Leadership style, as one of the important factors affecting organizational management and leadership effectiveness, has received a lot of attention and focus from the management community [1]. In the early stages of leadership theory research, Chinese scholars tended to base their work on Western leadership theories and value systems. However, different cultural contexts nurture and shape distinct leadership styles, which means that one leadership style has different effects in different contexts. It is unreasonable to apply leadership styles from Western cultural contexts to Chinese cultural societies. Consequently, The structure of Chinese society, characterized by a”differential order pattern”, has emerged. Existing research has confirmed its widespread existence and practical effectiveness in Chinese enterprise organizations [2]. As leaders’ behavior is influenced by their unique culture, they treat their employees differently from inside and outside. This is reflected in a “differential” style of leadership [3]. Specifically, differential leadership typically classifies individuals into insiders and outsiders based on three criteria: closeness (the degree of intimacy or proximity to the leader loyalty (the level of allegiance to the leader and the organization) and talent (the individual’s exceptional abilities). Furthermore, in Chinese family enterprises that emphasize kinship, parental authority, a highly partial differential leadership style is more likely to exist. The leaders tend to favor insiders by providing them with preferential treatment and greater access to resources, a privilege not extended to outsiders. This unequal favoritism motivates all members to strive harder to gain the leader’s recognition, despite its inherent unfairness. Therefore, exploring the differential leadership style of Chinese enterprise leaders within the context of Chinese family enterprises holds significant theoretical and practical value.

In the VUCA era, with the increasing competition among family enterprises in the transition economy, the uncertainty of the economic and social environment has brought the views and suggestions of employees to a wider attention. Employees, as a crucial part of enterprise management, possess numerous key information and can keenly identify potential crises in enterprise management. However, under external pressure, they often choose silence to express their opinions. This employee silence not only adversely affects their emotional communication and interpersonal relationships but also undermines the quality of decision-making by corporate management [4]. Under the influence of China’s traditional “circle” culture, a ripple-like relationship network has been formed within China’s enterprises, that is, the leader is the core and spreads to the outside layer by layer, and then derives the leadership style with local characteristics. Existing research on the impact of differential leadership on employee silence behavior, especially empirical research, has largely been conducted along two independent threads: the insiders and outsiders. The delineation and formation of the insiders and outsiders in the workplace stem from leaders’ perceptions of different emotional responses from their subordinates. However, the inter group boundaries between insiders and outsiders are permeable to a certain extent, with insiders potentially being excluded from the group by the leader and outsiders having the opportunity to become insiders through their efforts. Therefore, regardless of whether they are insiders or outsiders under differential leadership, employees will engage in positive behaviors to win the favor of their leaders [5]. For insiders under differential leadership, they tend to reduce employee silence and actively contribute suggestions for organization to maintain their current roles and avoid replacement by other organizational members. Equally, outsiders under differential leadership also strive to adopt proactive strategies to achieve upward mobility and find ways to become part of the insiders’ group. Leaders who effectively utilize this differentiated management strategy and intentionally strengthen their leadership over employees while adhering to the principle of putting the public interest first can generate positive workplace stimulation and improvement effects [6].

This study adopts the method of dynamic game and uses the perspective of the interaction between insiders and outsiders to study the impact of insiders’ and outsiders’ on silent behavior based on the perceived benefits of the dynamic status flow of differential order leadership. We believe that differential leaders, as representatives of the organization (or team), are the formulators of organizational (or team) decisions and strategies, artificially creating a division between “insiders” and “outsiders” among employees. Thus, both insiders and outsiders strive to pursue their maximum benefits. Insiders’ interests are mainly reflected in improving their own benefits and performance levels and maintaining their status as members of the leader’s insider group. Outsiders’ interests are mainly reflected in improving their own benefits and achieving mobility in group status [7]. Therefore, the status mobility of employees within family enterprises is a process involving both insiders and outsiders, requiring a dynamic game between them based on perceived benefits and significantly impacting their performance levels through this process. This study addresses two key aspects within the context of family enterprises in Chinese traditional culture. First, it compensates for the inadequacy of research on self-efficacy and out-group favoritism within the organizational framework of family enterprises by constructing an analytical framework that examines the influence of “differential leadership—self-efficacy/out-group favoritism—employee silence behavior” in family enterprises. Second, it focuses on the relatively novel topic of the relationship between differential leadership and employee silence behavior in family-owned enterprises, both theoretically and practically. From a micro-level perspective, this study provides a new direction for alleviating employee silence behavior and facilitating successful transformation in Chinese family enterprises. In doing so, the research not only enriches the theoretical understanding of leadership styles specific to the Chinese cultural context but also offers practical implications for improving organizational dynamics and promoting sustainable development in family businesses.

This study considers a simplified version of the Prisoner’s Dilemma game and designs a game model of differential leadership affecting employees’ non-silence behavior [8]. The study refines the participants of non-silence behavior into insiders and outsiders, assuming that the categories of insiders and outsiders as defined by the leader are completely consistent with the employees’ own perception of being insiders or outsiders. In the actual workplace, there is an objective reality of information asymmetry between employees. Therefore, based on their own actual earnings, they will be compared with other members of the organization, so as to form an index of actual earnings within the organizational network. It is assumed that the actual benefit generated by both participating employees taking non-silence behavior is P , the actual benefit generated by both participating employees taking silence behavior is R , and the different behavior choices of the participating employees result in the actual benefit S for the employee implementing non-silence behavior, and the actual benefit T for the employee implementing silence behavior. That is, the parameters P , R , S , T represent the actual benefits resulting from an individual’s game with another individual who adopts the same or different behavioral strategies. Therefore, the overall actual benefit C i ( t ) of individual i after t rounds of the game can be expressed as follows: C i t = ∑ j ∈ ∂ i 1 4 1 + s i 1 + s j R + 1 4 1 + s i 1 − s j S + 1 4 1 − s i 1 + s j T + 1 4 1 − s i 1 − s j P (1) In Equation 1, where s i = 1 indicates that individual i adopts a non-silence strategy, s i = − 1 indicates that individual i adopts a silence strategy, and ∂ i represents the set of i ’s neighbors.

This study focuses on the effect of differential leadership on the silent behavior of its own employees and outsiders. we assume that both insiders and outsiders participating in the game are rational economic agents. In the context of incomplete information symmetry, they pursue the maximization of their own interests during their respective positional mobility processes. However, the interest demands of these two gaming entities do not fully align. The expected benefits for insiders primarily manifest as improvements in their personal interests and performance levels, as well as maintaining their status and favorable impressions within the leader’s insider group. In contrast, the expected benefits for outsiders mainly involve enhancements in their personal interests and performance levels, along with achieving mobility in group status. Moreover, despite insiders and outsiders working together over the long term, it is difficult for each to gain a total understanding of the other’s information [9]. Therefore, the comprehensive benefits arising from different behaviors chosen by employees under differential leadership can be formulated as follows: c C I A t = ∑ j ∈ ∂ i 1 2 1 + s j R + 1 2 1 − s j S C I S t = ∑ j ∈ ∂ i 1 2 1 + s j T + 1 2 1 − s j P C O A t = C I A t − β U t C O S t = C I S t − β U t (2) In Equation 2, where C I A ( t ) represents the comprehensive actual benefits generated by insiders participating in the game who adopt non-silence behaviors, C I S ( t ) represents the comprehensive actual benefits generated by insiders who adopt silence behaviors, C O A ( t ) represents the comprehensive actual benefits generated by outsiders participating in the game who adopt non-silence behaviors, and C O S ( t ) represents the comprehensive actual benefits generated by outsiders who adopt silence behaviors. Thus, the actual benefit space for insiders choosing different behavioral strategies is denoted as S t 1 {adopting non-silence behaviors C I A ( t ) , adopting silence behaviors C I S ( t ) }, and the actual benefit space for outsiders’ behavioral strategies is denoted as S t 2 {adopting non-silence behaviors C O A ( t ) , adopting silence behaviors C O S ( t ) }. Additionally, β represents the degree of prejudice or aversion displayed by the leader towards outsiders, and U ( t ) represents the actual benefit gap between insiders and outsiders due to the leader’s differential treatment of employees.

Due to the uncertainty of information, employees cannot guarantee that leaders will definitely provide them with the same actual benefits as other employees when choosing to adopt non-silence behaviors. Employees merely observe and compare the behaviors of others and believe that there is a certain probability of obtaining equivalent benefits after they engage in the same non-silence behaviors. Since this benefit is not necessarily granted by the leader but is a potential benefit perceived by the employee, it is considered a perceived benefit. Therefore, there is a discrepancy between individual perceived benefits and actual benefits. Based on the weight effect, this study takes perceived benefits as the main focus of the process. The perceived benefit for individual i is defined as follows: φ i = C i t exp − − ln P s i γ (3) In Equation 3, where P s i = C i ( t ) δ s i , 1 + C i ( t ) δ s i , − 1 ∑ k = 1 N C k , δ ( x , y ) is the δ function, defined as δ ( x , y ) = 1 , x = y 0 , x ≠ y , and γ ∈ [ 0,1 ] denotes the rationality coefficient of the individual.

In particular, the employee groups can be categorized into non-silence insiders, silence insiders, non-silence outsiders, and silence outsiders. Therefore, this study sets forth the perceived benefits generated by different types of employees engaging in various behavioral strategies: φ I A = C I A t exp − − ln P S I A γ φ I S = C I S t exp − − ln P S I S γ φ O A = C O A t exp − − ln P S O A γ φ O S = C O S t exp − − ln P S O S γ (4) In Equation 4, where φ I A represents the perceived benefits derived from non-silence behavior adopted by insiders engaging in the game, while φ I S represents the perceived benefits from their silence behavior, with φ I A > φ I S . Similarly, φ O A signifies the perceived benefits from non-silence behavior exhibited by outsiders, and φ O S indicates the perceived benefits from their silence behavior, with φ O A > φ O S . Insiders, motivated by self-efficacy, engage in non-silence behavior to pursue greater benefits, doing so as a response to their actual possession of “psychological capital” and with the aim of maximizing their interests. Conversely, outsiders, driven by out-group favoritism, engage in non-silence behavior to gain future benefits by reversing their current disadvantaged position [10]. These outsiders form positive behavioral orientations based on their aspiration to possess “psychological capital”. Consequently, compared to the actual possession of “psychological capital” represented by self-efficacy, the aspirational possession of “psychological capital” represented by out-group favoritism leads to employees engaging in the same non-silence behavior but not achieving the same perceived benefits, with φ I A > φ O A . Based on these assumptions and extensive empirical research demonstrating a positive correlation between work engagement and employee performance [11], employees believe that demonstrating work engagement through non-silence behavior can gain performance recognition from leaders and potentially earn certain rewards.

Furthermore, employees individually decide whether to change their strategies based on the perceived benefits derived from choosing the behavior of their colleagues. This process can be described as follows: Firstly, employee i with behavioral strategy s i will randomly select a colleague j with behavioral strategy s j to compare the perceived benefits of their behaviors. Secondly, employee i will decide whether to adopt the behavioral strategy of employee j . This study applies the Fermi’s Golden Rule, which is a probabilistic simulation approach for individuals to select the behavioral strategy of colleague j . P s i ← s j = 1 1 + exp − φ j − φ i / k (5) In Equation 5, where φ i and φ j represent the perceived benefits of employee i and the perceived benefits derived from employee i choosing the behavior of employee j , respectively. In physics, this corresponds to the k value of inverse temperature, and in this study, it provides a measure of the intensity of natural selection. For k = ∞ , we obtain P s i ← s j = 1 / 2 , which implies that employees react weakly to differences in perceived benefits, and the strategies of individuals with higher perceived benefits do not demonstrate a unique advantage. Without losing generality, this study sets the k value to 0.1, meaning that employees who perform better are likely to transmit their strategies to other colleagues, but employees may also sometimes learn behavioral strategies from less successful colleagues.

(1) Employees’ non-silence behavior involves a game-playing process between the insiders and the outsiders. Through the aforementioned dynamic game analysis between insiders and outsiders, it is evident that not only do insiders require leaders’ support and encouragement to enhance their personal gains and performance levels, as well as to maintain their status and positive impressions within the leader’s insider group, but outsiders also need leaders’ acceptance and assistance to improve their personal gains, performance levels, and achieve mobility within the group hierarchy. Therefore, both insiders and outsiders need to engage in non-silence behavior to win the favor of leaders in order to achieve their optimal perceived benefits.

In summary, this study adopts a dynamic evolutionary game approach to establish a dynamic game model with incomplete information between insiders and outsiders, examining the impact of differential leadership on non-silence or silence behavior among insiders and outsiders. By analyzing the dynamic changes in perceived benefits for both insiders and outsiders, the research findings reveal that both insiders and outsiders need to demonstrate non-silence behavior to gain leaders’ attention and favor in order to achieve and maintain benefit seeking. Self-efficacy for insiders is the key driver of their non-silence behavior, while out-group favor for outsiders is the key driver. Furthermore, proactive personality further builds an organizational voice climate, generates perceived benefits, and provides relevant insights and reflections for the high-quality development of family enterprises.