$;

(ii) Under the cooperative promotion strategy of a sustainability culture,${\displaystyle \frac{\mathsf{\partial }{e}^{\ast CO}}{\mathsf{\partial }{ϵ}_{\Delta }}}>0,{\displaystyle \frac{\mathsf{\partial }{p}_0^{\ast CO}}{\mathsf{\partial }{ϵ}_{\Delta }}}<0,{\displaystyle \frac{\mathsf{\partial }{p}_1^{\ast CO}}{\mathsf{\partial }{ϵ}_{\Delta }}}>0,{\displaystyle \frac{\mathsf{\partial }{D}_0^{\ast CO}}{\mathsf{\partial }{ϵ}_{\Delta }}}<0$, and${\displaystyle \frac{\mathsf{\partial }{D}_1^{\ast CO}}{\mathsf{\partial }{ϵ}_{\Delta }}}>0$.

Proposition 3 demonstrates the impact of the initial disparity of sustainability cultures between the two firms (${ϵ}_{\Delta }$) on the optimal promoting level of a sustainability culture, selling prices, demands, and operating profits for the two firms. Specifically, in the case of the competitive promotion strategy of a sustainability culture, increasing the initial disparity of sustainability cultures between the two firms is more likely to hurt firm 0 but benefit firm 1. The reason is that as the gap in the initial disparity of sustainability cultures for the two firms widens, firm 0 (1) will decrease (increase) the optimal promotion level of a sustainability culture. As a result, when consumers buy product 0 (1), the utility that consumers obtain from a sustainability culture promotion will decrease (increase), leading the demand for product 0 (1) to decrease (increase). In this circumstance, to attract consumers to buy product 0, firm 0 has to reduce its selling price. Nevertheless, the effect of price reduction (i.e., incremental demand due to reduced price) cannot offset the decrease in demand stemming from a lower optimal promotion level of a sustainability culture. Consequently, the demand for firm 0 ultimately decreases. By contrast, a higher optimal promotion level of a sustainability culture for firm 1 results in a higher demand for firm 1, which allows firm 1 to raise its selling price. Even though the rising selling price of firm 1 will decrease its demand, the incremental demand thanks to a higher optimal promotion level of a sustainability culture is dominant. Moreover, even when the two firms adopt the cooperative promotion strategy of a common sustainability culture, the above finding remains true in the terms of the selling price and demand for them. However, under this circumstance, the optimal promotion level of a common sustainability culture will become higher as the initial disparity of sustainability cultures between the two firms grows.

To summarize, Proposition 3 shows that a greater initial disparity in sustainability cultures benefits firm 1 but harms firm 0 by shifting optimal promotion levels, demands, and prices asymmetrically. This effect holds under both competitive and cooperative promotion strategies, although the cooperative case leads to a higher joint promotion level as the disparity in sustainability cultures grows. In addition, if the initial disparity in sustainability cultures is interpreted as a proxy for firm size, Proposition 3 suggests that a larger liquor firm is better positioned to promote its sustainability culture.

Proposition 4. 

(i) Under the competitive promotion strategy of a sustainability culture,

$\left\{\begin{array}{c}{\displaystyle \frac{\mathsf{\partial }{e}_0^{\ast C}}{\mathsf{\partial }{t}_{ϵ}}}<0,{\displaystyle \frac{\mathsf{\partial }{D}_0^{\ast C}}{\mathsf{\partial }{t}_{ϵ}}}<0,{\displaystyle \frac{\mathsf{\partial }{e}_1^{\ast C}}{\mathsf{\partial }{t}_{ϵ}}}>0,{\displaystyle \frac{\mathsf{\partial }{D}_1^{\ast C}}{\mathsf{\partial }{t}_{ϵ}}}>0, if {ϵ}_{\Delta }<{\displaystyle \frac{1}{3}}\left({\displaystyle \frac{1}{k_0}}-{\displaystyle \frac{1}{k_1}}\right) and k_0<k_1, \\ {\displaystyle \frac{\mathsf{\partial }{e}_0^{\ast C}}{\mathsf{\partial }{t}_{ϵ}}}\ge 0,{\displaystyle \frac{\mathsf{\partial }{D}_0^{\ast C}}{\mathsf{\partial }{t}_{ϵ}}}\ge 0,{\displaystyle \frac{\mathsf{\partial }{e}_1^{\ast C}}{\mathsf{\partial }{t}_{ϵ}}}\le 0,{\displaystyle \frac{\mathsf{\partial }{D}_1^{\ast C}}{\mathsf{\partial }{t}_{ϵ}}}\le 0, otherwise,\hfill \end{array}\right.\left\{\begin{array}{c}{\displaystyle \frac{\mathsf{\partial }{p}_1^{\ast C}}{\mathsf{\partial }{t}_{ϵ}}}>0, if {ϵ}_{\Delta }<{ϵ}_{\Delta }^{\#},\\ {\displaystyle \frac{\mathsf{\partial }{p}_1^{\ast C}}{\mathsf{\partial }{t}_{ϵ}}}\le 0, otherwise,\end{array}\right.$and${\displaystyle \frac{\mathsf{\partial }{p}_0^{\ast C}}{\mathsf{\partial }{t}_{ϵ}}}>0$.

(ii) Under the cooperative promotion strategy of a sustainability culture,${\displaystyle \frac{\mathsf{\partial }{e}^{\ast CO}}{\mathsf{\partial }{t}_{ϵ}}}<0,{\displaystyle \frac{\mathsf{\partial }{p}_0^{\ast CO}}{\mathsf{\partial }{t}_{ϵ}}}>0,{\displaystyle \frac{\mathsf{\partial }{p}_1^{\ast CO}}{\mathsf{\partial }{t}_{ϵ}}}>0,{\displaystyle \frac{\mathsf{\partial }{D}_0^{\ast CO}}{\mathsf{\partial }{t}_{ϵ}}}>0, and {\displaystyle \frac{\mathsf{\partial }{D}_1^{\ast CO}}{\mathsf{\partial }{t}_{ϵ}}}<0$.

Proposition 4 shows the impact of the unfit costs between sustainability cultures of products and consumers’ sustainability culture preference $\left(t_{ϵ}\right)$ on the optimal promotion level of the sustainability culture, prices, and demands for the two firms. When the two liquor firms adopt the competitive promotion strategy of a sustainability culture, the unfit costs between sustainability cultures of products and consumers’ sustainability culture preference always have a positive impact on the selling price of firm 0. However, the impact of the unfit costs between sustainability cultures of products and consumers’ sustainability culture preference on the selling price of firm 1 is mixed: When the initial disparity of the sustainability cultures between the two firms is small enough, the unfit costs between sustainability cultures of products and consumers’ sustainability culture preference positively affect the selling price of firm 1 but negatively affect it otherwise. Similarly, when the initial disparity of sustainability cultures between the two firms is small and the cost coefficient of firm 0 is less than that of firm 1, the impacts of the unfit costs between sustainability cultures of products and consumers’ sustainability culture preference on the optimal promotion level of a sustainability culture and demand are negative for firm 0 but are positive for firm 1. Nonetheless, the situation will reverse when the two conditions cannot hold simultaneously.

When the two liquor firms adopt the cooperative promotion strategy of a sustainability culture, the unfit costs between sustainability cultures of products and consumers’ sustainability culture preference always have positive impacts on firm 0’s selling price and demand and firm 1’s selling price but a negative impact on the optimal promotion level of a sustainability culture and firm 1’s demand.

The finding of Proposition 4 complements the extant literature. Unlike previous research focusing solely on functional differentiation (Sánchez-Pérez et al. [31]), Proposition 4 demonstrates how the unfit costs between sustainability cultures of products and consumers’ sustainability culture preference interact with cultural factors to create asymmetric impacts on liquor firms with different levels of sustainability culture. Moreover, this finding enriches conventional pricing strategy research (Hydock and Wathieu [29]) by showing the important role played by cultural mismatch costs’ influence promotion strategies in affecting sustainability culture promotion.

Proposition 5. 

Under the cooperative promotion strategy of a sustainability culture,${\displaystyle \frac{\mathsf{\partial }{e}^{\ast CO}}{\mathsf{\partial }{\gamma }_{\Delta }}}>0,{\displaystyle \frac{\mathsf{\partial }{p}_0^{\ast CO}}{\mathsf{\partial }{\gamma }_{\Delta }}}<0,{\displaystyle \frac{\mathsf{\partial }{p}_1^{\ast CO}}{\mathsf{\partial }{\gamma }_{\Delta }}}>0,{\displaystyle \frac{\mathsf{\partial }{D}_0^{\ast CO}}{\mathsf{\partial }{\gamma }_{\Delta }}}<0, and {\displaystyle \frac{\mathsf{\partial }{D}_1^{\ast CO}}{\mathsf{\partial }{\gamma }_{\Delta }}}>0$.

Proposition 5 reveals the impact of the disparity in conversion rates of a common sustainability culture on the optimal promotion level of a common sustainability culture, prices, and demands for the two firms. Specifically, widening the disparity in the conversion rates of a common sustainability culture helps to raise the optimal promotion level of a common sustainability culture and firm 1’s selling price and demand but decreases firm 0’s selling price and demand. This is because a higher conversion rate of a common sustainability culture represents that firm 1 could more efficiently take advantage of the sustainability culture. As a result, broadening the disparity in conversion rates of a common sustainability culture is beneficial to firm 1 but harmful to firm 0. This finding implies that although a firm with a weak sustainability culture collaborating with a firm with a strong sustainability culture to promote a common sustainability culture may contribute to higher profitability for them, a larger gap in conversion rates of a common sustainability culture keeps them in a competitive status when sharing the corresponding incremental profit. Additionally, Proposition 5 offers a novel perspective by examining the role of asymmetric cultural conversion capabilities in sustainability strategies. Departing from prior research on conversion rates (e.g., Yoo et al. [49]), Proposition 5 demonstrates that a disparity in conversion capability may lead to uneven benefit distribution within alliances, with critical thresholds potentially undermining cooperative stability.

6. Numerical Study

6.1. The Impact of $\beta ,{ϵ}_{\Delta },t_{ϵ},$ and ${\gamma }_{\Delta }$ on Operating Profits

(1)

The case of adopting the competitive promotion strategy of a sustainability culture.

This subsection graphically displays the correlation coefficient of a sustainability culture and product $\beta$, the initial disparity in sustainability cultures between the two firms ${ϵ}_{\Delta }$, and the unfit costs between sustainability cultures of products and consumers’ sustainability culture preference $t_{ϵ}$ in Figure 4, Figure 5 and Figure 6.

To explore how the operating profits of the two firms are affected by the correlation coefficient of a sustainability culture and product ($\beta$) and the unfit costs between sustainability cultures of products and consumers’ sustainability culture preference $t_{ϵ}$, the parameters are fixed as follows: $t_v=1000,{ϵ}_{\Delta }=k_1=k_0=100$, $\beta \in \left(\mathrm{0,1}\right),$ and$t_{ϵ}\in \left(\mathrm{0,1}\right).$ As shown in Figure 4a,b, for both firms 0 and 1, as both the correlation coefficient of a sustainability culture and product ($\beta$) and the unfit costs between sustainability cultures of products and consumers’ sustainability culture preference $t_{ϵ}$ increase, the operating profits of the two firms are likely to become larger. Intuitively, increasing $\beta$ and $t_{ϵ}$ help to raise the selling price and demand for firm 0, and thus, the profit of firm 0 increases accordingly. As for the profit of firm 1, although increasing $\beta$ and $t_{ϵ}$ lead both its selling price and demand to decrease, it also results in a lower promotion level of a sustainability culture. Moreover, since the promotion level of the sustainability culture is reduced, the costs of promoting the sustainability culture drop correspondingly. This cost-saving effect may become so significant that the profitability of firm 1 rises instead of being dragged down by decreasing revenue in this circumstance. Additionally, because $t_{ϵ}$ can be also viewed as the disparity between the two firms’ sustainability cultures, this finding reveals that, apart from differentiation in products, differentiating sustainability culture can also bolster profitability of firms.

Figure 5a,b reveal how the operating profits of the two firms are affected by the correlation coefficient of a sustainability culture and product $\beta$ and the initial disparity in sustainability cultures between the two firms ${ϵ}_{\Delta }$. In this case, the parameters are fixed as follows: $t_v=1000,t_{ϵ}=0.5,k_1=k_0=1$00, $\beta \in \left(\mathrm{0,1}\right),$ and${ϵ}_{\Delta }\in \left(0, 200\right).$ As shown in Figure 4a,b, for the correlation coefficient of the sustainability culture and product $\beta \in \left(\mathrm{0,1}\right);$ as the initial disparity in sustainability cultures between the two firms ${ϵ}_{\Delta }$ rises, it will hurt the profitability of firm 0 but benefit the profitability of firm 1. This finding is consistent with Proposition 3. Furthermore, although Proposition 2 suggests that increasing the correlation coefficient ($\beta$) between the sustainability culture and product may enhance the profitability of firm 0 under certain conditions, this positive effect is dominated by the negative effect of enlarging the initial disparity in sustainability cultures between the two firms. Therefore, the key factor determining the difference in operating profits between a firm with a weak sustainability culture (firm 0) and a firm with a strong sustainability culture (firm 1) is the initial disparity in their sustainability cultures.

Figure 6a,b illustrate how the operating profits of the two firms are affected by the unfit costs between sustainability cultures of products and consumers’ sustainability culture preference $t_{ϵ}$ and initial disparity in sustainability cultures between the two firms ${ϵ}_{\Delta }$. In this case, the parameters are fixed as follows: $t_v=1000,\beta =0.5,k_1=k_0=100$, $t_{ϵ}\in \left(\mathrm{0,1}\right),$ and${ϵ}_{\Delta }\in \left(0, 200\right).$ Figure 6a,b, show the unfit costs between sustainability cultures of products and consumers’ sustainability culture preference $t_{ϵ}\in \left(\mathrm{0,1}\right)$: when the initial disparity in sustainability cultures between the two firms ${ϵ}_{\Delta }$ becomes bigger, the changes in the two liquor firms’ operating profits are similar to the case of Figure 5a,b. Again, this observation represents that, for a firm with a weak sustainability culture and a firm with a strong sustainability culture, their profitability is mainly determined by the degree of difference in sustainability cultures between them.

In a summary, when adopting the competitive promotion strategy of a sustainability culture, increasing the correlation between sustainability cultures and products and the unfit costs between sustainability cultures of products and consumers’ sustainability culture preference raises profits for both liquor firms. However, increasing the initial disparity in sustainability cultures benefits firm 1 but harms firm 0.

(2)

The case of adopting the cooperative promotion strategy of a sustainability culture

In the case of adopting the cooperative promotion strategy of a sustainability culture, one can also observe the following graphic display of the correlation coefficient of a sustainability culture and product $\beta$, the initial disparity in sustainability cultures between the two firms ${ϵ}_{\Delta }$, the unfit costs between sustainability cultures of products and consumers’ sustainability culture preference $t_{ϵ}$, and the disparity in conversion rates of a common sustainability culture ${\gamma }_{\Delta }$ in Figure 7, Figure 8, Figure 9, Figure 10, Figure 11 and Figure 12. To clearly show the impacts of these parameters, it is assumed that the two firms equally split the costs of promoting a common sustainability culture, i.e., $\lambda =1/2$.

Figure 7a,b display how the operating profits of the two firms are affected by the correlation coefficient of the sustainability culture and product $\beta$ and unfit costs between sustainability cultures of products and consumers’ sustainability culture preference $t_{ϵ}$. In this case, the parameters are fixed as follows: $t_v=1000,k=1,{\gamma }_{\Delta }=0.2,{ϵ}_{\Delta }=k_1=k_0=100$, $\beta \in \left(\mathrm{0,1}\right),$ and $t_{ϵ}\in \left(\mathrm{0,1}\right).$ In general, the profitability of the two firms is more likely to be improved when the correlation coefficient of the sustainability culture and product $\beta$ and unfit costs between sustainability cultures of products and consumers’ sustainability culture preference $t_{ϵ}$ increase. Like the case of Figure 4, this is because, on the one hand, the differentiation in sustainability culture benefits the two firms. On the other hand, an increase in the correlation coefficient of the sustainability culture and product might augment the operating profit of firm 0 by both increasing revenue and decreasing the costs of promoting a sustainability culture and augment the operating profit of firm 1 by decreasing costs of promoting a sustainability culture.

As for Figure 8a,b, the parameters are fixed as follows: ${ t}_v=1000,t_{ϵ}=0.5,{\gamma }_{\Delta }=0.2,k=1,k_0=k_1=100$, $\beta \in \left(\mathrm{0,1}\right),$ and ${ϵ}_{\Delta }\in \left(0, 200\right).$ In this case, for the correlation coefficient of the sustainability culture and product $\beta \in \left(\mathrm{0,1}\right),$as the initial disparity in sustainability cultures between the two firms ${ϵ}_{\Delta }$ widens, the operating profit of firm 0 decreases, while the operating profit of firm 1 increases. This result is in line with Figure 5. This also represents that even in the case of the cooperative promotion strategy of a sustainability culture, the initial disparity in sustainability cultures between the two firms still decides their status in the market. Furthermore, this observation remains true in Figure 9a,b, where the parameters are fixed at $t_v=1000, \beta =0.5,{\gamma }_{\Delta }=0.2,k=1,k_0=k_1=100$, $t_{ϵ}\in \left(\mathrm{0,1}\right),$ and ${ϵ}_{\Delta }\in \left(0, 200\right).$ However, this trend partially diminishes when considering how the operating profits of the two liquor firms are affeced by the disparity in conversion rates of a common sustainability culture ${\gamma }_{\Delta }$ and the initial disparity in sustainability cultures between the two firms ${ϵ}_{\Delta }$, as shown in Figure 10a,b, where the parameters are fixed at $t_v=1000,t_{ϵ}=\beta =0.5,k=1,k_0=k_1=100$, ${\gamma }_{\Delta }\in \left(\mathrm{0,1}\right),$ and${ϵ}_{\Delta }\in \left(0, 200\right).$ In this case, although a smaller ${ϵ}_{\Delta }$ is good for the profitability of firm 0, a bigger ${ϵ}_{\Delta }$ does not mean higher profitability for firm 1, which is different from the case of Figure 9b. This is because the disparity in conversion rates of a common sustainability culture ${\gamma }_{\Delta }$ replaces the initial disparity in sustainability cultures between the two firms ${ϵ}_{\Delta }$ as the crucial factor affecting the profitability of the firm 1.

Interestingly, this kind of reverse phenomenon is separately observed in Figure 11a,b and Figure 12a,b. Specifically, Figure 11a,b show how the operating profits of the two firms are affected by the correlation coefficient of the sustainability culture and product $\beta$ and the disparity in conversion rates of a common sustainability culture ${\gamma }_{\Delta }$. In this case, the parameters are fixed at $t_v=1000,t_{ϵ}=0.5,k=1,{ϵ}_{\Delta }=k_0=k_1=100,$ $\beta \in \left(\mathrm{0,1}\right),$ and ${\gamma }_{\Delta }\in \left(\mathrm{0,1}\right).$ Under this circumstance, relative to the disparity in conversion rates of a common sustainability culture ${\gamma }_{\Delta }$, the correlation coefficient of the sustainability culture and product $\beta$ plays a more important role in affecting the operating profits of the two firms. Likewise, we can examine what takes place when considering how the operating profits of the two firms are affected by the unfit costs between sustainability cultures of products and consumers’ sustainability culture preference $t_{ϵ}$ and the disparity in conversion rates of a common sustainability culture ${\gamma }_{\Delta }$ in Figure 12a,b, where the parameters are fixed at $t_v=1000,\beta =0.5,k=1,{ϵ}_{\Delta }=k_0=k_1=100,t_{ϵ}\in \left(\mathrm{0,1}\right),$ and ${\gamma }_{\Delta }\in \left(\mathrm{0,1}\right).$Relative to the disparity in conversion rates of a common sustainability culture ${\gamma }_{\Delta }$, the unfit costs between sustainability cultures of products and consumers’ sustainability culture preference $t_{ϵ}$ is more essential to increase the operating profits of the two firms.

Overall, the cooperative strategy shows that while initial sustainability culture disparity plays a key role, factors like the correlation between sustainability culture and products and conversion rate disparities also significantly impact the liquor firms’ profitability.

6.2. The Impact of $\beta ,t_{ϵ},and{\gamma }_{\Delta }$ on Cost-Sharing Proportion

In this subsection, a contour line is used to show how the correlation coefficient of a sustainability culture and product $\beta$, unfit costs between sustainability cultures of products and consumers’ sustainability culture preference $t_{ϵ}$, and disparity in conversion rates of a common sustainability culture ${\gamma }_{\Delta }$ affect the cost-sharing proportion for promoting a common sustainability culture. Specifically, the following parameters setup is used: Case(1) $t_v=1000,{\gamma }_{\Delta }=0.2,{ϵ}_{\Delta }=k_1=k_0=100,t_{ϵ}=0.5, k=1;$ Case(2) $t_v=1000,{\gamma }_{\Delta }=0.2,{ϵ}_{\Delta }=k_1=k_0=100,\beta =0.5, k=1;$ Case(3) $t_v=1000, {ϵ}_{\Delta }=k_1=k_0=100, t_{ϵ}=\beta =0.5, k=1$ in Figure 11a, b, and c, respectively.

Figure 13a–c display the impacts of the correlation coefficient of a sustainability culture and product $\beta$, unfit costs between sustainability cultures of products and consumers’ sustainability culture preference $t_{ϵ}$, and disparity in conversion rates of a common sustainability culture ${\gamma }_{\Delta }$ on the on cost-sharing proportion for promoting a common sustainability culture. As shown in Figure 13a,b, for a given relative bargaining power $\theta$, the cost-sharing proportion for promoting a common sustainability culture increases the correlation coefficient of a sustainability culture and product $\beta$ and unfit costs between sustainability cultures of products and consumers’ sustainability culture preference $t_{ϵ}$. This finding implies that compared to a firm with a strong sustainability culture, a firm with a weak sustainability culture undertakes more costs of promoting a common sustainability culture when raising the correlation coefficient of a sustainability culture and product $\beta$ and/or when there are unfit costs between sustainability cultures of products and consumers’ sustainability culture preference $t_{ϵ}$. Nevertheless, Figure 13c graphically shows that enlarging the disparity in conversion rates of a common sustainability culture ${\gamma }_{\Delta }$ has an opposite effect: A firm with a weak sustainability culture will bear less costs for promoting a common sustainability culture relative to a firm with a strong sustainability culture. Intuitively, a higher sustainability culture conversion rate ${\gamma }_{\Delta }$ makes firm 0 suffer but benefits firm 1. Thus, the beneficiary (firm 1) should undertake more costs for promoting a common sustainability culture.

7. Conclusions

7.1. Main Results

In response to the increasing concern for sustainability in the liquor industry, liquor firms have begun to embed a sustainability culture into their product attributes. To realize this new attempt, liquor firms can adopt a competitive or cooperative promotion strategy of a sustainability culture. In this research, a game theoretical model has been built to characterize the two strategies adopted by liquor firms. By analyzing the equilibrium, the following main results are obtained.

First, only if the initial disparity in sustainability cultures between the two firms is in a mediate range, liquor firms should adopt a cooperative promotion strategy of a sustainability culture. Second, the impact of the correlation coefficient of a sustainability culture and liquor product on the optimal promotion level of a sustainability culture is negative in the case of adopting the cooperative promotion strategy but non-monotonic when adopting the competitive promotion strategy of a sustainability culture. Third, when the competitive promotion strategy of a sustainability culture is adopted, the initial disparity in sustainability cultures between the two firms negatively affects the optimal promotion level of a sustainability culture for the liquor firm with a weak sustainability culture but positively affects the optimal promotion level of a sustainability culture for the liquor firm with a strong sustainability culture; when the cooperative promotion strategy of a sustainability culture is adopted, the initial disparity in sustainability cultures between the two firms always positively affects the optimal promotion level of a common sustainability culture.

Our analytical results confirm hypotheses H2 and H3 proposed in the Introduction (see Propositions 1 and 3), but hypothesis H1 is only partially supported. As shown in Proposition 2, the impact of the correlation coefficient of a sustainability culture and liquor product on the optimal promotion level of a sustainability culture is negative in the case of adopting the cooperative promotion strategy but non-monotonic when adopting the competitive promotion strategy of a sustainability culture. The reason is that when adopting the competitive promotion strategy of a sustainability culture, if the initial disparity in sustainability cultures between the two firms is small and the liquor firm with a strong sustainability culture has a costs disadvantage in promoting sustainability culture, the liquor firm with a strong sustainability culture would raise the promotion level of sustainability culture to compensate for its potential loss. Similarly, if the initial disparity in sustainability cultures between the two firms is big and the liquor firm with a weak sustainability culture has a costs disadvantage in promoting sustainability culture, the liquor firm with a weak sustainability culture would do the same thing.

The findings of this paper contribute to both the existing literature and to practical business strategies. Specifically, the results of this study significantly advance the research on coopetition strategy and sustainability culture in three aspects: (1) Enriching the coopetition literature by focusing on a specific industry and providing a novel perspective on coopetition strategy, particularly in relation to the initial disparity in sustainability cultures among different liquor firms. (2) Building a dynamic coopetition–culture relationship. Prior research predominantly frames competition and cooperation as mutually exclusive strategies [66,67,68], treating sustainability culture as a static organizational attribute [69,70]. (3) By using a two-dimensional Hotelling model with endogenous cultural evolution, this paper provides a framework that captures how sustainability culture dynamically coevolves with strategic choices. This bridges the gap between cultural economics and game theory, offering a new lens to analyze China’s unique “rivalrous synergy” in heritage industries [71,72].

7.2. Managerial Implication

Based on the above research results, the managerial implications of this paper are as follows.

For the managers of liquor firms, first, they should carefully assess the initial disparity in sustainability cultures when considering forming partnerships or competitive strategies. A cooperative promotion strategy is advisable only when the disparity is within a moderate range. Otherwise, either the liquor firm with a strong sustainability culture or the liquor firm with a weak sustainability culture would refuse to engage in a cooperative promotion strategy of a common sustainability culture. Second, they must recognize the nuanced impact of the correlation between sustainability culture and liquor products on the promotion level of a sustainability culture. When adopting a cooperative strategy, the managers of liquor firms should account for the negative influence of this correlation on the optimal promotion level. Under a competitive strategy, the managers of liquor firms should realize the non-monotonic impacts of the correlation between sustainability culture and liquor products.

For the employees of liquor firms, they should strongly support raising the promotion level of a sustainability culture, particularly by focusing on the key factors (such as the correlation between sustainability culture and product and the unfit costs between sustainability cultures of products and consumers’ sustainability culture preference) that influence operating profits, as these directly impact their own payoffs.

For the liquor companies and industry, the consistently positive impact of sustainability culture disparity suggests that liquor firms can strategically leverage their differences in sustainability culture to cocreate value under a cooperative promotion strategy. As such, liquor firms should value the importance of collaboration frameworks in promoting a common sustainability culture, which facilitates the mutual enhancement of sustainability cultures while maximizing the effectiveness of sustainability culture promotion.

7.3. Future Research

Finally, this study has several limitations, and future research could address the following aspects. First, building on this article, an analysis of the evolution of sustainability culture promotion and market positioning from a long-term perspective would provide valuable insights. This would help to understand how liquor firms adjust their strategies in response to market changes and competitor dynamics, particularly in terms of sustainability culture embeddedness. Second, given that most liquor firms distribute their products through retailers, another interesting research question is to examine the role of retailers in influencing the promotion of sustainability culture. Thus, incorporating sustainability culture promotion into the supply chain structure is also an important future research direction. Additionally, although firms with varying levels of sustainability culture may correspond to different sizes of firms, it is important to acknowledge that evaluating the sizes of liquor firms based on revenue volume or production costs would be a more appropriate approach. Therefore, the impact of liquor firms’ scale on the finding of this paper is left as a direction for future research.