The Optimal CSR and Sustainability Approach in a Spatial Duopoly: A Comparative Study

Abstract

In the context of increasing consumer environmental awareness (CEA), firms are progressively adopting corporate social responsibility (CSR) strategies that seek to align profitability with environmental objectives. This paper develops a mathematical model to explore the implications of CSR under two distinct scenarios: one that incorporates both social and environmental impacts and another that focuses solely on environmental concerns. The analysis is situated within a spatial mixed duopoly, where a CSR-oriented firm competes with a purely profit-maximising rival. A game-theoretical framework is employed, in which the CSR firm’s objective function is modelled as a weighted sum of private profits and the environmentally driven welfare of consumers. Equilibrium analysis demonstrates that CSR engagement improves market outcomes relative to a benchmark without CSR and generates positive externalities for the non-CSR firm. Moreover, the scenario prioritising environmental impact alone yields superior sustainability and welfare outcomes for both consumers and firms, despite identical demand and product differentiation conditions. These findings enhance our understanding of how CEA interacts with CSR strategies in imperfectly competitive markets, offering valuable insights for managerial decision-making and the formulation of environmental policy.

1. Introduction

In the contemporary economic environment, there is a growing trend of for-profit firms adopting corporate social responsibility (CSR) as a key tool to contribute to sustainable development and environmental protection. CSR has evolved significantly since its early conceptualisation in the mid-20th century, when it was primarily seen as a philanthropic or reputational tool. Today, it is understood as a strategic approach whereby firms voluntarily integrate social and environmental concerns into their operations and stakeholder interactions. While enhancing legitimacy and stakeholder trust, CSR also entails risks such as greenwashing, increased operational costs, and conflicts with shareholder interests when not strategically aligned [1]. By integrating CSR into their business strategies, firms can become more aware of their environmental and social impacts, taking measures to mitigate negative effects and maximise positive outcomes. Within the framework of CSR, firms replace or complement the role traditionally held by public institutions in their pursuit of the common good. They establish a corporate self-discipline that prioritises not only economic profit but also ethical considerations, environmental sustainability, and the well-being of both the community and stakeholders as key drivers of business performance. CSR has become a widely adopted corporate strategy since Porter and Kramer identified it as a source of competitive advantage, further elaborated by Kramer and Porter [2,3]. Today, these initiatives are encompassed within ESG (Environment–Social–Governance) strategies, generating declarations of intent and, more importantly, addressing the needs of consumers with a clear environmental awareness through increasingly sustainable production practices [4,5,6,7]. This trend is further supported by Rani et al. [8], who identify a significant growth in ESG and CSR research, particularly in areas related to sustainability, stakeholder engagement, and financial outcomes.

This strategic shift towards sustainability is not driven solely by an internal corporate responsibility logic but also by a transformation in consumer preferences, as individuals increasingly incorporate ethical and environmental considerations into their purchasing decisions. Thus, consumers’ decision-making capacity, shaped by their level of environmental awareness (CEA), becomes a critical factor influencing the success of sustainability-oriented business strategies.

In differentiated markets, as examined in this study, consumers assess not merely price or quality but also the extent to which a firm’s values align with their own environmental principles. This phenomenon is well-documented in the literature, which demonstrates that substantial segments of the market are willing to pay premium prices for products that are certified as sustainable or produced by firms committed to responsible practices [9,10].

Accordingly, consumers’ environmental commitment generates a competitive advantage for firms that authentically embed sustainability within their business models, fostering a market dynamic in which corporate strategic decisions and citizen preferences are mutually reinforcing. In this way, sustainability transcends its role as a mere ethical obligation or regulatory requirement and becomes a competitive attribute, with the consumer acting as a catalyst for the transition towards more environmentally respectful economic models.

To study the impact of CSR on market sustainability, we develop a model in an oligopolistic market that simultaneously incorporates CEA and CSR. Some authors focus on the global interests of stakeholders, while others limit their analysis to partial interests. We examine these two approaches separately within a mixed spatial duopoly in which only one firm adopts CSR policies.

Traditionally, a mixed duopoly refers to a market where a public firm, aiming to maximise social welfare, competes with a profit-maximising private firm [11]. This concept, introduced by Merrill and Schneider [12], has been widely explored in the context of privatisation and public policy. Several studies have focused on environmental regulation and CSR within this framework. For example, Lambertini and Tampieri, Leal et al., and García et al. analyse environmental concerns in mixed oligopolies [13,14,15]. Bárcena and Sagasta extend this by incorporating CSR into the analysis [16]. Other contributions explore strategic behaviour in these markets. Heywood and Ye study sequential entry and spatial price discrimination [17]. More recently, Yakita and Zhang, Wang et al., Kim et al., and Xu and Zhao examine how CSR strategies interact with privatisation and cost asymmetries [18,19,20,21]. Li and Sun focus on environmental R&D cooperation, while Leal et al. assess policy tools like tradable permits in the presence of a consumer-friendly firm [22,23]. Most of these models are Cournot-type with homogeneous goods and maintain the classical public–private ownership distinction.

In contrast to this traditional approach, the present study proposes an alternative framework: a private duopoly with heterogeneous objectives. In this setting, both firms are privately owned but differ in their strategic orientation—one incorporates CSR into its objective function, while the other remains purely profit-maximising. Here, the term mixed refers not to ownership structure but to the asymmetry in the firms’ goals.

This perspective aligns with a growing body of literature that examines imperfect competition between private firms with varying degrees of ethical or environmental commitment, such as Becchetti et al. and Ohnishi [24,25] Our contribution extends this line of research by incorporating horizontal product differentiation (horizontal product differentiation takes place when, at a given price, different consumers prefer different varieties of the goods, so all varieties have a positive demand) and CEA, thereby offering new insights into how strategic asymmetries affect market outcomes, sustainability, and welfare.

While previous studies have examined CSR in mixed oligopolies, most have focused either on homogeneous goods or on single CSR strategies, without comparing their relative effectiveness. Moreover, the role of CEA has often been treated as exogenous or uniform. Our study contributes to filling this gap by incorporating a heterogeneous CEA into a spatial duopoly framework and comparing two distinct CSR approaches: the triple bottom line (TBL), which integrates social and environmental objectives, and the double bottom line (DBL), which focuses solely on environmental goals. This comparative perspective allows us to assess the strategic and welfare implications of each CSR orientation, offering new insights into how firms and policymakers can promote sustainability in differentiated markets.

In this paper, we present a private mixed spatial duopoly, assuming that only one of the firms has CSR policies, while consumers are environmentally conscious (CEA).

We assume that consumer awareness is heterogeneous; that is, some consumers may prefer a product with a lower sustainability to one with a higher sustainability. Examples include the preference of some consumers for non-organic agri-food products over organic ones; more polluting means of transport (e.g., diesel) over less polluting ones (e.g., biofuels); and household energy sources, using natural gas over electricity from renewable sources. Another illustration is products with eco-labels indicating sustainability due to sustainable production or extraction methods, such as wood from managed forests certified by FSC or PEFC labels. Compared to non-certified products, these products have different levels of sustainability and are differentiated by this eco-labelling. This assumption is supported by recent empirical evidence showing that environmental awareness is not uniform across consumers, with significant differences in sustainability-related attitudes and behaviours even within the same demographic groups [26]. Furthermore, the heterogeneity in consumer awareness extends to social dimensions of sustainability, such as concerns about labour conditions, fair trade practices, and human rights in global supply chains. Some consumers actively seek products that reflect social justice commitments—such as fair wages, ethical sourcing, or the absence of child labour—while others may remain indifferent or prioritise cost over social impact. Recent studies have shown that consumers’ consciousness for fair consumption significantly influences their willingness to buy and pay for fair trade products, highlighting the role of social awareness in ethical purchasing decisions [27]. Additionally, research indicates that emotional factors, such as feelings of pride or guilt, can significantly affect consumers’ intentions to purchase fairness-oriented products, suggesting that emotional engagement plays a crucial role in ethical consumption behaviours [28]. The multidimensional nature of consumer awareness implies that firms must navigate diverse value-based expectations, making both environmental and social responsibility central to product differentiation and competitive strategies in sustainability-oriented markets.

To analyse our model, we use the two before-mentioned complementary approaches. First, we adopt a global approach, in which both social and environmental aspects are considered simultaneously. In this case, the CSR indicator is defined as the sum of consumer and firm surplus, thereby integrating socio-environmental concerns. The CSR firm follows a TBL strategy, pursuing economic, social, and environmental goals. Accordingly, its objective function is a linear combination of profit and socio-environmental surplus. Second, we examine a partial approach that focuses exclusively on environmental impacts. This modelling choice does not disregard the social dimension of CSR. Instead, it aims to isolate the specific contribution of environmental responsibility to market sustainability. This is particularly relevant in light of the increasing emphasis on ecological concerns in consumer behaviour, corporate strategy, and public policy. The firm in this case adopts a DBL strategy, oriented toward economic and environmental goals [29]. By comparing both approaches, we are able to assess the relative effectiveness of broad versus focused CSR strategies in promoting sustainability and welfare.

We choose this modelling framework over traditional Cournot or Bertrand models with homogeneous goods, because it allows us to capture two key features of modern markets: horizontal product differentiation and heterogeneous consumer preferences regarding sustainability. Unlike standard models, our spatial duopoly approach reflects the real-world diversity in CEA and enables a more nuanced analysis of how CSR strategies influence market outcomes. Moreover, by focusing on a private duopoly with asymmetric objectives, we move beyond the classical public–private dichotomy and address a growing trend in which private firms voluntarily adopt CSR principles without regulatory mandates. Those two approaches allow us to address the following questions:

• How does the adoption of CSR affect the sustainability of the system?
• Are there spillover effects of CSR on non-CSR firms? To what extent do they affect the sustainability of the system?
• Is it preferable to promote the adoption of business strategies with a global or partial approach?

The analysis is conducted using a two-stage game applied to both CSR approaches. First, each firm selects the sustainability level for its product and then sets its price. This process determines the optimal sustainability levels, the average market sustainability level, the product prices, and the benefits. The variation in results for each firm is analysed based on cost, CEA, and the weighting of CSR. Finally, the results of the two approaches are compared to assess the impacts generated by each, providing tools for decision-making in corporate sustainability (this comparative approach is also supported by recent findings on the welfare and competition effects of CSR strategies under environmental externalities [30]). The structure of our model generalises some specific models described by other authors, such as D’Aspremont et al., Bárcena-Ruiz et al., and He and Deng [31,32,33].

The main results can be summarised as follows: (i) CEA and CSR influence prices, sustainability levels, and product differentiation within the sustainability balance. The consideration of CSR firms in the market can affect the overall sustainability level of the system and foster competition. (ii) Sustainability equilibrium is characterised by the symmetric behaviour of firms. This result is attributed to the demand effect, as unchanged market shares lead to strategic business behaviour. Symmetry leads to a contagion effect, with the non-CSR firm seeking to follow its CSR rival, resulting in improved sustainability. (iii) Ecological or green firms promote an improvement in the sustainability of production and, consequently, higher consumer welfare compared to firms focused on global CSR. Private firms increase their advantage by offering greener products to the same extent as green firms; however, we find that the level of product differentiation remains identical in either case.

This research demonstrates that CSR with a socio-environmental or exclusive environmental focus improves the equilibrium in terms of price and sustainability compared to the standard model. The results are even more favourable if the CSR objective is exclusively environmental. In this context, the findings can orient firms and governments in defining the types of environmental policies to be implemented. Overall, this study contributes to the literature by offering a novel framework that integrates CSR heterogeneity and CEA into a spatial competition model, with implications for both corporate strategy and public policy.

This article is structured as follows: Section 2 presents the model; Section 3 and Section 4 analyse the optimal strategies for mixed social or ecological duopolies versus purely profit-focused firms; Section 5 compares the behaviour of DBL and TBL firms by determining the best corporate strategy to improve the system’s sustainability. Finally, conclusions, limitations, and contributions are discussed in Section 5 Proofs of the main results not included in the text for reasons of conciseness are provided in Appendix A.

2. Model

We consider a spatial mixed duopoly where the good produced is characterised by environmental sustainability attributes, and consumers are characterised by their levels of CEA rather than traditional preferences or tastes. Environmental conscience is part of the consumer’s decision to purchase a good. The model adopts horizontal differentiation and incorporates CEA to reflect the varying degrees of environmental concern among consumers, capturing realistic market dynamics where consumer preferences for sustainability influence their purchasing decisions. In this market, firm 1 implements CSR policies, while firm 2 is ecological but for-profit. The CSR firm aims to positively influence stakeholders through socio-environmental (global) or purely environmental (partial) strategies. To describe the market, we consider a spatial configuration à la Hotelling (1929) [34], where the market space is referred to as the sustainability space {0,1}. The levels of product sustainability $x_1,x_2$ of firms 1 and 2, such that $x_1\le x_2$, belong to space {0,1}. Thus, the market is represented by goods with sustainability characteristics ranked in increasing order, i.e., firm 1 produces less environmentally friendly goods but incorporates CSR into its business policy to compensate for its low level of sustainability. Consumers $x$ are evenly distributed across space {0,1} according to their preference for sustainability, which we attribute to environmental awareness. We define two types of consumer awareness: (1) subjective, which represents the level of sustainability that a consumer has, and (2) social, which encompasses socially expected sustainability. We incorporate environmental concern directly into individual preferences. Therefore, we formalize a consumer’s utility $x$ when buying the good, $x_i$, at the prices, $p_i$, as:

$$u\left(x,x_i\right)=w\left(x,x_i\right)-p_i,where w(x,x_i)=r-t(x_i{-x)}^2-\gamma (x_i-{\theta )}^2,i=\mathrm{1,2}$$

(1)

(our utility specification in Equation (1), which coincides with He and Deng [33] and has strong similarities with Conrad [35]).

$w(x,x_i)$ indicates a consumer’s willingness to pay when purchasing the product, $x_i$, where r represents the intrinsic gross utility that a consumer $x$ obtains when purchasing a unit of the product. It is assumed that $r$ is large enough for each consumer to purchase the desired product. The term $t(x_i {-x)}^2$ is the cost that the consumer $x$ faces when buying from the firm selling the product, $x_i$, and is interpreted as the increasing marginal disutility as the product’s sustainability level deviates from the consumer’s ideal point, reflecting the subjective CEA. (The chosen consumer utility function is grounded in established economic theory and empirical observations. This approach aligns with the spatial competition models of Hotelling [34] and their subsequent adaptations by Eriksson [36] and Conrad [35].) The parameter $t$ expresses the strength of personal awareness. The term $\gamma (x_i-{\theta )}^2$ represents the social effect of CEA due to the purchase of a product $x_i$ whose sustainability characteristic differs from that of the social expectation $\theta$. We set the social expectation level of the environmental quality of products $\theta$ as the average level of environmental quality of products purchased by all consumers, which integrates the influence of producers and consumers, whose expression corresponds to

$$\theta ={\int }_0^{\widehat{x}}{x}_{1}dx+{\int }_{\widehat{x}}^1{x}_{2}dx=x_1\widehat{x}+x_2(1-\widehat{x})$$

(2)

This term can be viewed as a social norm effect. This interpretation reflects how social expectations influence consumers’ purchasing decisions, aligning with our model that incorporates both subjective environmental awareness and social norms. This dual consideration of subjective and social effects provides a comprehensive view of consumer decision-making in the context of environmental sustainability, offering a realistic representation of market dynamics influenced by CSR and environmental awareness.

Based on this assumption, one part of consumer expectations regarding the environmental quality of products is higher than the social expectation, while the other part is lower. This assumption provides an opportunity for firms to apply price and product differentiation strategies based on the two components of CEA.

$\widehat{x}$ represents the indifferent consumer and is obtained by equating the utility functions when purchasing from firms 1 and 2. The indifferent consumer is given by

$$\widehat{x}={\displaystyle \frac{p_2-p_1}{2z\left[t-\gamma z\right]}}+s+{\displaystyle \frac{\gamma z\left[2s-1\right]}{2\left[t-\gamma z\right]}}$$

(3)

where $z$ and $s$ correspond to

$$z=x_2-x_1,s={\displaystyle \frac{{(x}_1+x_2)}{2}},0<z<{\displaystyle \frac{t}{\gamma }}$$

(4)

$z$ represents the differentiation in environmental sustainability offered by firms 1 and 2, while $s$ denotes the average sustainability across the two firms. Expression (3) of the indifferent consumer is presented as the sum of three distinct terms. The first term depends not only on the price difference, $\left(p_2-p_1\right),$ and the difference in sustainability levels, $z,$ but also on the effect of the subjective and social norms of the CEA. The second term depends solely on the average sustainability level between the two firms. The third term represents a combination of the subjective and social factors of consumer awareness when both firms choose different levels of sustainability.

Given that consumers $x,$ with $x<\widehat{x},$ buy from firm 1 and the rest of the consumers from firm 2, the demand functions are formulated as follows:

$$q_1=\widehat{x},q_2=1-\widehat{x}$$

(5)

The two elements of CEA affect demand, prompting firms to adjust their pricing strategies and sustainability features to align with the new market scenario.

Regarding production, we assume that producing more sustainably incurs a higher cost proportional to the level of sustainability. Consequently, firm 2, which produces a more sustainable good, will bear a higher cost. We denote as $c$ the marginal cost in terms of the level of sustainability $x_i$ of the firm $i, i=1,2.$ The profit function is given by

$${\pi }_i=\left(p_i-c{x}_i\right)q_i$$

(6)

In recent decades, CSR has become increasingly prominent in business management debates. As mentioned above, in this paper, only the least sustainable firm, i.e., firm 1, incorporates CSR policies. This approach is based on the idea that less sustainable firms have a greater need to improve their socio-environmental impact and can benefit more significantly from adopting CSR practices. Additionally, by implementing CSR policies, these firms can enhance their public image and reputation. An example of this type of competitive market can be seen in neighbourhoods where sustainable businesses (green shops) without CSR policies coexist with less sustainable ones (hypermarkets) with CSR policies (eco-labels).

We consider two specifications of CSR. In the first scenario, we assume that the CSR firm complements business profits with the impact it has on socio-environmental well-being. Thus, we refer to a mixed TBL or social duopoly, where the socially responsible firm pursues a TBL of economic, social, and environmental objectives (denoted by the letter $S$).

Following the literature, the impact of the CSR strategy will be given by the social surplus, which is considered as the sum of consumer surplus, $CS,$ and producer surplus, $PS$ (see, for example, [37,38]).

$$W^S=CS+PS,CS={\int }_0^{{\widehat{x}}^S}u(x^S,x_1^S)dx+{\int }_{{\widehat{x}}^S}^{1}u(x^S,x_2^S)dx,PS={\pi }_1^S+{\pi }_2^S$$

Substituting Equations (1)–(3), (6), and (4) and considering $R={\int }_0^{1}r dx,$ we obtain that

$$W^S=R-\left[z^S\left(t-\gamma z^S\right){\left({\widehat{x}}^S\right)}^2-z^S\left(2t{s}^S-\gamma z^S+c\right){\widehat{x}}^S+c{x}_2^S-t{x}_2^S\left(1-x_2^S\right)+{\displaystyle \frac{t}{3}}\right]$$

(7)

In the second scenario, we adopt a more restrictive approach where the CSR firm considers the environmental externalities caused by its activities solely in terms of consumer sensitivity to them. Consequently, the firm’s strategic plan is based on two pillars, economic and environmental benefits, rather than three. The mixed duopoly is therefore a DBL or ecological duopoly, which we denote by the letter $E.$ The impact of CSR, $W^E$, incorporates only the CEA and is represented by the aggregate willingness to pay of consumers when they purchase products with a sustainability characteristic $x_1$ o $x_2.$

$$W^E={\int }_0^{{\widehat{x}}^E}w(x^E,x_1^E)dx+{\int }_{{\widehat{x}}^E}^{1}w(x^E,x_2^E)dx$$

Substituting (1), (2), (3), and (4), we obtain that

$$W^E=R-\left[z^E\left(t-\gamma z^E\right){\left({\widehat{x}}^E\right)}^2-z^E\left(2t{s}^E-\gamma z^E\right){\widehat{x}}^E-t{x}_2^E\left(1-x_2^E\right)+{\displaystyle \frac{t}{3}}\right]$$

(8)

A firm can decide what type of CSR to implement, depending on its mission and values. For instance, in the energy industry, there is a clear interest in a CSR with a more environmental bias to minimise environmental impacts. This contrasts with social economy firms that develop a triple bottom line CSR, focusing on social welfare. The global approach to CSR may initially generate a greater stakeholder buy-in and enhance the firm’s reputation. However, performance is often reduced when the firm engages in multiple responsibilities, so the partial approach that appears more restrictive may yield better results.

The objective function of firm 1 is the weighted sum (see [11] for the case of the public firm, [23] for the green firm, and [39] for social responsibility in the payoff of the firm) of the economic profit and the social or environmental surplus, and it is formulated as follows:

$$V_1^j=\alpha {\pi }_1^j+\left(1-\alpha \right)W^j,j=S,E$$

(9)

To weight CSR, we consider the parameter $\alpha$, such that $0\le \alpha \le 1$, as the value that firm 1 places on economic profit, so that $\left(1-\alpha \right)$ determines the level of CSR. Different values of the parameter $\alpha$ reflect the firm’s sensitivity to monetary profit relative to CSR considerations. When 0 $\le \alpha \le {\displaystyle \frac{1}{2}}$, it means that the firm prioritises CSR, whereas ${\displaystyle \frac{1}{2}}\le \alpha \le 1$ indicates a preference for private profit. In the literature on imperfect competition, the usual function considered in CSR models is of the type $V_i={\pi }_i+\alpha W$, where only the consumer welfare function is weighted (generally, this type of function is used in homogeneous goods models; see [40], among other authors). However, the function $V_i=\alpha {\pi }_i+\left(1-\alpha \right)W$ allows for easy comparison with the various versions of horizontal differentiation models. If $\alpha =0$, firm 1 resembles a social planner with exclusively social and ecological concerns. Conversely, if $\alpha =1$, the firm will be a purely profit-making entity. This formulation of the objective function for the CSR-oriented firm enables us to recover key theoretical results from the literature on horizontal product differentiation [31,32,33,41].

The interaction between firms 1 and 2 will be analysed in terms of sustainability and price. The development of the interaction is represented as a two-stage game. In the first stage, both firms simultaneously choose their level of sustainability. In the second stage, they set their prices, with the level of sustainability remaining fixed and irreversible. The resolution is conducted using the backward induction method.

In the following sections we present the results. We determine the optimal strategies of the social mixed duopoly $\left(S\right)$ and, subsequently, those of the ecological mixed duopoly $\left(E\right)$. Finally, the two approaches are analysed comparatively to determine the most appropriate approach to achieve sustainability.

3. Results

3.1. Optimal Socially Mixed Duopoly Strategies, (S)

3.1.1. Price Equilibrium

At this stage of the game the firms compete on price. Assuming that the rival’s price is fixed, each firm maximises its objective function with respect to its price, given the sustainability characteristics of the product $\left(x_1^S,{ x}_2^S\right)$. From the first-order conditions and considering the objective functions of firms 1 and 2, respectively, given by expressions (9) and (6), the equilibrium prices are obtained:

$$p_1^{S\mathrm{*}}=c{x}_1^S+{\displaystyle \frac{\left(2\alpha -1\right)c{z}^S}{\left(2\alpha +1\right)}}+z^S{\displaystyle \frac{\left[2\left(2\alpha -1\right)t{s}^S-\left(2\alpha +1\right)\gamma z^S+2t\right]}{\left(2\alpha +1\right)}}$$

(10)

$$p_2^{S\mathrm{*}}=c{x}_2^S-{\displaystyle \frac{c{z}^S}{\left(2\alpha +1\right)}}+{\displaystyle \frac{z^S\left[-2t{s}^S-\left(2\alpha +1\right)\gamma z^S+2\left(\alpha +1\right)t\right]}{\left(2\alpha +1\right)}}$$

(11)

The price difference is given by

$${p_2^{S\mathrm{*}}-p}_1^{S\mathrm{*}}={\displaystyle \frac{z^S\left[2\alpha t\left(1-2s^S\right)+c\right]}{\left(2\alpha +1\right)}}$$

(12)

Demands are defined using (12) in (3) and (5):

$$q_1^{S\mathrm{*}}={\widehat{x}}^{S\mathrm{*}}={\displaystyle \frac{1}{2}}-{\displaystyle \frac{\left[t\left(1-2s^S\right)-c\right]}{2\left(2\alpha +1\right)\left(t-\gamma z^S\right)}},q_2^{S\mathrm{*}}=(1-{\widehat{x}}^{S\mathrm{*}})={\displaystyle \frac{1}{2}}+{\displaystyle \frac{\left[t\left(1-2s^S\right)-c\right]}{2\left(2\alpha +1\right)\left(t-\gamma z^S\right)}}$$

(13)

The objective functions are given using (10) and (11) in (9) and (6):

$$V_1^{S\mathrm{*}}=\left(1+\alpha \right)\left(t-\gamma z^S\right)z^S({q_1^S)}^2+\left(1-\alpha \right)\left[R-{\displaystyle \frac{t}{3}}-c{x}_2^S+t{x}_2^S\left(1-x_2^S\right)\right]$$

(14)

$${\pi }_2^{S\mathrm{*}}=2z^S\left(t-\gamma z^S\right)(q_2^S{)}^2.$$

(15)

Considering the condition on $z$ given in expression (4), it is verified that the objective functions of the two firms, ${ V}_1^{S*}$ and ${\pi }_2^{S*}$, are non-negative. In the following, the levels of sustainability in this first stage of the game are examined.

3.1.2. Sustainability Equilibrium

To determine the optimal levels of sustainability, we consider the objective functions (14) and (15) from the price equilibrium. Solving the first-order conditions, we get

Proposition 1. 

The equilibrium sustainability characteristics for each firm are given by

$$x_1^{S\mathrm{*}}={\displaystyle \frac{1}{2}}\left(1-{\displaystyle \frac{c}{t}}\right)-{\displaystyle \frac{\left(2\alpha +1\right)t}{4\left[\left(2\alpha +1\right)\gamma +t\right]}},x_2^{S\mathrm{*}}={\displaystyle \frac{1}{2}}\left(1-{\displaystyle \frac{c}{t}}\right)+{\displaystyle \frac{\left(2\alpha +1\right)t}{4\left[\left(2\alpha +1\right)\gamma +t\right]}}$$

(16)

Provided that

$$c\le {\displaystyle \frac{\left[2\left(2\alpha +1\right)\gamma -\left(2\alpha -1\right)t\right] t}{2 \left[\left(2\alpha +1\right)\gamma +t\right]}}=c^{S*}$$

(17)

Proof. 

(see Appendix A). □

Condition (17) of Proposition 1 shows that there is a cost threshold beyond which there can be no equilibrium. Indeed, this threshold corresponds to extreme optimal sustainability levels, with firm 2 reaching its maximum level $x_2^{S\mathrm{*}}=1$, and firm 1 its minimum level $x_1^{S\mathrm{*}}=0$. Paradoxically, for the highest level of sustainability cost, represented by $c^{S*}$, firm 1 prefers to produce a good with a lower level of sustainability and firm 2 one with the highest level. This outcome reflects a strategic positioning: by maximising differentiation, each firm avoids intense price competition, thereby protecting its profit margins. On the other hand, we verify that the threshold $c^{S*}$ is increasing with respect to CSR, i.e., the higher the firm’s CSR, the higher the possibility of having an equilibrium in the market (${\displaystyle \frac{\partial c^{S*}}{\partial \alpha }}=-{\displaystyle \frac{t^3}{{\left[\left(2\alpha +1\right)\gamma +t\right]}^2}}<0$), thus c^S* is increasing with respect to CSR). From a practical perspective, this finding suggests that firms need to carefully balance their sustainability efforts and cost structures to achieve market equilibrium. For instance, firms in the energy sector might invest in advanced technologies to enhance their sustainability, while managing costs effectively. Additionally, industries such as agri-food or textiles, where consumer demand for sustainable products is high, can leverage CSR to differentiate themselves and achieve competitive advantages. Therefore, it would be in the government’s interest to implement policies to promote a CSR that induces equilibria in markets. Such policies could include tax incentives for sustainable practices, subsidies for green technologies, stricter environmental regulations, or promoting CEA. These measures would not only increase market sustainability but would also improve overall consumer welfare by encouraging firms to adopt higher levels of CSR.

Regarding the sustainability levels of firms at the equilibrium, the result is due to the market share effect. To share the market fairly $\left(q_1^{S\mathrm{*}}=q_2^{S\mathrm{*}}={\displaystyle \frac{1}{2}}\right)$, the firms set the average of the two goods on offer as the reference product. With this profile, the two entities adopt symmetric strategies by choosing goods equidistant from this average (this symmetry is a recurring feature in the spatial duopoly of horizontal differentiation and is a strategic element for firms). Considering the generic structure of the good averages $\left(x_1,x_2\right)$ described in expression (4), the point of symmetry in equilibrium is independent of the level of CSR and is given by

$$s^{S\mathrm{*}}\left(c,t\right)={\displaystyle \frac{1}{2}}\left(x_1^{S\mathrm{*}}+x_2^{S\mathrm{*}}\right)={\displaystyle \frac{1}{2}}\left(1-{\displaystyle \frac{c}{t}}\right).$$

(18)

From condition (17), it is found that ${0\le s}^{S*}\left(c,t\right)\le 1$.

In this case, the average level of production $s^{S\mathrm{*}}$ coincides with the consumers’ expected level of sustainability, ${\theta }^{S\mathrm{*}}$, as given in expression (2). At equilibrium, the average expectation of consumers regarding the sustainability of the goods produced is met. The two parameters, $c$ (the marginal cost in terms of the level of sustainability) and $t$ (personal awareness), have opposite effects on the average level of sustainability. The former worsens it, while the latter improves it. Therefore, as previously discussed, it would be beneficial for public authorities to implement environmental awareness campaigns targeting consumers and to provide incentives—such as subsidies—to firms, in order to promote market sustainability.

This analysis highlights the importance of balancing production costs and consumer awareness to achieve optimal sustainability levels. By understanding these dynamics, this article aims to provide insights into how firms and policymakers can work together to enhance market sustainability and meet consumer expectations.

The expression for product differentiation is given by

$$z^{S\mathrm{*}}\left(\alpha \right)={\displaystyle \frac{\left(2\alpha +1\right)t}{2\left[\left(2\alpha +1\right)\gamma +t\right]}}.$$

(19)

Product differentiation is affected not only by $t$ and $\gamma$ but also by the CSR policy implemented. It is verified that for any value of $t$ and $\gamma$, $z^{S\mathrm{*}}$ increases with respect to the weighting $\alpha$ (${\displaystyle \frac{\partial z^{S\mathrm{*}}}{\partial \alpha }}={\left({\displaystyle \frac{t}{\left(2\alpha +1\right)\gamma +t}}\right)}^2>0$) and therefore decreases with respect to the CSR level. Increasing corporate responsibility moderately improves the sustainability of the system, leading to individuals consuming somewhat more sustainable goods.

When firms do not integrate corporate responsibility $\left(\alpha =1\right)$, product differentiation reaches its maximum at ${ z}^{S*}\left(1\right)={\displaystyle \frac{3t }{2\left[3\gamma +t\right] }}$. When $\alpha =0$, the differentiation is minimal and is reached at ${ z}^{S*}\left(0\right)={\displaystyle \frac{t }{2\left[\gamma +t\right] }}.$ Figure 1 shows how sustainability varies depending on the degree of firms’ CSR, with $\alpha =0$, $\alpha =1$, and the most general case $\alpha \in \left[\mathrm{0,1}\right]$. We plot the sustainability of each firm’s production, the average level of sustainability, and the differentiation between the two firms’ products. We observe that when firm 1 increases its interest in CSR, firm 2 not only fails to improve but also decreases its sustainable positioning. Despite this antagonism, the overall effect on the system improves as the differentiation gap narrows, i.e., products become less differentiated.

We calculate the prices of the products by substituting (16) and (17) into (10) and (11),

$$p_1^{S\mathrm{*}}=c{x}_1^{S\mathrm{*}}+z^{S\mathrm{*}}\left(t-\gamma z^{S\mathrm{*}}\right),p_2^{S\mathrm{*}}=c{x}_2^{S\mathrm{*}}+z^{S\mathrm{*}}\left(t-\gamma z^{S\mathrm{*}}\right)$$

(20)

The profitable firm has a higher gross price to compensate for its higher production costs. The net prices are equal $\left({ p}_2^{S*}-c{x}_2^{S*}\right)=\left({ p}_1^{S*}-c{x}_1^{S*}\right)=z^{S*}\left(t-\gamma z^{S*}\right)$; the economic profits of the two firms are equal and are given by

$${\pi }_1^{S\mathrm{*}}={\pi }_2^{S\mathrm{*}}={\displaystyle \frac{1}{2}}{z}^{S\mathrm{*}}\left(t-\gamma z^{S\mathrm{*}}\right)$$

(21)

Greater concern for the socio-environmental impact of firm 1, i.e., a higher degree of CSR, increases competition and results in lower business benefits. The integration of CSR improves the social and environmental well-being of consumers as shown below.

We calculate the welfare expression $W^{S*}$, given in expression (7), substituting ${\widehat{x}}^s$ by (1/2).

$$W^{S\mathrm{*}}=\left[R-{\displaystyle \frac{t}{3}}-c x_2^{S\mathrm{*}}+t x_2^{S\mathrm{*}}\left(1-x_2^{S\mathrm{*}}\right)+{\displaystyle \frac{1}{4}}\left(t-\gamma z^{S\mathrm{*}}\right)z^{S\mathrm{*}}\right]$$

(22)

Analysing the variation in the social and environmental surplus $W^{S*}$ with respect to the CSR and the CEA, the following result is obtained:

Corollary 1. 

In the duopoly equilibrium $S$, for any $\alpha \in [0,1]$, $c\ge 0$, $t\ge 0$, $\gamma \ge 0$, one has

$${\displaystyle \frac{\partial W^{S\mathrm{*}}}{\partial \alpha }}\le 0,{\displaystyle \frac{\partial W^{S\mathrm{*}}}{\partial c}}\le 0, {\displaystyle \frac{\partial W^{S\mathrm{*}}}{\partial t}}\le 0$$

${\displaystyle \frac{\partial W^{S*}}{\partial \gamma }}\le 0$, for $\gamma \in [2t, \infty ]$ o for $\gamma \in [0, 2t]$ and $\alpha \in \left[0,{\displaystyle \frac{\gamma +t}{2t-\gamma }}\right]$, ${\displaystyle \frac{\partial W^{S*}}{\partial \gamma }}\ge 0$, for $\gamma \in [0, 2t]$ and $\alpha \in \left[{\displaystyle \frac{\gamma +t}{2t-\gamma }},1\right]$.

Proof. 

(see Appendix A). □

Social welfare $W^{S\mathrm{*}}$ increases as the level of CSR rises but decreases as production costs increase. As an economic policy, it is therefore in the interest of the authorities to promote CSR in firms and to support firms in reducing their costs for sustainable production. Regarding the effects of subjective environmental awareness, $t$, and social awareness, $\gamma ,$ these factors indicate high consumer expectations. In fact, the higher the awareness, the lower the welfare. Such requirements can be interpreted as pressures on firms and government to continuously improve sustainability. Therefore, if a firm wants to enhance its impact on stakeholders, it must reduce its production costs and maintain constant attention to environmental aspects.

3.2. Optimal Strategies of the Ecological Mixed Duopoly, (E)

Following the same analytical sequence as in the previous case, we determine the optimal strategies of the mixed ecological duopoly by first analysing price competition and then evaluating sustainability choices.

3.2.1. Price Equilibrium

From the first-order conditions of the objective functions of firms 1 and 2, given respectively by expressions (6) and (9), we obtain the following prices:

$${\mathrm{p}}_1^{\mathrm{E}\mathrm{*}}=\mathrm{c}{\mathrm{x}}_1^{\mathrm{E}}+{\displaystyle \frac{\mathrm{c}{\mathrm{z}}^{\mathrm{E}}}{\left(2\mathrm{\alpha }+1\right)}}+{\mathrm{z}}^{\mathrm{E}}{\displaystyle \frac{\left[2\left(2\mathrm{\alpha }-1\right)\mathrm{t}{\mathrm{s}}^{\mathrm{E}}-\left(2\mathrm{\alpha }+1\right)\mathrm{\gamma }{\mathrm{z}}^{\mathrm{E}}+2\mathrm{t}\right]}{\left(2\mathrm{\alpha }+1\right)}}$$

(23)

$${ p}_2^{E*}=c{ x}_2^E-{\displaystyle \frac{\alpha c{z}^E}{\left(2\alpha +1\right)}}+{\displaystyle \frac{z^E\left[-2 t{s}^E-\left(2\alpha +1\right)\gamma z^E+2\left(\alpha +1\right)t\right]}{\left(2\alpha +1\right)}}$$

(24)

The price difference is given by

$${{\mathrm{p}}_2^{\mathrm{E}\mathrm{*}}-\mathrm{p}}_1^{\mathrm{E}\mathrm{*}}={\displaystyle \frac{\mathrm{\alpha }{\mathrm{z}}^{\mathrm{E}}\left[2\mathrm{t}\left(1-2{\mathrm{s}}^{\mathrm{E}}\right)+\mathrm{c}\right]}{\left(2\mathrm{\alpha }+1\right)}}$$

(25)

Substituting (25) into (3) gives the indifferent consumer ${\widehat{x}}^{E*}$ and, therefore, the demands $\left(q_1^{E*},q_2^{E*} \right)$, the objective function of firm 1, $V_1^E,$ and the economic profit of firm 2, ${\pi }_2^{E*}$

$${ q}_1^{E*}={\widehat{x}}^{E*}={\displaystyle \frac{1}{2}}-{\displaystyle \frac{ \left[t \left(2s^E-1\right)-\alpha c\right]}{2 \left(2\alpha +1\right)\left(t-\gamma z^E\right)}},{ q}_2^{E*}={\displaystyle \frac{1}{2}}+{\displaystyle \frac{ \left[t \left(2s^E-1\right)-\alpha c\right]}{2 \left(2\alpha +1\right)\left(t-\gamma z^E\right)}}$$

(26)

$$V_1^E\left({p_1^{E*}, p}_2^{E*}\right)=\left(1+\alpha \right) \left(t-\gamma z^E\right)z^E ({q_1^{E*})}^2+\left(1-\alpha \right)\left[ R-{\displaystyle \frac{t}{3}}+t{ x}_2^E\left(1-{ x}_2^E\right)\right]$$

(27)

$${\pi }_2^{E*}=2 z^E \left(t-\gamma z^E\right)(q_2^{E*}{)}^2$$

(28)

From the condition of $z$ in expression (4), we find that the objective functions of the two firms, $V_1^{E\mathrm{*}}$ and ${\pi }_2^{E\mathrm{*}},$ are positive. Next, we determine the optimal business policies in terms of sustainability.

Having established the price equilibrium, we now turn our attention to the sustainability equilibrium to further understand the strategic interactions between the firms.

3.2.2. Sustainability Equilibrium

The first stage of the game is solved. In this stage, the sustainability levels that maximise the objective functions of both firms, $V^{E*}$ and ${\pi }_2^{E*}$, are chosen simultaneously. The solution is given in the following proposition:

Proposition 2. 

The equilibrium sustainability characteristics are given by

$${ x}_1^{E*}={\displaystyle \frac{1}{2}}\left(1-{\displaystyle \frac{\alpha c }{ t}}\right)-{\displaystyle \frac{\left(2\alpha +1\right)t }{4\left[\left(2\alpha +1\right)\gamma +t\right] }}, { x}_2^{E*}={\displaystyle \frac{1}{2}}\left(1-{\displaystyle \frac{\alpha c }{ t}}\right)+{\displaystyle \frac{\left(2\alpha +1\right)t }{4\left[\left(2\alpha +1\right)\gamma +t\right] }}$$

(29)

Whenever it is verified

$$c\le {\displaystyle \frac{\left[2\left(2\alpha +1\right)\gamma -\left(2\alpha -1\right)t\right] t}{2\alpha \left[\left(2\alpha +1\right)\gamma +t\right]}}=c^{E*}$$

(30)

Proof. 

(see Appendix A). □

As in the case of social duopoly, there is a cost threshold given by $c^{E*}$ beyond which there can be no equilibrium. For the same reasons as with the social duopoly, it is also in the interest of the authorities to implement policies to promote environmental CSR by firms. CSR has a greater impact on the sustainability of firms in an ecological versus a social duopoly. The symmetry between the two firms corresponds to the average market sustainability level. Its expression is given by

$${ s}^{E*}\left(\alpha , c,t\right)={\displaystyle \frac{1}{2 }}\left(x_1^{E*}+x_2^{E*}\right)={\displaystyle \frac{1}{2}}\left(1-{\displaystyle \frac{\alpha c}{t}}\right).$$

(31)

From condition (30), it is found that ${0\le s}^{S*}\left(c,t\right)\le 1$. Symmetry remains a strategic factor for firms, and the level of sustainability expected from consumers, ${\theta }^{E*},$ given in expression (2), coincides with the average sustainability level $s^{E*}$. Here, the symmetry depends on the weighting $\alpha$, as it decreases with respect to $\alpha$, which is an important and interesting result. The variation in ${ s}^{E*}\left(\alpha , c,t\right)$ with respect to the other factors $c$ and $t$ is similar to that of the duopoly S.

When comparing what happens in duopolies $S$ and $E$, we see that both the point of symmetry and the levels of sustainability are different. However, product differentiation reamins the same, $z^{E*}=z^{S*}$. The indifferent consumer is still at the midpoint, and the demands are equal, $q_1^{E*}=q_2^{E*}={\displaystyle \frac{1}{2}}$.

Both firms enhance their sustainability as CSR levels increase, a phenomenon we can define as a contagion effect of the CSR firm on the rival for-profit firm. However, the improvement of firm 2, which does not adopt CSR, is smaller. This difference is due to the fact that symmetry now depends on CSR.

To determine the prices, we substitute (31) into (23) and (24) and obtain the following

$${ p}_1^{E*}=c{x}_1^{E*}+z^{E*}\left(t-\gamma z^{E*}\right)+\left(1-\alpha \right) c{z}^{E*}, { p}_2^{E*}{=p}_1^{E*}+\alpha c{z}^{E*}$$

(32)

The profitable firm has a gross price, $p_2^{E*}$, that is higher. However, as it has a high cost of production, its economic profit is lower than that of its rival.

$${ \pi }_1^{E^{*}}={\displaystyle \frac{z^{E*}}{2}}\left[\left(t-\gamma z^{E*}\right)+\left(1-\alpha \right) c\right], { \pi }_2^{E*}{=\pi }_1^{E*}-{\displaystyle \frac{1}{2}}\left(1-\alpha \right) c{z}^{E*}$$

(33)

In Figure 2 we show the spillover effect between firm 1 and 2, assuming different levels of interest in CSR of $\alpha =0$, $\alpha \in \left[\mathrm{0,1}\right],$ and $\alpha =1$. In this case where the firm follows a DBL approach, the effect is positive in the system, as increases in environmental concern in firm 1 in the form of improved sustainable production. lead to a similar effect in firm 2. Consequently, consumers can choose between increasingly greener products.

Increasing the degree of sustainability of production causes firm 2 to have a lower profit than firm 1, with profits decreasing as the CSR weighting of its rival increases. Therefore, a priori, firm 2 will have incentives to implement CSR strategies.

In terms of environmental welfare $W^E$ in the case of double-bottom-line CSR, substituting ${\widehat{x}}^E$ by (1/2), $s^E$ by ${\displaystyle \frac{1}{2}}\left(1-{\displaystyle \frac{\alpha c}{ t}}\right)$, and ${ x}_2^E$ and $z^E$ by ${ x}_2^{E*}$ and $z^{E*}$ in expression (8), we obtain that

$${ W}^{E*}=\left[ R-{\displaystyle \frac{t}{3}}-{\displaystyle \frac{1}{2}}\alpha c{z}^{E*}+t{ x}_2^{E*}\left(1-{ x}_2^{E*}\right)+{\displaystyle \frac{1}{4}}\left(t-\gamma z^{E*}\right) z^{E*}\right]$$

(34)

Examining the variation in welfare with respect to the profit weighting $\alpha \in \left[\mathrm{0,1}\right]$; marginal cost of sustainability, $c$; and the CEA, $\left(t, \gamma \right)$, we show that

Corollary 2. 

The variation in $W^{E*}$ with respect to $\alpha \in (0,1)$, $c\ge 0$, $t\ge 0$, $\gamma \ge 0$ is similar to $W^{S*}$.

Proof. 

(see Appendix A). □

The observations on welfare, as well as policy orientations, are identical to those mentioned above in Corollary 1.

In the next section we will proceed to a detailed comparative analysis between the two approaches, TBL and DBL, and we will analyse the impacts of social duopoly $S$ versus double bottom duopoly $E$.

4. Discussion—Comparative Analysis

Considering the cost thresholds given in Propositions 1 and 2, which are respectively $c^{S*}$ and $c^{E*}$, it is easily verified that $c^{S*}\le c^{E*}$. Therefore, the equilibrium $\left({ x}_1^{S*}, x_2^{S*}\right)$ for the social duopoly $\left(S\right)$ and $\left({ x}_1^{E*}, x_2^{E*}\right)$ for the ecological duopoly $\left(E\right)$ exist simultaneously for any marginal cost $c$ such that $c\le c^{S*}$. In this case, we can compare the results of the socially mixed duopoly $\left(S\right)$ with those of the ecological duopoly $\left(E\right)$ in terms of optimal sustainability strategies, prices, firms’ economic profits, and welfare functions $W^{S*}$ and ${ W}^{E*}$.

This comparative approach is also supported by empirical evidence showing that firms, particularly SMEs, often prioritise environmental concerns in their strategic orientation. For example, Gallardo-Vázquez and Sánchez-Hernández identify environmental protection as a central strategic driver in SMEs, while Paiva et al. highlight the role of environmental awareness in the diffusion of CSR practices [42,43]. These findings reinforce the relevance of isolating the environmental dimension of CSR, as done in our DBL framework, to better understand its specific impact on sustainability outcomes.

We obtain the following:

Proposition 3. 

The ecological mixed duopoly $\left(E\right)$ is more sustainable in terms of production than the social mixed duopoly $\left(S\right)$. The distribution of the optimal sustainability strategies is such that

$${0\le x}_1^{S*}{\le x}_1^{E*}\le {x_2^{S*}\le x}_2^{E*}\le 1$$

(35)

Proof. 

(see Appendix A). □

Improvements in both the sustainability levels of firms and the average level of sustainability are given by

$$I\left(\alpha , c, t\right)={ x}_1^{*E}-x_1^{*S}={ x}_2^{*E}-x_2^{*S}={\theta }^{E*}-{\theta }^{S*}={\displaystyle \frac{\left(1-\alpha \right)c }{ 2t}}$$

(36)

These enhancements are similar for each firm and increase as the weight given to CSR rises. To illustrate the gains in sustainability, we plot the expressions in Figure 3.

As previously established, the degree of product differentiation remains identical across both duopolies, implying that the intensity of competition between firms remains equal $\left(z^{E*}=z^{S*}\right)$. However, in terms of pricing and sustainability, the CSR firm in duopoly E sets a higher price and offers a greater level of sustainability than the ecological firm in duopoly S. As a result, it achieves a higher level of economic profit.

The green firm produces a more sustainable good ${(x}_1^{E*}\ge x_1^{S*})$. This results in higher production costs, but it still manages to achieve a better margin $\left[{ p}_1^{E*}-c{ x}_1^{E*}\right]=\left[p_1^{S*}-c{x}_1^{S*}\right]+\left(1-\alpha \right) c{z}^{E*}$ and a higher economic profit ${ \pi }_1^{E*}={\pi }_1^{S*}+{\displaystyle \frac{1}{2}}\left(1-\alpha \right){cz}^{E*}$ compared to the social firm. The private firm in both duopolies produces a more sustainable good ${(x}_2^{E*}\ge x_2^{S*})$, maintains the same margin $\left[{ p}_2^{E*}-c{ x}_2^{E*}\right]=\left[p_2^{S*}-c{x}_2^{S*}\right]$, and, therefore, achieves the same profits ${ \pi }_2^{E*}={\pi }_2^{S*}$.

Returning to the welfare functions $W^{S*}$ and ${ W}^{E*}$, comparing the results of the two equilibria we obtain

Proposition 4. 

Ecological welfare is greater than social welfare $W^{E*}\ge W^{S*}$.

Proof. 

(see Appendix A). □

There is an improvement in terms of welfare when firms focus on environmental aspects, as opposed to more global or TBL approaches. This highlights the challenges of achieving effective environmental protection when specific environmental objectives are embedded within broader goals (such as the SDGs). Therefore, it would be more appropriate for the government to implement policies that are specifically focused on environmental areas to improve sustainability outcomes. On the other hand, although firms are usually more concerned with their economic interests, they will benefit more if they invest in improving the sustainability of their production. The long-term benefits of adopting environmental CSR strategies include enhanced market sustainability, increased consumer trust, and a competitive advantage in the marketplace. Examples of firms that have successfully integrated environmental CSR into their business models include Patagonia and Tesla, which have achieved both improved sustainability and economic performance.

These findings extend previous research on CSR in mixed duopolies by showing that, under a heterogeneous CEA, a DBL strategy can outperform a TBL approach in both sustainability and profitability. While earlier studies have explored CSR in Cournot settings or with homogeneous consumers, our model introduces horizontal differentiation and endogenous CEA, offering a more realistic framework [13,23]. More recent contributions have advanced the theoretical modelling of CSR in mixed markets, particularly under environmental externalities and strategic asymmetries [21,30]. However, these studies do not explicitly compare CSR orientations. Our result that DBL strategies generate stronger spillover effects and a higher welfare under symmetric competition is a novel contribution that refines the understanding of CSR’s strategic role in differentiated markets and complements these recent developments.

5. Conclusions

To promote the sustainable development of markets, it is imperative that firms make effective and voluntary commitments through CSR. This requirement is satisfied within the framework of our model: the external effect arises from the fact that the firm internalises CEA in its strategic plan, which generates positive outcomes for various stakeholders, particularly consumers. Through this approach, consumer concerns are addressed, and sustainability is improved by aligning production with appropriate sustainability standards. We develop a model that encompasses CSR and CEA within a horizontally differentiated ‘mixed’ duopoly setting, in which a CSR-oriented private firm and a greener yet profit-oriented firm compete first on sustainability and then on price. Two distinct approaches to CSR are explored. The first is based on three pillars, economic, social, and environmental (TBL), while the second focuses on two: economic and environmental (DBL). These scenarios are examined individually to assess their respective social and environmental impacts on stakeholders, with the aim of assessing whether business strategies with a global approach (TBL) are superior or inferior to those with a partial approach (DBL). In both cases, the objective function of the CSR-oriented firm is assumed to be a weighted sum of its private benefit and the surplus of the interest groups (firm and consumer).

Our analysis shows that, in both approaches, the demand effect dominates, leading firms to adopt symmetric behaviour to share the market fairly. In the first approach, symmetry does not depend on CSR; the CSR-oriented firm enhances its optimal level of sustainability, while the for-profit firm reduces it to the same extent. Despite the negative impact of CSR on the for-profit firm, the overall sustainability effect improves, the differentiation of goods decreases, and individuals consume reasonably more sustainable products, thus generating a positive externality for consumers.

With the second approach, the symmetry between firms depends on CSR and increases with respect to CSR. In that case, there is a clear spillover effect, as both firms improve their level of sustainability, with a higher adjustment for the CSR-oriented entity. However, due to the symmetry effect, product differentiation is the same as in the first approach, and competition also intensifies. Although demand and differentiation are similar in both duopolies, the firm with an environmental CSR obtains better profit margins even in a market where competition is more intense. The introduction of CSR has a positive impact on market competition, although its effects differ depending on the adoption of TBL or DBL strategies. Therefore, if the objective is to increase the sustainability of the system, it is preferable to promote the structuring of business clusters with CSR.

Building on these results, the contributions of this study can be summarised as follows. In this paper, we generalise several findings from the literature on spatial duopoly à la Hotelling. The core novelty of this work is the development of a spatial duopoly framework that integrates a heterogeneous CEA with two distinct CSR strategies—TBL and DBL. This comparative structure enables the evaluation of the most sustainable business strategies under each and to identify the most effective strategic configuration. By modelling competition in two stages—first on sustainability, then on price—we uncover how CSR spillovers and consumer awareness shape equilibrium outcomes.

From a policy perspective, our findings suggest that governments could implement measures to encourage firms to adopt CSR strategies, particularly those with an environmental focus. These initiatives could include tax incentives, subsidies for sustainable practices, stricter environmental regulations, and the promotion of environmental awareness among consumers. Such policies would enhance overall market sustainability and consumer welfare, fostering a more sustainable economic system.

These findings are consistent with recent theoretical contributions [21,30,44], which explore CSR’s adoption under environmental externalities, competition modes, and ownership structures.

Despite its contributions, this study has certain limitations that suggest avenues for future research. One direction involves relaxing some of the theoretical assumptions. Extending the model to include multiple CSR-adopting firms could offer a more comprehensive view of market dynamics, potentially generalising the findings and deepening our understanding of CSR in spatial competition.

Incorporating heterogeneous production methods—with varying implementation costs—and modelling the dynamic effects of rising environmental awareness on innovation would also enrich the analysis. Other relevant extensions could include considering alternative forms of CSR, such as pollution abatement, and introducing information asymmetries. While these additions would increase the analytical complexity, they could yield more realistic insights into firms’ behaviour and policy implications. These suggestions align with recent developments in ESG investment strategies [45] and the theoretical foundations of CSR disclosure [46].

Finally, as this study relies on analytical modelling, it does not include numerical simulations. Future work could incorporate simulations to test the sensitivity of the results to parameter changes and to illustrate the theoretical findings more concretely—particularly regarding the costs and environmental consequences of adopting cleaner technologies.