Introduction

As the increasing tension of market competition and the development of recognition on firms’ social attributes, corporate social responsibility (CSR) has emerged as a central topic in the management literature and is now integrated into practitioners’ strategic framework (Aguilera et al., 2007; Carroll, 1999; Flammer et al., 2019). Scholars have actively engaged in the ongoing debate to rationalize the reasonableness, value, and importance of CSR for firms, approaching it from perspectives such as individual recognition, resource dependence, and institutional evolution (Haack et al., 2021; Tan, 2009; Walker et al., 2019). Emphasizing the legitimacy and performance implications of CSR outcomes, they highlight it as a crucial element in today’s business landscape (Awaysheh et al., 2020; Shiu and Yang, 2017; Wang and Qian, 2011). Interestingly, despite being a symmetric concept to CSR, corporate social irresponsibility (CSI) has received relatively little attention in the CSR literature, despite the widespread perception of its significant negative influence and the constant observation of CSI behaviors (Lange and Washburn, 2012; Scheidler and Edinger-Schons, 2020; Walker et al., 2019). Therefore, it is necessary to explore the underlying mechanisms behind the phenomenon of CSI—the flip side of the CSR coin—given its distinct theoretical construct and the assumption that a firm’s success and survival are, to some extent, dependent on meeting normative expectations in external environments (Alcadipani and de Oliveira Medeiros 2020; Kölbel et al., 2017; Lange and Washburn, 2012).

When it comes to CSI, firms are primarily concerned with how consumers perceive and react to irresponsible behaviors (Kang et al., 2016; Sweetin et al., 2013). Therefore, previous research has focused on the factors that influence consumers’ perceptions and reactions to CSI (Jasinenko et al., 2020). While this line of research offers valuable insights into why, when, and how firms deal with certain types of CSI, there are still conceptual gaps in understanding why and when firms behave socially irresponsibly instead of responsibly from a dynamic and interactive perspective. This gap is partly due to the different perspectives and methodologies used by scholars in various disciplines when studying CSI. Management researchers tend to focus on firm-level topics, such as the impact of CSI on firms’ financial performance or risks, often finding CSI to be associated with negative outcomes (Awaysheh et al., 2020; Kang et al., 2016). In contrast, marketing researchers emphasize a static individual-level perspective to understand when, why, and how consumers respond to CSI (e.g., Scheidler and Edinger-Schons, 2020). As a result, while the notion that CSI can lead to negative outcomes is implicit in management research, there is limited insight into the micro mechanisms that drive a firm’s CSI behavior during interactions with consumers in an industrial ecosystem. On the other hand, marketing research has explored when, why, and how consumers perceive and react to CSI, but the scholarly attention has been static (e.g., Carvalho et al., 2015), overlooking dynamic interactions in the market.

This paper aims to investigate the conditions under which firms engage in socially irresponsible behavior when interacting with consumers within an evolutionary system. We focus specifically on scenarios in which medium to large companies in the consumer market engage in CSI behaviors that do not violate laws, which allows us to narrow our research topic and make meaningful contributions to the existing literature. A fundamental premise of this research is that firms choose between CSR-compliant or CSI strategies through a dynamic coevolution process involving both firms and consumers. The outcomes at the firm level are contingent upon the interactions between individual firms and consumers. Therefore, we adopt an individual-level evolutionary perspective to study the evolution of firms’ CSI strategies. In doing so, this study seeks to integrate and expand upon previous perspectives on CSI from the literature of strategic management and marketing.

We propose an evolutionary game model to investigate the dynamic interaction between firms and consumers based on the value capture theory (Gans and Ryall, 2017). In our model, companies can decide strategically whether they behave in a socially responsible or irresponsible manner in their business activities. Similarly, consumers can have either strong or weak CSR perception. For example, consumers are more inclined to support companies’ environmentally friendly initiatives when pollution intensifies due to the emissions of a significant number of companies. Conversely, consumers may be less sensitive to environmentally friendly actions when pollution is not severe. Since the CSR strategies of companies and the CSR perception of consumers change through interactions and imitations of the actors, a dynamic evolutionary game model provides a suitable framework for modeling such long-term developments. Within our model, firms are incentivized to adopt CSR-compliant behavior as a cooperative strategy, while CSI firms face the risk of punishment, such as reduced prices and increased transaction costs (da Silva Rocha, 2017). The results of our evolutionary model reveal the possibility of a moral trap, in which firms behave socially irresponsibly, and consumers hold weak CSR perception. This outcome is contingent on factors such as transition costs, industrial structure, and consumers’ willingness to pay for CSR in a specific market. Furthermore, we note that path dependence is a significant feature in the evolution of CSI behavior. Our findings make several contributions to the literature on CSI. First, we provide an interactive perspective on the occurrence of CSI, considering the role of consumers in shaping firms’ CSR-related strategies through continuous transactions. This study is one of the first to explore the micro mechanisms of CSI by integrating insights from both strategy and marketing research. Second, we highlight the pivotal role of industrial structure in firms’ adoption of CSI strategies, an aspect that has been largely neglected in the existing literature. Third, our research underscores the critical but often overlooked role of path dependence in influencing CSI strategies. In other words, we enrich the CSI literature by emphasizing the significance of initial institutional development and the influence of self-reinforcement in the marketplace.

In the rest of the paper, we begin with a brief literature review on CSI in “Conceptual background”. Then, we present the evolutionary model in “An evolutionary game model”. In “Evolutionary Equilibrium of Game Strategy”, we report the results of the evolutionary game. In “Numerical examples and sensitivity analysis”, numerical examples and sensitivity analysis are presented to extend the model results. Finally, in “Conclusions”, we end with a discussion as well as a limitation and future research.

Conceptual background

While pursuing economic profits remains the ultimate goal for corporations, the importance of committing to social responsibility has gradually gained recognition in today’s business landscape (Carroll, 1979; Carroll, 1999). Simultaneously, corporate irresponsible behaviors have also drawn attention and criticism, including issues related to pollution, food safety, and the mishandling of employee and supplier interests, among others (Bowen, 1953; Murphy and Schlegelmilch, 2013). As two facets of corporate social responsibility behaviors, CSR and CSI have garnered increasing attention due to the expanding role of corporations in society. Notably, some government functions have been assumed by corporations, a trend propelled by their growing scale, influence, globalization, and the emergence of digital economies (Illia et al., 2017; Murphy and Schlegelmilch, 2013). While CSR has been extensively studied and developed in this research area (Aguilera et al., 2007; Flammer et al., 2019; Galbreath, 2009), CSI received less scholarly attention until recent years (Lange and Washburn, 2012; Lin-Hi and Müller, 2013; Riera and Iborra, 2017).

Although limited, the literature has discussed the definition, scope, antecedents, consequences, and ethical issues of corporate social irresponsibility (e.g., Riera and Iborra, 2017; Shiu and Yang, 2017). Existing research has offered valuable insights into why and when firms engage in socially irresponsible behavior, considering consumers’ perception and response to CSI actions (Murphy and Schlegelmilch, 2013). Notably, two prominent streams of research have emerged, drawing on frameworks from strategic management and marketing (Du et al., 2011; Pearce and Manz, 2011). The strategic management perspective, focusing on a firm-level approach, has examined the relationship between CSI and firms’ performance or risks, generally suggesting negative effects due to stakeholders’ response to CSI (Kölbel et al., 2017). However, the outcome could be ambiguous, contingent on contextual factors (Sun and Ding, 2021). Sometimes, CSI may reduce costs and increase profits, as revealed by Price and Sun (2017), who also find that CSR moderates the negative relationship between CSI and performance. Firms practicing both CSR and CSI may demonstrate better performance than those doing neither. Taking an institutional view, Walker, Zhang, and Ni (2019) observe a negative relationship between CSI and firm performance in liberal market economies, while such a negative relationship is not significant in coordinated market economies. Sun and Ding (2021) discover that CSI’s negative effects depend on the firm’s capability, environmental dynamism, and industrial competition, with these effects becoming insignificant under low competitive pressure.

On the other hand, marketing scholars have directed their attention to individual-level factors that influence consumers’ perception and reactions to CSI behaviors (He et al., 2021; Jasinenko et al., 2020). They argue that CSI is subjectively judged by individual consumers based on their moral norms, causality inferences, and perceived impacts of such behaviors (Lange and Washburn, 2012). As a result, individual heterogeneity, including factors such as recognition, culture, ideology, and demographic characteristics, can lead to variations in perception of CSI (Carvalho et al., 2015; Jasinenko et al., 2020; Wagner et al., 2008; Williams and Zinkin, 2008). Furthermore, the perception of CSI can evoke moral emotions, which in turn motivate consumers’ willingness and behaviors to punish irresponsible corporations (Antonetti and Maklan, 2016a; 2016b; Grappi et al., 2013; Sweetin et al., 2013). While these studies provide insights into CSI by considering consumers’ roles, the micro mechanisms underlying a firm’s CSI behavior during interactions with consumers in an industrial ecosystem have not been fully elucidated due to limitations in theoretical perspectives and methodologies. Consequently, we develop an evolutionary model to further explore and extend this line of research.

In the context of this study, corporate social irresponsibility is defined as “A socially irresponsible act is a decision to accept an alternative that is thought by the decision maker to be inferior to another alternative when the effects upon all parties are considered. Generally, this involves a gain by one party at the expense of the total system” (Armstrong, 1977, p. 185). Based on CSI literature, CSI behaviors could involve the violation of law or not (Lin-Hi and Müller, 2013). Because contracts are often incomplete and there is a lack of comprehensive legal regulations on a global level, corporate actions have the potential to negatively impact others, even when corporations are not in violation of the law (Scherer and Palazzo, 2011). A recent instance of lawful yet irresponsible conduct can be observed in the real state sector in China, where real state firms assumed disproportionate risks within the boundaries of legality (BBC, 2023). This conduct brought the entire real state market and financial sector to the brink of collapse, leading to various detrimental consequences for society at large (Lin-Hi and Müller, 2013). Our focus in this research is on CSI that does not violate any laws, considering it as the opposite side of being compliant with corporate social responsibility. This includes actions such as unethical sales practices, using harmful food additives, and misleading consumers (Carroll, 1979). For instance, a well-known case is Foshan Haitian Flavouring and Food Company, which faced a “double standard” storm of food additives, causing widespread consumer resistance (Reuters, 2022). This CSI event did not violate any laws but significantly reduced Haitian’s market share and profits. On the other hand, Qianhe Condiment and Food Company, by complying with CSR, gained more market share (Teller Report, 2022). It’s important to note that a firm engages in various activities concurrently, encompassing manufacturing, logistics, and sales. This complexity makes it challenging to evaluate a firm’s overall adherence to CSR practices. However, when we narrow our focus to specific aspects of CSR, like pollution, the assessment becomes more transparent. This paper primarily centers on a specific area, providing a well-defined context for discussing CSI behaviors. Nonetheless, it’s essential to acknowledge that this approach does have its limitations.

Typically, auditors and consumers represent two critical groups of stakeholders whose recognition and behaviors significantly influence firms’ CSI behaviors (Murphy and Schlegelmilch, 2013). Auditors play a crucial role in inspecting, punishing, and potentially reporting noncompliant firms (da Silva Rocha and Salomão, 2019). On the other hand, consumers adjust their trade partners and behaviors based on their information, perception, and preferences (Riera and Iborra, 2017). Although both auditors and consumers play a role in shaping firms’ overall CSR compliance, their actions and effects are distinct due to their diverse information sources, analytical frameworks, standards, and behavioral tendencies.

Auditors are responsible for inspecting firms’ CSI behaviors based on legal requirements. On the other hand, consumers’ perception and behaviors are influenced by media and their own characteristics. When a CSI behavior is clearly defined by the law, the essential paradox lies in how we can optimize institutional arrangements to effectively regulate the market. However, there are instances where a CSI behavior is not strictly defined and exists in a vague boundary. For example, in the food industry, the use of food additives and camouflaged advertising may not directly violate the laws, but they are considered CSR non-compliant behaviors that can cause problems in the market. In this paper, our focus is on CSI behaviors that do not violate the laws but are easily affected by consumers. In such cases, we believe that the interaction between firms and consumers becomes more crucial in influencing the evolution of the two populations’ CSI behaviors.

Additionally, CSI has assumed a pivotal role in modern management practices, particularly in the digital economy, where media transparency prevails, especially among medium to large-sized firms (Kölbel et al., 2017). In consumer markets, the significance of CSI is amplified, as consumers increasingly prioritize CSI information in their consumption decisions (Scheidler and Edinger-Schons, 2020). While it is acknowledged that other stakeholders, such as governments and non-governmental organizations, also influence firms’ CSI behaviors, we contend that the interaction between firms and consumers holds paramount importance, especially in the case of medium to large-sized firms operating in consumer markets, where their visibility is more pronounced (Valor et al., 2022). Consequently, our model is designed to scrutinize the dynamic interplay between firms and consumers. Within this specific research context, the demarcation between CSR and CSI behaviors is relatively distinct, and firms are bestowed with the flexibility to opt for either strategy based on the attendant benefits and costs that surface during their interactions with consumers. Therefore, our model encompasses both socially responsible and socially irresponsible firms within the firm population. Correspondingly, within the consumer population, there are individuals with strong CSR perception who actively consider CSR and CSI information in their decision-making processes, as well as consumers who primarily prioritize the utilitarian value of products. This leads to a spectrum of CSR perception within the consumer population.

An evolutionary game model

To focus on dynamic interactions between firms’ CSI behaviors and consumers’ perception, we assume that there are two populations: firms and consumers in our evolutionary model. Based on value capture theory, in our model, for a CSR compliant firm, the private profit \(p - c\) is strictly monotonically increasing on a price parameter p > 0 and decreasing on the costs of production or services p > c > 0 (Gans and Ryall, 2017). For an irresponsible firm, its costs will be lowed to \(c - k \,>\, 0\) (Price and Sun, 2017). When it faces a consumer with weak CSR perception, its profit is \(\alpha p - c + k\, >\, p - c\), where \(1\, >\, \alpha\, >\, 0\) suggesting that it will reduce the price and still make more profits than a CSR compliant firm. If not, it will not adopt an irresponsible behavior. This assumption is consistent with the observation in the real world. A firm is motivated to conduct a CSI behavior because it expects to make more profits even it must decrease the price of its product (Riera and Iborra, 2017). On the contrary, when it makes a transaction with a consumer with strong CSR perception, the profit is \(\alpha p - c + k - \beta \tau\), where τ indicates transaction costs due to trust problems. β represents the bargaining power of consumers over firms in the industrial ecosystem (Brandenburger and Stuart, 2007).

For a consumer with strong CSR perception, its profit is \(v + w - p\) when it faces a CSR compliant firm, where v and w are the utility and increased willingness to pay for the firm’s products or services, respectively (Makadok and Ross, 2018). When it faces an irresponsible firm, its profit is \(v - \alpha p - \tau (1 - \beta )\). For a consumer with weak CSR perception, its profit is \(v - p\) when it faces a CSR compliant firm. When it faces an irresponsible firm, its profit is \(v - \alpha p\). The payoff matrix is shown in Table 1. Firms and consumers possess the flexibility to adapt their strategies by weighing the benefits derived from their choices against the average benefits within their respective populations. While we initially designate firms and consumers as distinct adopters of specific strategies at a given point in time, they retain the capacity to alter their strategies over the course of the timeline. This aligns with practical observations where, from a holistic standpoint, firms and consumers frequently find themselves navigating a middle ground, emphasizing the dynamic and adaptive nature of strategic choices in response to changing circumstances.

Table 1 The payoff matrix of the game between firms and consumers.
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Evolutionary equilibrium of game strategy

In this section, we analyze the evolutionary equilibrium of the game using replicator dynamics, a method widely utilized in the literature to study interactions between two populations (da Silva Rocha, 2013; da Silva Rocha et al., 2015). This approach assumes that populations are well-mixed, meaning any firm can be visited by any consumer. Furthermore, replicator dynamics describe the dynamic evolution of the proportion of the population adopting a specific strategy. According to the principle of evolutionary game theory, if the payoff of a strategy is higher than the average fitness of the population, the proportion of the strategy will increase over time (Friedman, 1991). There are some other assumptions: (1) only natural selection of strategies is considered and there is no mutation, (2) agents in the evolutionary game are bounded rational and learn from others i.e., firms will learn from other firms with better performance, (3) the game’s equilibrium stable strategy is a result of learning, imitation, and adjustment. In our model, we assume that the proportion of companies pursuing a CSR-compliant strategy is x, in which case the proportion of CSI companies is 1 − x. Similarly, this paper assumes that the proportion of strong CSR perception consumers is y, then the proportion of weak CSR perception consumers is 1 − y (Friedman, 1991). According to the replicating dynamic continuous deterministic equation, the growth rate of a certain group of strategy participants is equal to the difference between the fitness of the strategy group and the average fitness of the total group (Taylor and Jonker, 1978). Its dynamic equation is expressed as:

$$\left\{ \begin{array}{l}\frac{{dx}}{{dt}} = x(\varepsilon D_1Y^T - XD_1Y^T)\\ \frac{{dy}}{{dt}} = y(\varepsilon D_2X^T - YD_2X^T)\end{array} \right.$$
(1)

In the above equation, \({{{\mathrm{D}}}}_{{{\mathrm{1}}}} = \left[ {\begin{array}{*{20}{c}} {p - c} & {p - c} \\ {\alpha p - c + k - \beta \tau } & {\alpha p - c + k} \end{array}} \right]\) is firms’ payoff matrix, \({{{\mathrm{D}}}}_{{{\mathrm{2}}}} = \left[ {\begin{array}{*{20}{c}} {v + w - p} & {v - \alpha p - \tau (1 - \beta )} \\ {v - p} & {v - \alpha p} \end{array}} \right]\) is consumers’ payoff matrix. \(\varepsilon = \left\{ {1,0} \right\}\) is a unit vector. \({{{\mathrm{X}}}} = \left\{ {{{{\mathrm{x}}}},1 - {{{\mathrm{x}}}}} \right\}\) and \({{{\mathrm{Y}}}} = \left\{ {{{{\mathrm{y}}}},1 - {{{\mathrm{y}}}}} \right\}\) are the proportion vector for firms and consumers. \({{{\mathrm{U}}}}_1 = \varepsilon {{{\mathrm{D}}}}_1{{{\mathrm{Y}}}}^{{{\mathrm{T}}}}\) and \({{{\bar{\mathrm U}}}} = {{{\mathrm{XD}}}}_1{{{\mathrm{Y}}}}^{{{\mathrm{T}}}}\) are respectively the fitness of the firms who adopt CSR strategy and the average fitness of all firms. \(V_1 = \varepsilon D_2X^T\) and \({{{\bar{\mathrm V}}}} = {{{\mathrm{YD}}}}_2X^{{{\mathrm{T}}}}\) are respectively the fitness of strong CSR perception consumers and the average fitness of all consumers. This leads to the following replicator dynamic equation:

$$\left\{ \begin{array}{ll} \frac{{d{{{\mathrm{x}}}}}}{{dt}} = x(1 - x)\left\{ y[(p - c) - (\alpha p - c + k - \beta \tau )]\right.\\ \left.\qquad+ \,(1 - y)[(p - c) - (\alpha p - c + k)]\right\} = F(x) \\ \frac{{dy}}{{dt}} = y(1 - y)\left\{ x[(v + w - p) - (v - p)]\right.\\ \left.\qquad+ \,(1 - x)[v - \alpha p - \tau (1 - \beta ) - (v - \alpha p)]\right\} = F(y) \end{array} \right.$$
(2)
$$\left\{ {\begin{array}{ll} {\frac{{d{{{\mathrm{x}}}}}}{{dt}} = x(1 - x)(\beta \tau y + p - \alpha p - k) = F(x)} \\ {\frac{{dy}}{{dt}} = y(1 - y)\{ x[w + \tau (1 - \beta )] - \tau (1 - \beta )\} = F(y)} \end{array}} \right.$$
(3)

Based on the idea that a certain strategy is said to evolutionary stable if the population share of mutants is sufficiently small (Mailath, 1998). We set F(x) = 0, F(y) = 0, and obtain four or five possible evolutionary stationary points on the plane M = {(x, y)|0 ≤ x, y ≤ 1}. If \(p(1 - \alpha ) + \beta \tau\, > \,k \,> \,p(1 - \alpha )\) (scenario 1), there are five stationary points on the plane:(0,1), (0,1), (1,0), (1,1), \(\left( {{{{\mathrm{x}}}}^ \ast = {\textstyle{{\tau (1 - \beta )} \over {w + \tau (1 - \beta )}}},{{{\mathrm{y}}}}^ \ast = {\textstyle{{k - p(1 - \alpha )} \over {\beta \tau }}}} \right)\). If \(k - p(1 - \alpha )\, > \,\beta \tau\) (scenario 2), there are four stationary points on the plane: (0,1), (0,1), (1,0), (1,1).

According to the method proposed by Friedman (1991), we could determine whether a dynamic evolutionary system is stable or not through the Jacobian matrix. In a discrete system, the evolutionary equilibrium point reaches stability only when detJ > 0 and trJ < 0 for the Jacobian matrix:

$$J = \left[ {\begin{array}{*{20}{c}} {\frac{{\partial F(x)}}{{\partial x}}} & {\frac{{\partial F(x)}}{{\partial y}}} \\ {\frac{{\partial F(y)}}{{\partial x}}} & {\frac{{\partial F(y)}}{{\partial y}}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {(1 - 2x)(\beta \tau y + p - \alpha p - k)} & {\beta \tau x(1 - x)} \\ {y(1 - y)[w + \tau (1 - \beta )]} & {(1 - 2y)\left\{ {x\left[ {\left( {w + \tau (1 - \beta )} \right.} \right] - \tau \left( {1 - \beta } \right)} \right\}} \end{array}} \right]$$

The detJ:

$$\begin{array}{l}\det J = (1 - 2x)(\beta \tau y + p - \alpha p - k)(1 - 2y)\left\{ {x\left[ {\left( {w + \tau (1 - \beta )} \right.} \right]} \right.\\ - \,\left. {\tau (1 - \beta )} \right\} - \beta \tau x(1 - x)y(1 - y)[w + \tau (1 - \beta )]\end{array}$$
(4)

The trJ:

$${{{\mathrm{tr}}}}J = (1 - 2x)(\beta \tau y + p - \alpha p - k){{{\mathrm{ + }}}}(1 - 2y)\left\{ {x\left[ {\left( {w + \tau (1 - \beta )} \right.} \right] - \tau (1 - \beta )} \right\}$$
(5)

Table 2 shows the results of the determinant and trace of the Jacobian matrix for the possible five evolutionary equilibrium points. Based on the value of parameters above, there are two scenarios which lead to different equilibrium points and evolutionary stable strategies.

Table 2 Determinant and trace of the Jacobian matrix corresponding to equilibrium points.
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Using the determinant and trace of the Jacobian matrix mentioned earlier, we derived the evolutionary stable strategies for the populations. Two scenarios, determined by different parameters in the payoff matrix, are presented in Table 3. The stability analysis results are also shown in Table 3, and Fig. 1 illustrates the replication phase diagram for Scenarios 1 and 2.

Table 3 Stability analysis of the equilibrium for two scenarios.
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Fig. 1: The replication dynamic phase diagram.
figure 1

The x-axis and y-axis represent the proportions of firms and consumers opting for “CSR compliant” and “strong CSR perception” strategies, respectively. The phase diagrams visually depict the dynamic trends of these proportions within the evolutionary system under specific states of x and y. a illustrates the phase diagram of Scenario 1, while b depicts the phase diagram of Scenario 2.

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Scenario 1 \(p(1 - \alpha ) + \beta \tau\, >\, k\, >\, p(1 - \alpha )\). There are two possible evolutionary stable equilibrium points for the system based on the initial states. If the initial state is in the OBCD region in Fig. 1, the equilibrium point is C (1, 1), where firms choose CSR-compliant strategies, and consumers have strong CSR perception. If the initial state is in the OBAD region in Fig. 1, the equilibrium point is A (0, 0), where firms choose CSI strategies, and consumers have weak CSR perception.

Scenario 2 \(k\, > \,p(1 - \alpha ) + \beta \tau\). In this scenario, the evolutionary stable point is A (0, 0), with firms adopting CSI strategies, and consumers having weak CSR perception. Irrespective of consumers’ CSR perception, firms using CSI strategies yield higher net utility compared to those employing CSR-compliant strategies. Consequently, weak CSR perception consumers enjoy greater net profit than their strong CSR perception counterparts.

In sum, there are two possible ESS: (0,0), (1,1) depending on the parameters and initial conditions of the system. It is shown that efficient market only happens when \(p(1 - \alpha ) + \beta \tau\, > \,k \,> \,p(1 - \alpha )\) and initial status is in the area OBCD in Fig. 1. In other words, a healthy market can be achieved when the advantages of employing the CSI strategy \(k - p(1 - \alpha )\) are outweighed by the rising transaction costs \(\beta \tau\), and when there is an initial presence of more CSR-compliant firms and consumers with strong CSR perception in the two populations. The results also indicate that the decrease of consumers’ bargaining power mitigates the possibility of an efficient market. Strengthening the bargaining power of consumers increases the possibility of an efficient market.

Numerical examples and sensitivity analysis

Numerical examples

Based on the evolutionary equilibrium analysis of our model, we further test the results by numerical examples using Python. The parameter combination settings adopted in this section are shown in Table 4. The parameters have been configured to simulate two distinct consumer markets where prices, production costs, and other variables are largely comparable. However, a key distinction lies in the degree of market segmentation, with one market being more fragmented while the other exhibits greater centralization (Blyler and Coff, 2003). Consequently, the bargaining power of consumers significantly differs between these two markets, as outlined in Table 4. Based on various parameter settings and the initial conditions of the two-group system, different evolutionary states can be observed in the numerical simulations.

Table 4 The parameter settings of simulations.
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The simulation results were shown as follows:

Case 1. Considering the parameters in Case 1, where \(p(1 - \alpha ) + \beta \tau > k > p(1 - \alpha )\) and \({{{\mathrm{x}}}}^ \ast = {{{\mathrm{0}}}}{{{\mathrm{.5}}}},{{{\mathrm{y}}}}^ \ast = 0.5\), the bargaining power of firms and consumers is comparable, indicating that transaction costs are equally distributed between the two agent groups. With the initial state of the system (x, y) set to (0.1, 0.1), (0.45, 0.45), (0.55, 0.55), (0.9, 0.9), two evolutionary stable outcomes are observed: (CSI, Weak CSR perception) and (CSR, Strong CSR perception). In cases where the initial state is configured as (0.1, 0.1) or (0.45, 0.45), firms tend to adopt the CSI strategy, while consumers lean towards weak CSR perception. Conversely, when the initial state is set as (0.55, 0.55) or (0.9, 0.9), firms are more inclined to adopt the CSR-compliant strategy, and consumers are more likely to have strong CSR perception. The numerical simulation results align with the equilibrium analysis of the evolutionary game model as described in the previous section (Fig. 2).

Fig. 2: The depiction of the strategies' evolution and the phase diagram of the evolutionary model in Case 1.
figure 2

a The evolution of the strategies between firms and consumers in Case 1. Note: The x-axis represents time, while the y-axis depicts the share of the population opting for “CSR compliant” and “strong CSR perception” strategies. a Illustrates how the initial state of the system influences the evolutionary stable strategies in Case 1 over time. b The phase diagram of the evolutionary model in Case 1. Note: The x-axis and y-axis represent the proportions of firms and consumers opting for “CSR compliant” and “strong CSR perception” strategies, respectively. b Elucidates how the initial state of the system influences the evolutionary stable strategies in Case 1 through a phase diagram.

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Case 2. In the context of Case 2, the parameter values indicate that \(k > p(1 - \alpha ) + \beta \tau\), signifying that firms have greater bargaining power compared to consumers. This implies that consumers bear the majority of transaction costs. Given the initial state of the system (x, y) as (0.1, 0.1), (0.45, 0.45), (0.55, 0.55), (0.9, 0.9), there is one evolutionary stable outcome: (CSI, Weak CSR perception). In this scenario, firms adopt the CSI strategy, while consumers have weak CSR perception. The numerical simulation results align with the equilibrium analysis presented in the previous section (Fig. 3).

Fig. 3: The depiction of the strategies' evolution and the phase diagram of the evolutionary model in Case 2.
figure 3

a The evolution of the strategies between firms and consumers in Case 2. Note: The x-axis represents time, while the y-axis depicts the share of the population opting for “CSR compliant” and “strong CSR perception” strategies. a Elucidates how the initial state of the system influences the evolutionary stable strategies in Case 2 over time. b The phase diagram of the evolutionary model in Case 2. Note: The x-axis and y-axis represent the proportions of firms and consumers opting for “CSR compliant” and “strong CSR perception” strategies, respectively. b Elucidates how the initial state of the system influences the evolutionary stable strategies in Case 2 through a phase diagram.

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Sensitivity analysis

As demonstrated in the equilibrium analysis and numerical examples above, the evolutionary outcomes of the two-group system are highly influenced by the industrial structures, which in turn affect the relative bargaining power between firms and consumers. Therefore, in this section, we conducted a sensitivity analysis to examine the impact of industrial structures on the system’s equilibrium. The outcomes of sensitivity analysis are shown in Table 5. Furthermore, consumers’ added willingness to pay for CSR has an impact on the OBCD area in Case 2, although it doesn’t alter the outcome of the evolutionary equilibrium. To delve into the effects of industrial structure and consumers’ willingness to pay for CSR, we varied the parameters β and w while keeping all other parameters constant (v = 15, p = 10, c = 5, k = 2, α = 0.9, τ = 4). The results of this sensitivity analysis are presented in Table 5.

Table 5 The effects of industrial environments on the system equilibrium.
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From the results of the sensitivity analysis, we can derive the following insights:

When consumers have low bargaining power, a pattern emerges where firms tend to adopt a CSI strategy while consumers exhibit a weak CSR perception. In this scenario, the market experiences inefficiency and falls into a morality trap. The added willingness to pay for CSR doesn’t impact the system’s evolutionary outcomes.

When consumers’ bargaining power reaches a sufficiently high level, there are two possible evolutionary equilibria for the system: (CSI, Weak CSR perception) and (CSR, Strong CSR perception). The final outcome is contingent on the initial states of the system, revealing a path-dependent feature of the system. If the initial state falls within the OBCD area, it indicates a healthy market where firms behave socially responsibly, and consumers have a strong CSR perception. As the bargaining power of consumers and the willingness to pay for CSR increase, the OBCD area expands, suggesting a greater likelihood of a healthy market.

Conclusions

In our study, we concentrated on investigating the interplay between firms’ CSI behavior (that remains within legal bounds) and consumers’ CSR perception within a context where firms weigh the advantages of CSI against transaction costs, and consumers grapple with the trade-off between minimizing transaction costs and maximizing utility. We devised an evolutionary game model to scrutinize these trade-offs, considering the competing interests of both firms and consumers. We commenced with a baseline evolutionary game model, employing replicator dynamics to scrutinize the equilibrium within our framework. Subsequently, we expanded our model through numerical simulations and sensitivity analyses. The simulation results unveil two potential evolutionary outcomes: (CSR, Strong CSR perception) and (CSI, Weak CSR perception), contingent on consumers’ perception, industrial contexts, and initial conditions.

The equilibrium analysis conducted using replicator dynamics provides valuable insights into firms’ CSI strategies and consumers’ CSR perception from a long-term perspective (Murphy and Schlegelmilch, 2013). This analysis is grounded in a context where consumers perceive CSI behaviors, and transaction costs are allocated in a specific industrial structure (He et al., 2021). The results of the equilibrium analysis underscore the significance of the initial state of the system as a crucial precondition for fostering an efficient and healthy market. This finding indicates that in cases where CSI behaviors do not violate the laws, an unhealthy market situation can easily emerge unless the social environment is initially well-established.

The extended model provides valuable and comprehensive insights into the evolution of the system, considering the influence of contextual factors on the evolutionary outcomes. We ascertain that an escalation in consumers’ bargaining power contributes to an elevated likelihood of achieving an efficient market. Conversely, diminished consumers’ bargaining power incentivizes an unhealthy market state. As the bargaining power of consumers and their willingness to pay for CSR behaviors increase, the area of initial states leading to the outcome of (CSR, Strong CSR perception) expands. This suggests that the possibility of a healthy market, characterized by firms’ CSR compliance and consumers’ strong CSR perception, becomes higher.

Our study’s findings make a significant contribution to the ongoing discourse on firms’ CSI behaviors. By adopting an interactive and dynamic perspective, our research sheds light on the intricate micro-level mechanisms underpinning CSI, thereby enhancing our understanding of this crucial aspect of corporate behavior (Lange and Washburn, 2012). Prior research predominantly centered on the static and varied reactions of consumers to CSI, frequently overlooking the dynamic interplay between firms and consumers during market interactions (Jasinenko et al., 2020). By integrating the value capture theory and drawing on insights from both strategic management and market research, we reveal that CSI behaviors are more prone to arise when firms possess significant bargaining power compared to consumers. Moreover, we identify that consumers’ willingness to pay for CSR can reduce the likelihood of CSI, although this influence is not entirely deterministic. Furthermore, our study underscores the importance of considering path dependence, where the dynamic industrial environment can influence the adoption of CSI or CSR compliance strategies. The initial state of a system becomes crucial in shaping the evolutionary outcome in a specific market, reflecting a self-reinforcing feature for firms’ CSI behaviors.

There are several promising avenues for further expanding and enriching this study. (1) Structured Population Model: To better capture the effects of localization on the evolution of firms’ CSI behaviors, a structured population model could be developed. This model could consider the influence of local incumbents on firms’ decisions to adopt corporate social behaviors. Firms may be more inclined to learn and imitate CSR practices from local firms in their vicinity, leading to region-specific patterns of CSI adoption. (2) Heterogeneous Ability and Payoffs: Introducing heterogeneity in abilities and payoffs among firms and consumers would add a more realistic dimension to the model. In real-world scenarios, firms and consumers often possess varying levels of resources, capabilities, and preferences. Accounting for this heterogeneity could provide valuable insights into how the dynamics of CSI behaviors and CSR perception unfold across diverse market participants. This consideration would shed light on how regulatory frameworks influence firms’ strategic choices concerning CSI behaviors and consumers’ responses to such practices. By adopting these approaches, the study’s findings would be strengthened, and a more comprehensive understanding of the interplay between firms’ CSI behaviors and consumers’ CSR perception in complex market environments could be achieved.