The Dark Side of Leader Narcissism: The Relationship Between Leaders’ Narcissistic Rivalry and Abusive Supervision

Narcissists often attain leadership positions, but at the same time do not care for others and often engage in unethical behaviors. We therefore explored the role of leader narcissism as an antecedent of abusive supervision, a form of unethical leadership. We based our study on the narcissistic admiration and rivalry concept (NARC) and proposed a direct positive effect of leaders’ narcissistic rivalry—the maladaptive narcissism dimension—on abusive supervision. In line with trait activation and threatened egotism theory, we also proposed a moderated mediation assuming that leaders high in narcissistic rivalry would be particularly prone to showing abusive supervision in reaction to followers’ supervisor-directed deviance, as this form of follower behavior would threaten their self-esteem. We conducted a field study with leader–follower dyads (Study 1) and an experimental vignette study with leaders (Study 2). Leaders’ narcissistic rivalry was positively related to abusive supervision (intentions) in both studies. This effect was independent of followers’ supervisor-directed deviance and leaders’ perceived self-esteem threat. We discuss our findings in light of the NARC, as well as threatened egotism theory, and offer directions for future research. Finally, we make practical recommendations for organizations.

Over the last two decades, research has shown that followers and organizations as a whole suffer from abusive supervision, a form of unethical leadership defined as leaders' "sustained display of hostile verbal and nonverbal behaviors, excluding physical contact" (Tepper, 2000). Abusive supervision includes morally unacceptable behaviors, such as lying to followers, talking badly about them, or making them responsible for the leader's own mistakes. Extant research has shown that abusive supervision is associated with a wide range of harmful outcomes in followers, such as lower levels of life satisfaction, diminished well-being, and less productivity (for overviews, see e.g., Martinko et al., 2013;Schyns & Schilling, 2013). These findings highlight that abusive supervision is a serious problem for organizations and individuals and make it all the more important to study its antecedents (for reviews, see Martinko et al., 2013;Tepper et al., 2017;Zhang & Bednall, 2016).
In our study, we strive to complement prior research on the antecedents of abusive supervision and provide new theoretical insights using existing theory to identify factors associated with this specific form of destructive leadership. As abusive supervision refers to leader behaviors, investigating leader-related antecedents is key. Business ethics scholars have been particularly concerned with the role of leader narcissism as an antecedent of abusive supervision, as narcissism is linked to unethical and self-serving behaviors (e.g., Harrison et al., 2018). Narcissism is defined as "a relatively stable individual difference consisting of grandiosity, self-love and inflated self-views" (Campbell et al., 2011). It is particularly relevant in the study of leadership because narcissists are highly motivated to get ahead and often attain leadership positions (e.g., Grijalva et al., 2015). This is even more important, as narcissists are interpersonally difficult (Morf & Rhodewalt, 2001), which may be reflected in the way narcissistic leaders behave toward their followers (Hansbrough & Jones, 2014).
However, empirical findings have been ambiguous, with some studies reporting a direct association between leader narcissism and abusive supervision (e.g., Waldman et al., 2018;Whitman et al., 2013) and others reporting none (Nevicka et al., 2018;Wisse & Sleebos, 2016). On the one hand, these inconclusive findings are problematic because they still leave open the question of whether narcissism is good or bad for organizations (e.g., Campbell et al., 2011). On the other hand, previous ambiguous results also highlight the need to theoretically rethink the role of narcissism in negative leadership. This is especially relevant in light of robust evidence connecting narcissism to leader emergence (Grijalva et al., 2015). Hence, we build our study on the narcissistic admiration and rivalry concept (NARC; Back et al., 2013) and aim to provide theoretical insights into how narcissism and abusive supervision interrelate in order to clarify previous, inconclusive findings on narcissism and abusive supervision (Nevicka et al., 2018;Waldman et al., 2018;Whitman et al., 2013;Wisse & Sleebos, 2016).
Unlike prior research, which has neglected the facet structure of narcissism (Nevicka et al., 2018;Waldman et al., 2018;Whitman et al., 2013;Wisse & Sleebos, 2016), the NARC differentiates between agentic and antagonistic sides of narcissism, which each have distinct social consequences (Back et al., 2013;Helfrich & Dietl, 2019). Prior research employing the NARC in an organizational setting has shown, for instance, that the agentic side of narcissism (called narcissistic admiration) is positively associated with empowerment, whereas the antagonistic side of narcissism (called narcissistic rivalry) is negatively associated with empowerment (Helfrich & Dietl, 2019). Overall, according to the NARC, the negative consequences of narcissism (i.e., aggressive, immoral, and manipulative behaviors) can be traced back to narcissistic rivalry, whereas narcissistic admiration should be unrelated to social conflict (Back et al., 2013). Therefore, we assume that only leaders' narcissistic rivalry (but not their narcissistic admiration) is positively related to abusive supervision. By building our study on the two-dimensional narcissism model of the NARC, we extend prior research on leader narcissism and abusive supervision, which has not differentiated between dimensions of narcissism.
Furthermore, from an ethics perspective, it would be onesided to look for causes of abusive supervision only in the leader. Hence, we turned to relevant theory to derive antecedents for abusive supervision relating to the situation as, according to trait activation theory (Tett & Burnett, 2003;Tett & Guterman, 2000), traits are triggered by situational cues. In line with this reasoning, we do not expect leadership to occur in a vacuum, and consider the role of followers as situational triggers of abusive supervision (Padilla et al., 2007;Thoroughgood et al., 2018). For instance, prior research has shown that followers are likely to experience more abusive supervision when they behave in deviant ways (Mawritz et al., 2017;Simon et al., 2015), show avoidant behaviors (Simon et al., 2015), or perform poorly (Liang et al., 2016), supporting the notion that followers might trigger abusive supervision, at least in some leaders. We wondered whether narcissistic leaders would behave abusively, particularly in response to certain follower behaviors. Hence, we took an integrative approach and examined the interactive effects of leader narcissism and follower behaviors as possible antecedents of abusive supervision, attempting to examine when and why leaders high in narcissistic rivalry show abusive supervision.
Based on threatened egotism theory (Baumeister et al., 1996;Bushman & Baumeister, 1998), we propose that followers' supervisor-directed deviance constitutes a selfesteem threat for leaders high in narcissistic rivalry. We argue that such leaders are especially likely to perceive that these followers evaluate them negatively and in a way that contradicts their grandiose self-views, thus threatening their inflated, but fragile, self-esteem. In response, we expect those leaders to show abusive supervision in order to reaffirm their superiority. In sum, we assume that followers' supervisor-directed deviance (moderator) triggers narcissistic leaders' abusive supervision via perceived selfesteem threat (mediator). We show the theoretical model of our research in Fig. 1.
Prior research on abusive supervision has relied mainly on follower ratings of abusive supervision by asking followers how often their leaders showed abusive behaviors (see Mackey et al., 2017;Tepper et al., 2017). However, it is also important to examine abusive supervision from the leaders' perspective, as self-awareness of negative leadership is an important prerequisite for leader development (Day, 2000). In the current research project, we combine both perspectives by examining follower ratings of abusive supervision in Study 1, and leader ratings of abusive supervision intentions in Study 2. By doing so, we enhance prior research in an important way by combining both follower and leader perspectives on abusive supervision.

Narcissism and Leadership
Whereas narcissists are motivated to get ahead and often emerge as leaders (e.g., Grijalva et al., 2015;Nevicka et al., 2011), they are not motivated to get along with others (Bradlee & Emmons, 1992). Furthermore, in interpersonal contexts, narcissists are not interested in, and indeed have problems building and maintaining, positive relationships with others (Morf & Rhodewalt, 2001), including in the workplace (Rosenthal & Pittinsky, 2006). Narcissists are selfish, put their own interests above others', derogate others (Park & Colvin, 2015), and tend to behave aggressively (Seah & Ang, 2008), all of which makes it likely that narcissistic leaders will show abusive supervisory behaviors (e.g., Krasikova et al., 2013;Tepper, 2007).
However, despite these theoretical assumptions, the empirical results have been ambiguous. Whereas some authors did not find a direct association between leader narcissism and abusive supervision (Nevicka et al., 2018;Wisse & Sleebos, 2016), others did (Waldman et al., 2018;Whitman et al., 2013). One reason for these mixed findings could be the previous use of unidimensional narcissism measures, which reflect different aspects of narcissism but do not differentiate between assertive and antagonistic aspects of narcissism. In particular, Wisse and Sleebos (2016) employed the four narcissism items from the Dirty Dozen scale (Jonason & Webster, 2010), which has been criticized for not capturing the unique features of narcissism (Lee et al., 2013). By contrast, Nevicka et al. (2018) and Waldman et al. (2018) used different short versions of the Narcissistic Personality Inventory (Emmons, 1984;Raskin & Hall, 1979), calculating total NPI scores that combine different dimensions of narcissism. Thus, the potential differential effects of antagonistic and agentic aspects of narcissism on abusive supervision might have cancelled each other out in these studies. Finally, Whitman et al. (2013) used Campbell et al.'s (2004 Psychological Entitlement Scale, and thus captured only one core feature of leader narcissism (i.e., leaders' psychological entitlement), while neglecting other, more antagonistic, aspects. In sum, it seems there is a potential association between leader narcissism and abusive supervision. However, it is unclear which dimensions of narcissism are relevant as previous research has used unidimensional measures combining both assertive (e.g., extraversion, self-assurance, charmingness) and antagonistic (e.g., hostility, malicious envy, aggression) aspects.
Narcissism includes both a bright (assertiveness) and a dark side (antagonism), each relating differently to leadership (Campbell & Campbell, 2009;Hogan & Kaiser, 2005), and it would seem important to employ a narcissism measure to differentiate both. Thus, we base our study on a theoretical model that explicitly takes this differentiation into account, namely, the NARC (Back et al., 2013). The NARC differentiates between agentic and antagonistic sides of narcissism, that is, narcissistic admiration and narcissistic rivalry. These two dimensions of narcissism are associated with distinct behavioral strategies (i.e., assertiveness versus antagonism) related to opposing interpersonal outcomes (e.g., social success vs social conflict, respectively). Therefore, the NARC is a potentially useful theoretical approach to clarify previously inconclusive findings on narcissism and abusive supervision as it (1) differentiates between narcissism dimensions (different from previous research treating narcissism as an unidimensional construct), and as (2) the behavioral dynamics associated with these two dimensions are related to opposing interpersonal outcomes, thus potentially revealing which aspects of narcissism are related to abusive supervision and which are not. More precisely, we argue that only the antagonistic side of narcissism (narcissistic rivalry) is associated with abusive supervision, while the agentic side (narcissistic admiration) is not. In the next section, we outline the NARC in more detail.

The Narcissistic Admiration and Rivalry Concept (NARC)
The NARC posits that narcissists' central goal is to build and maintain highly positive self-views, an idea that is in line with other models of narcissism (e.g., Campbell & Campbell, 2009;Morf & Rhodewalt, 2001). However, according to Back et al. (2013), narcissists differ in the social strategies they adopt to achieve and maintain their grandiose selfviews. Narcissistic admiration describes a self-enhancing interpersonal strategy associated with striving for uniqueness, grandiose fantasies, and charming behaviors. These behavioral dynamics lead to social success (e.g., being perceived as assertive or sociable; Back et al., 2013), and consequently strengthen the narcissist's grandiose self-view. In contrast, narcissistic rivalry describes a defensive interpersonal strategy associated with striving for supremacy and devaluing others, and includes aggression. The strategy is likely to lead to social failure (e.g., being perceived as untrustworthy or unlikeable; Back et al., 2013), and consequently perpetuates the narcissist's negative views of others. Narcissistic admiration and narcissistic rivalry correlate moderately to strongly with each other (Back et al., 2013;Leckelt et al., 2015;Wurst et al., 2017), meaning that the two dimensions can co-occur, but do not have to. In sum, this two-dimensional approach describes how narcissists behave toward others and is therefore relevant for leadership contexts, which typically rely heavily on interactions between leaders and followers. As narcissistic rivalry reflects the antagonistic side of narcissism, which is supposed to lead to social conflict (Back et al., 2013), we argue that leaders' narcissistic rivalry will be related to abusive supervision. In contrast, narcissistic admiration reflects the agentic side of narcissism, entailing charismatic, charming behavior. The latter is related to popularity and social status and is not supposed to be associated with dysfunctional interpersonal orientation and relationship outcomes (Back et al., 2013). Thus, we assume that this narcissism dimension plays a minor role in abusive supervision. In the next section, we outline our argument in detail and summarize the relevant research.

Leaders' Narcissistic Rivalry and Abusive Supervision
According to the NARC, only narcissistic rivalry (but not narcissistic admiration) is related to problematic behaviors and negative interpersonal outcomes. For instance, narcissistic rivalry (but not narcissistic admiration) has consistently negative associations with empathy, trust, forgiveness, and gratitude (Back et al., 2013). Furthermore, in romantic relationships, only narcissistic rivalry (but not narcissistic admiration) is related to lower relationship quality and a higher occurrence of conflict (Wurst et al., 2017). Additionally, individuals high in narcissistic rivalry (but not those high in narcissistic admiration) show arrogant and aggressive behaviors and are perceived as untrustworthy, which results in a decrease in popularity over time (Leckelt et al., 2015). In sum, individuals high in narcissistic rivalry have little interest in others, are unable to maintain close relationships, and are likely to engage in aggressive behaviors toward others. Accordingly, we expect that the behavioral dynamics associated with narcissistic rivalry in interpersonal contexts (e.g., conflicts or aggressiveness; Leckelt et al., 2015;Wurst et al., 2017) will also be relevant for leadership contexts.
More precisely, we propose that leaders high in narcissistic rivalry try to protect their grandiose self-views by behaving in hostile ways and by putting others down (Back et al., 2013). We argue that it is likely that the propensity of leaders high in narcissistic rivalry to aggress will translate into aggression against their followers because followers are relatively safe targets. Due to the power imbalance, followers will probably not retaliate. In addition, research on the characteristic intra-and interpersonal dynamics of the antagonistic narcissism dimension suggests that individuals with high narcissistic rivalry maintain and defend their selfview by derogating and devaluing others (Back et al., 2013). Their belief in their own superiority is inextricably linked to the belief in others' inferiority and justifies the mistreatment of others (Grapsas et al., 2019). Thus, we assume that individuals high in narcissistic rivalry see their abusive behavior as justified. By showing abusive supervision, leaders high in narcissistic rivalry can act out their aggressive tendencies.
A few examples of abusive supervision can help illustrate this process. For instance, by putting followers down and ridiculing them, leaders high in narcissistic rivalry may feel superior and thus strengthen their own status. Furthermore, by not giving followers credit for their work and by reminding them of past mistakes, leaders high in narcissistic rivalry can make their followers feel small and prevent them from growing professionally. Also, blaming followers for the leader's own mistakes can be seen as the self-protective strategy of a leader high in narcissistic rivalry, and this can help the leader defend their grandiose self-views. In sum, leaders high in narcissistic rivalry might use abusive supervision as a means to protect their superior status as a leader. Therefore, we propose: Hypothesis 1 Leaders' narcissistic rivalry will be positively associated with abusive supervision.

Followers' Supervisor-Directed Deviance and Perceived Self-Esteem Threat
Beyond a general predisposition to behave aggressively and show abusive supervision, we wondered when and why leaders high in narcissistic rivalry would show abusive supervision. According to the NARC, individuals high in narcissistic rivalry are particularly likely to aggress when their grandiose, but fragile self-views are threatened (Back et al., 2013). This assumption is rooted both in trait activation theory (Tett & Burnett, 2003;Tett & Guterman, 2000) and threatened egotism theory (Baumeister et al., 1996;Bushman & Baumeister, 1998).
Trait activation theory takes an interactionist approach and highlights the role of trait-relevant situational cues, which trigger the expression of traits (Tett & Burnett, 2003;Tett & Guterman, 2000). This means that the behavioral expression of a trait (i.e., leaders' narcissistic rivalry) depends at least in part on the situational circumstances. According to threatened egotism theory, the most important trait-relevant cue that might explain aggressive behavior in narcissists is "threatened egotism, particularly when it consists of favorable self-appraisals that may be inflated or ill-founded and that are confronted with an external evaluation that disputes them" (Baumeister et al., 1996). Thus, ego threats can be seen as threats to self-esteem (e.g., Stucke & Sporer, 2002;Vohs & Heatherton, 2001). When narcissists have the impression that their inflated self-views are not validated, or are challenged by others, their self-esteem is threatened, and they are likely to react to that threat with aggression (e.g., Bushman & Baumeister, 1998).
According to the NARC, individuals high in narcissistic rivalry are particularly attentive to cues that signal social failure (Back et al., 2013) or loss in status (Grapsas et al., 2019), and their self-esteem is fragile and highly contingent on external validation (Geukes et al., 2017). Consequently, individuals high in narcissistic rivalry are likely to perceive a mismatch between their own inflated self-esteem and any external evaluations of the self (e.g., indicated by cues signaling social failure or loss in status) and feel threatened by this mismatch. Whenever individuals high in narcissistic rivalry perceive self-esteem threats, their self-protection strategy is activated and triggers aggressive responses (Back et al., 2013). In support of this assumption, Back et al. (2013) found that individuals high in narcissistic rivalry engage in revenge-oriented behaviors in reaction to relationship transgressions.
A typical example of follower behavior that may threaten the grandiose self-esteem of leaders high in narcissistic rivalry is supervisor-directed deviance (Simon et al., 2015), as it consists of undesirable behaviors aimed at harming the leader (Bennett & Robinson, 2003), and may humiliate the leader. It encompasses behaviors such as making fun of, being rude toward, or making negative comments about the leader (Mitchell & Ambrose, 2007). We assume that supervisor-directed deviance challenges the grandiose, but fragile self-esteem of leaders high in narcissistic rivalry, as it undermines their status, provoking the impression that they are unable to control the follower, and signals that the follower does not respect them. We expect that leaders high in narcissistic rivalry will respond with abusive supervision toward the source of the self-esteem threat (i.e., the follower who showed supervisor-directed deviance) in order to punish the follower, re-establish leader status, and ultimately restore their grandiose self-views. They respond in such a way because they see their behavior as justified (Back et al., 2013;Baumeister et al., 1996;Grapsas et al., 2019). For instance, by putting down their followers, leaders high in narcissistic rivalry will aim to re-establish the impression that they are powerful and superior to their followers. We thus expect that leaders high in narcissistic rivalry will react with abusive supervision in response to perceived selfesteem threats induced by followers who showed supervisordirected deviance. In sum, we propose: Hypothesis 2 Supervisor-directed deviance will moderate the indirect effect of leaders' narcissistic rivalry on abusive supervision via perceived self-esteem threat. The indirect effect will be stronger when supervisor-directed deviance is high than when it is low.

Study 1
In order to examine the hypothesized relationship between leaders' narcissistic rivalry and abusive supervision in a field setting, we conducted an online study with leader-follower dyads.

Sample and Procedure
Study participants were recruited via personal and professional contacts, online platforms and the first author's university's press department and website. In the course of the survey, participants were asked to indicate the e-mail address of either their direct leader or one of their followers. These dyadic partners were then automatically invited to take part in the survey. We stressed anonymity and confidential treatment of the data in order to minimize concerns about the dyadic partners having insight into the data. Overall, 164 leaders and 192 followers completed the questionnaire. After matching the leaders and followers, the final sample consisted of 123 dyads because some participants could not be matched. A total of 35% of the leaders and 61% of the followers were women. Leaders were on average 46.84 years old (SD = 11.02) and followers were 38.32 years old (SD = 13.46). Leaders and followers had worked together for 4.91 years (SD = 5.83) on average. Leaders and followers came from diverse industries and most often worked in public administration, education, health, and social services (26.8%); trade, traffic, storage, and the catering industry (15.4%); and the service sector (13%).

Narcissistic Rivalry
We measured leaders' narcissistic rivalry with the respective nine items of the Narcissistic Admiration and Rivalry Questionnaire (NARQ; Back et al., 2013). Leaders indicated how much they agreed with the respective items on a 6-point Likert scale (1 = do not agree at all, 6 = agree completely). A sample item is "Most people won't achieve anything". Cronbach's alpha was 0.78.

Supervisor-Directed Deviance
Supervisor-directed deviance was measured with five items from Bennett and Robinson (2000). A sample item is "My follower says something hurtful to me" (Cronbach's α = 0.75). Leaders were asked to think about their matched follower and indicate on a 5-point Likert scale how frequently the respective follower exhibited the described behaviors (1 = never to 5 = always).

Perceived Self-Esteem Threat
In line with previous research (Leary et al., 2009;Stucke & Sporer, 2002), we measured perceived self-esteem threat with a German version of Rosenberg's self-esteem scale (RSE;von Collani & Herzberg, 2003). In general, the RSE assesses a person's self-esteem and thus a person's view of themselves. We employed the state version of the RSE to examine participants' self-esteem in reaction to past interactions with their followers assuming that their self-esteem would be threatened when followers behaved in ways that challenge the leaders' grandiose self-views (i.e., when they display supervisor-directed deviance). Prior research has shown that state self-esteem is sensitive to threatening events such as status threats (Mahadevan et al., 2016;Rudolph et al., 2020). When calculating the scale mean, we inverted the original items so that high values indicated high perceived self-esteem threat and low values indicated low perceived self-esteem threat. The items were put into the appropriate context by asking leaders to think about past interactions with their matched follower and indicate how often this follower elicited the described thoughts or feelings. A sample item is "I felt useless" (Cronbach's α = 0.75). Participants indicated their agreement with the 10 items on a 6-point Likert scale ranging from 1 (never) to 6 (almost always).

Abusive Supervision
We measured abusive supervision using the 15 items of the German version of Tepper's (2000) abusive supervision scale (Schilling & May, 2015). Followers indicated how often their leader showed the respective abusive behaviors (Cronbach's α = 0.81). A sample item is "My leader ridicules me". We used a 5-point Likert scale ranging from 1 (never) to 5 (always).

Control Variable
As narcissistic rivalry and admiration are moderately correlated (Back et al., 2013) and in line with prior research (e.g., Wurst et al., 2017), we controlled for leaders' narcissistic admiration in order to make sure that effects could be traced back to the maladaptive dimension of narcissism only. We measured narcissistic admiration with the nine items from the NARQ (Back et al., 2013; Cronbach's α = 0.87). Participants indicated their agreement with items such as "Being a very special person gives me a lot of strength" on a 6-point Likert scale (1 = do not agree at all, 6 = agree completely). We additionally ran all analyses without narcissistic admiration as a control variable. The results can be found in Online Appendix A.

Results
We present the means, standard deviations, correlations, and internal consistency estimates for the study variables in Table 1. To test Hypothesis 1, we conducted a linear regression analysis examining followers' ratings of abusive supervision as the outcome, leaders' narcissistic rivalry as the predictor, and leaders' narcissistic admiration as the covariate. Leaders' narcissistic rivalry was significantly and Table 1 Means, standard deviations, correlations, and internal consistency estimates N = 123 (for Study 1) and N = 313 (for Study 2). Alpha coefficients are given in parentheses along the diagonal with Study 1 appearing first and Study 2 appearing second. Correlations from Study 1 appear below the diagonal, and correlations from Study 2 appear above the diagonal a Study 2: 1 = low supervisor-directed deviance, 2 = medium/high supervisor-directed deviance *p < 0.05; **p < 0.01; ***p < 0.001  Table 2 (see model 1). Without leaders' narcissistic admiration as a covariate, we also found a direct positive association between leaders' narcissistic rivalry and followers' reported abusive supervision (β = 0.20, SE = 0.05, p = 0.026; see Online Appendix A), which renders further support for Hypothesis 1.
To test the moderated mediation posited in Hypothesis 2, we used the PROCESS macro for SPSS (Hayes, 2018). The results revealed that followers' supervisor-directed deviance did not moderate the indirect effect of leaders' narcissistic rivalry on abusive supervision via perceived self-esteem threat (index of moderated mediation: B = 0.02, SE = 0.05, 95% CI [− 0.07, 0.12]). This means that leaders' narcissistic rivalry was unrelated to perceived self-esteem threat, irrespective of followers' supervisor-directed deviance, and perceived self-esteem threat was unrelated to followers' ratings of abusive supervision. The direct effect from leaders' narcissistic rivalry on abusive supervision was still evident here (B = 0.14, SE = 0.06, p = 0.014). Leaders' narcissistic admiration was unrelated to follower-rated abusive supervision (B = − 0.06, SE = 0.04, p = 0.155) and was negatively related to perceived self-esteem threat (B = − 0.34, SE = 0.06, p < 0.001). This model explained 7.5% of the variance in abusive supervision ratings (p < 0.05). The results are presented in Table 2 (see models 2 and 3). In all, we could not find support for Hypothesis 2. The results without leaders' narcissistic admiration as control variable were similar: the index of moderated mediation was also insignificant (B = 0.04, SE = 0.05, 95% CI [− 0.03, 0.16]; see also Online Appendix A).
A closer look at the results reveals that the direct effect of leaders' narcissistic rivalry on perceived self-esteem threat was not significant in the low and medium values of the moderator, but was significant in the high value of the moderator (B = 0.27, SE = 0.10; p = 0.009). The indirect effects, however, were not significant in any value of the moderator because perceived self-esteem threat did not predict abusive supervision. Importantly, as the variance of supervisor-directed deviance was extremely low, both the low and medium values of the moderator were set at 1.00 by the PROCESS macro, and the "high" value was set at 1.20. Thus, these results have to be interpreted cautiously as being restricted by a potential floor effect and will be addressed in the discussion section. Furthermore, we decided to use an experiment in Study 2, as this allowed us to systematically manipulate followers' supervisordirected deviance.

Study 2
In Study 2, we tested all hypotheses using experimental vignettes, which allowed us to assess leaders' perceptions of self-esteem threat, together with their intentions regarding abusive supervision in response to followers' supervisordirected deviance (which was systematically manipulated in the experimental vignettes). We chose this methodological approach, as we were interested in the leaders' internal processes (i.e., perceived self-esteem threats) and their own intent to show abusive supervision. Experimental vignettes offer the possibility of capturing short-term dynamics and direct reactions. In addition, we used behavioral intention as the most proximate predictor of actual behavior (Ajzen, 1985(Ajzen, , 1991.

Sample and Procedure
Participants were recruited via a German panel service (respondi) and were paid €1.25 for their participation. Eligible participants had to be currently employed in a leadership position, work at least 20 h per week, and have at least three months of work experience. The study was conducted online and consisted of two measurement points. A total of 331 participants took part in the study. 1 We excluded nine participants, who stated that they did not consider the described vignettes credible at all, or who could not imagine themselves in the situation described in the experimental vignette. Furthermore, we excluded six participants who reported substantially different ages at the two measurement points, and three participants who had participated twice at T2. Our final sample consisted of 313 participants (low supervisor-directed deviance condition: N = 107; medium supervisor-directed deviance condition: N = 112; and high supervisor-directed deviance condition: N = 94). Participants had a mean age of 47.66 (SD = 9.9), and 31% were women. On average, participants worked 42 h per week (SD = 8.5); 14.7% held a low, 45.4% a medium, and 39.9% a high leadership position. Participants worked in diverse industries, most often in the service sector (12.8%), manufacturing sector (11.2%), and public administration (9.9%).
In order to reduce method bias, we separated the measurements in time (Podsakoff et al., 2012). At the first measurement point, we assessed our independent variable (narcissistic rivalry) and our control variable (narcissistic admiration), and collected sociodemographic information. At the second measurement point (one week later), participants read one of three experimental vignettes in which we manipulated supervisor-directed deviance. Participants were randomly assigned to read either a low, medium, or high supervisordirected deviance vignette. Subsequently, participants indicated how threatened they felt by the followers' behavior (perceived self-esteem threat, mediator) and their abusive supervision intentions (dependent variable).

Development and Content of Experimental Vignettes
Following recommendations by Lapierre et al. (2009), we developed three experimental vignettes that described low, medium, and high supervisor-directed deviance, respectively. In line with best practice recommendations (Aguinis & Bradley, 2014;Lapierre et al., 2009), we chose three levels of supervisor-directed deviance in an attempt to represent various interactions in the workplace where supervisordirected deviance can also vary. By doing so, we not only tested whether it makes a difference if a follower shows low or high supervisor-directed deviance, but also what happens in-between (when a follower shows a medium level of supervisor-directed deviance). Thus, distinguishing between three levels of supervisor-directed deviance is a more conservative test of our hypothesis than when comparing only low and high conditions. Each experimental vignette included an introduction followed by a specific description of a follower's supervisor-directed deviant behavior. First, all participants were instructed to put themselves in the role of a leader and read the scenarios carefully. Next, all participants received the same background information so that they could embed their responses contextually (Aguinis & Bradley, 2014). They were told to imagine that they were working for a software company and were asked to read information about the company and their job duties. In the vignettes, participants' duties were described as consisting of delegating work to followers, monitoring the followers' work progress, and evaluating the followers' performance. Participants were then told that they had to evaluate the work and interpersonal behavior of a follower named Alex while he worked on a specific project. The next paragraph in the vignette described Alex's behavior. His interpersonal behavior varied across the conditions. We based the behaviors and wording of our experimental vignettes on existing scales and studies that had previously examined workplace deviance (Bennett & Robinson, 2000;Spector & Fox, 2005;Spector et al., 2006). Consequently, in the low supervisor-directed deviance condition, Alex was described as a follower who never ridiculed or verbally abused his leader; in the medium supervisordirected deviance condition, he sometimes showed these behaviors; and in the high supervisor-directed deviance condition, he often showed these behaviors toward his leader. Afterwards, we measured our focal variables, manipulation check items, and, in addition, we asked participants how credible they found the experimental vignettes, and whether or not they could imagine themselves in the situation. The full experimental vignettes can be found in Online Appendix H.

Narcissistic Rivalry
We measured leaders' narcissistic rivalry using the same measure as in Study 1 (Cronbach's α = 0.88).

Perceived Self-Esteem Threat
We used the same assessment of perceived self-esteem threat as in Study 1. We adapted the original instructions of the RSE scale (von Collani & Herzberg, 2003) to fit the experimental vignettes (i.e., "Please think again about the scenario you just read and put yourself in the role of Alex's leader. How did you feel on the basis of Alex's behavior?"). Participants indicated their agreement with the items (Cronbach's α = 0.89) on a 6-point Likert scale ranging from 1 (do not agree at all) to 6 (agree completely).

Abusive Supervision Intentions
We measured abusive supervision intentions using the 15 items of the German version of Tepper's (2000) abusive supervision scale (Schilling & May, 2015). We asked participants how likely the leaders would be to show the indicated abusive supervisory behaviors in response to the follower's behaviors described in the vignettes. Therefore, participants' responses reflected specific behavioral intention indicators and not general behavioral tendencies. A sample item was "I would ridicule Alex" (Cronbach's α = 0.95). Participants indicated their agreement with these items on a 5-point Likert scale ranging from 1 (very unlikely) to 5 (very likely).

Manipulation Check
After reading the experimental vignettes and before answering the scales for measuring perceived self-esteem threat and abusive supervision intentions, participants responded to two items to rate the follower's supervisor-directed deviance. We used items from Robinson (2001, 2005), which reflected the content of our experimental vignettes ("Alex acted rudely toward you", "Alex said something hurtful to you").

Control Variable
We controlled for leaders' narcissistic admiration (Cronbach's α = 0.86) using the same measure as in Study 1 and using leader ratings of their own narcissistic admiration. Additionally, we ran all analyses without narcissistic admiration as control variable. The results can be found in Online Appendix A.

Results
Before testing our hypotheses, we conducted manipulation checks to see if our experimental manipulation of followers' supervisor-directed deviance had worked. As expected, ratings of supervisor-directed deviance differed between the three conditions (low supervisor-directed deviance: M = 1.33, SD = 0.65; medium supervisor-directed deviance: M = 3.97, SD = 1.20; high supervisor-directed deviance: M = 4.09, SD = 1.13), F(2, 310) = 244.73, p < 0.001. Post hoc Bonferroni tests revealed that the participants in the low supervisor-directed deviance condition rated the follower's behavior as significantly less deviant than in the medium (p < 0.001) and high (p < 0.001) supervisor-directed conditions. Ratings of supervisor-directed deviance did not differ significantly between the medium and high supervisordirected deviance groups (p = 1.00). Therefore, we decided to group the medium and high supervisor-directed deviance conditions together and test whether the indirect effect of leaders' narcissistic rivalry on abusive supervision intentions via perceived self-esteem threat differed between the low and medium/high group. Nevertheless, we also report results where we differentiated between the three groups as originally intended (see Online Appendix B).
We present the means, standard deviations, correlations, and internal consistency estimates for the study variables in Table 1. We tested Hypothesis 1 with a linear regression analysis, with leaders' narcissistic rivalry as the predictor and leaders' narcissistic admiration as a covariate. Supporting Hypothesis 1, leaders' narcissistic rivalry positively predicted abusive supervision intentions (β = 0.41, SE = 0.05, p < 0.001). In contrast, leaders' narcissistic admiration was unrelated to abusive supervision intentions (β = − 0.02, SE = 0.05, p = 0.760). Results are presented in Table 3 (see model 1). Without leaders' narcissistic admiration as covariate, we also found a direct positive association between leaders' narcissistic rivalry and abusive supervision intentions (β = 0.40, SE = 0.05, p < 0.001; see Online Appendix A), which further supports Hypothesis 1.
To test Hypothesis 2, we also used the PROCESS macro for SPSS (Hayes, 2018). There was no conditional indirect effect of leaders' narcissistic rivalry on abusive supervision intentions (index of moderated mediation: B = 0.03, SE = 0.04, 95% CI [− 0.04, 10]). However, the indirect effect of leaders' narcissistic rivalry on abusive supervision intentions via perceived self-esteem threat was significant in both experimental conditions (low supervisor-directed deviance: B = 0.07 SE = 0.03, 95% CI [0.02, 13]; medium/ high supervisor-directed deviance: B = 0.10, SE = 0.03, 95% CI [0.05, 16]). The direct effect from leaders' narcissistic rivalry on abusive supervision intentions was still evident here (B = 0.25, SE = 0.05, p < 0.001). Leaders' narcissistic admiration was unrelated to abusive supervision intentions (B = 0.02, SE = 0.04, p = 0.602). In all, these results did not support Hypothesis 2. This model explained 16% of the variance in abusive supervision intention ratings (p < 0.001). Table 3 presents the results (see models 2 and 3). In Online Appendix A, we report our results without leaders' narcissistic admiration as control variable. Again, we did not find support for a conditional indirect effect of leaders' narcissistic rivalry on abusive supervision intentions (index of moderation: B = 0.02, SE = 0.04, 95% CI [− 0.04, 0.10]). Furthermore, in Online Appendix B, we report our results with a three-level moderator (distinguishing between low, medium, and high supervisor-directed deviance). Again, our 1 3 results remained the same. There was no conditional indirect effect of leaders' narcissistic rivalry on abusive supervision intentions when using the three-level moderator (index of moderated mediation: B = 0.00, SE = 0.03, 95% CI [− 0.05, 0.06]), which further supports that Hypothesis 2 must be rejected.

Post Hoc Analyses
We conducted several additional analyses following the reviewers' suggestions. The results of these analyses can be found in Appendix.

Analyses with Different Operationalization of Self-Esteem Threat (Online Appendix C)
First, we used a second operationalization of perceived self-esteem threat to examine whether our results replicated with a different operationalization. Using our alternative perceived self-esteem threat operationalization via three bipolar items, we replicated our results in both studies. We found no conditional indirect effect of leaders' narcissistic rivalry on abusive supervision (

Analyses with Overall Narcissism Score (Online Appendix D)
We additionally tested Hypothesis 1 with an overall narcissism score. We used the overall narcissism score as predictor and follower-reported abusive supervision (in Study 1) and abusive supervision intentions (in Study 2) as outcome. Our results revealed a non-significant association between the overall narcissism score and the follower-reported abusive supervision in Study 1 (β = 0.01, SE = 0.05, p = 0.807), and a significant positive association between the overall narcissism score and the abusive supervision intentions in Study 2 (β = 0.32, SE = 0.05, p < 0.001).

Simple Mediation Analysis (Online Appendix E)
Furthermore, we conducted a simple mediation analysis with leaders' narcissistic rivalry as predictor, abusive supervision (intentions) as outcome, perceived self-esteem threat as mediator, and leaders' narcissistic admiration and condition as covariates. Results of this analysis revealed a non-significant indirect effect of leaders' narcissistic rivalry on abusive supervision via perceived self-esteem threat in Study 1 (β = 0.01, SE = 0.02, 95% CI [− 0.02, 0.06]) and a significant indirect effect of leaders' narcissistic rivalry on abusive supervision intentions in Study 2 (β = 0.08, SE = 0.02, 95% CI [0.04, 0.13].

Simple Moderation Analysis (Online Appendix F)
We also tested a simple moderation analysis, with leaders' narcissistic rivalry as predictor, followers' supervisordirected deviance as moderator, leaders' abusive supervision (intentions) as outcome, and leaders' narcissistic admiration as covariate. For both studies, results revealed that the interaction between leaders' narcissistic rivalry and supervisor-directed deviance was not significant in either Study 1 (β = 0.24, SE = 0.16, p = 0.15) or Study 2 (β = 0.18, SE = 0.04, p = 0.055).

Leaders' Narcissistic Admiration as Predictor (Online Appendix G)
Additionally, we ran our analyses with leaders' narcissistic admiration as predictor to examine whether there is a conditional indirect effect with leaders' narcissistic admiration as predictor, perceived self-esteem threat as mediator, followers' supervisor-directed deviance as moderator, and abusive supervision (intentions) as outcome. We conducted those analyses with leaders' narcissistic rivalry as control variable. There was no conditional indirect effect of leaders' narcissistic admiration on abusive supervision (intentions) via perceived self-esteem threat moderated by followers' supervisor-directed deviance in Study 1 (

Discussion
In our study, we strove to provide new insights on narcissism and abusive supervision to the literature. More precisely, we applied the NARC (Back et al., 2013), trait activation theory (Tett & Burnett, 2003;Tett & Guterman, 2000), and threatened egotism theory (Baumeister et al., 1996;Bushman & Baumeister, 1998) to a leadership context and examined factors connected to abusive supervision in order to better understand the antecedents of abusive supervision. Building on the NARC, we proposed and found that only leaders' narcissistic rivalry-the antagonistic dimension of narcissism-is consistently directly and positively associated with abusive supervision, while leaders' narcissistic admiration-the agentic dimension of narcissism-is not consistently related to abusive supervision (intentions), supporting the view that applying a differentiated model of narcissism to leadership is fruitful. Furthermore, building on and extending trait activation theory and threatened egotism theory, we proposed a moderated indirect effect, assuming that leaders high in narcissistic rivalry would perceive selfesteem threats in reaction to followers' supervisor-directed deviance, which in turn would lead to abusive supervision. However, while we found at least in part an indirect effect of leaders' narcissistic rivalry on abusive supervision (intentions) via perceived self-esteem threats, this effect was not moderated by followers' supervisor-directed deviance. Thus our studies only partially supported the notion of threatened egotism theory as the relationship between leaders' narcissistic rivalry and abusive supervision intentions was (partly) mediated by ego threat, but not triggered by follower behavior (also contradicting trait activation theory).
A methodological advantage of our research is that we conducted two studies with different methodological approaches (a field study and an experimental vignette study), which complement each other. By doing so, we could test our assumptions in a real work context, but also in an experimental context in which we manipulated our moderator variable systematically. In sum, our results show that leaders' narcissistic rivalry plays a pivotal role in abusive supervision, whereas follower behaviors (i.e., followers' supervisor-directed deviance) and leaders' internal processes (i.e., perceived self-esteem threats) seem to be less important to abusive supervision.

Theoretical Implications
First, we advanced the literature on leader narcissism as an antecedent of abusive supervision. We were particularly interested in leader narcissism as a precursor of abusive supervision because narcissists are likely to attain leadership positions (Grijalva et al., 2015). At the same time, they are likely to have trouble maintaining positive relationships and often behave in derogatory (Park & Colvin, 2015) or aggressive ways (Seah & Ang, 2008).
Yet interestingly, prior research on leader narcissism as an antecedent of abusive supervision has remained inconclusive and has revealed mixed results (Nevicka et al., 2018;Waldman et al., 2018;Whitman et al., 2013;Wisse & Sleebos, 2016). These might be due to the use of different onedimensional narcissism measures that consider narcissism as one global construct, or focus only on specific aspects, such as entitlement. It has been argued that narcissism is a multidimensional construct with agentic and antagonistic sides (e.g., Back et al., 2013), and that differentiating between these two sides can help identify their specific linkages with organizational outcomes (e.g., Helfrich & Dietl, 2019). We thus extended prior research using the NARC, which provides a more differentiated view on narcissism and distinguishes between the antagonistic (i.e., narcissistic rivalry) and agentic (i.e., narcissistic admiration) dimensions of narcissism, to derive theoretical assumptions about different dimensions of narcissism.
In line with theory, we found that leaders' narcissistic rivalry, but not their narcissistic admiration, was consistently positively associated with follower ratings of abusive supervision (Study 1), as well as leaders' abusive supervision intentions (Study 2). This shows that it is important to differentiate between the antagonistic and the agentic side of leader narcissism in abusive supervision research and that this differentiation can help clarify previous inconclusive findings which might be due to treating narcissism as a one-dimensional construct. Apparently, at work, narcissistic rivalry, as the antagonistic form of narcissism and a hostile self-protective strategy, leads to abusive supervision (intentions). Leaders high in narcissistic rivalry act out their hostile tendencies and strive for supremacy by putting their followers down. In contrast, the agentic side of leader narcissism, leaders' narcissistic admiration, is not consistently positively associated with abusive supervision (intentions). Interestingly, we found those effects both when abusive supervision was rated by followers (Study 1) and when it was rated by leaders (Study 2). Thus, we complemented prior research-which has mainly studied abusive supervision from the followers' perspective (Mackey et al., 2017;Tepper et al., 2017)-by showing that some leaders (i.e., those high in narcissistic rivalry) also state explicitly that they would behave abusively toward their followers. By doing so, we can show that leaders' narcissistic rivalry is positively associated with self-views, as well as other-ratings of abusive supervision, thus further extending prior research to include self-and other views of abusive supervision.
Second, on the basis of trait activation theory and threatened egotism theory, we aimed to explain why and when leaders high in narcissistic rivalry show abusive supervision. In particular, based on threatened egotism theory, we expected that leaders high in narcissistic rivalry would perceive self-esteem threats in response to followers' supervisor-directed deviance, and that these perceived self-esteem threats would lead to abusive supervision (intentions). Contrary to our expectations, we did not find an indirect effect of leaders' narcissistic rivalry on abusive supervision intentions via perceived self-esteem threats that was contingent on followers' deviant behavior in both studies. That is, follower deviance did not seem to influence leaders' tendency to show abusive supervision as a response to their egos being threatened.
A closer look at the results shows that in Study 1, leaders' narcissistic rivalry predicted self-esteem threats when supervisor-directed deviance was high. However, "high" in our case meant values only slightly above the scale endpoint, as deviance was low overall. Furthermore, in Study 2, the indirect effect of leaders' narcissistic rivalry on abusive supervision intentions via perceived self-esteem threat was significant in all experimental conditions, but the interaction between narcissistic rivalry and condition was not significant. That is, narcissistic rivalry and supervisor-directed deviance predicted perceived ego threats independently, but they did not interact. It seems that sensitivity to self-esteem threats in leaders who are high in narcissistic rivalry (Back et al., 2013;Baumeister et al., 1996;Geukes et al., 2017) is so strong that it overshadows variations in follower behavior. This reasoning is also in line with assumptions that individuals high in narcissistic rivalry generally have negative thoughts about others (Back et al., 2013), and that narcissists generally hold negative implicit beliefs about followers (Hansbrough & Jones, 2014). Thus, it seems that situational factors (e.g., follower behavior) are less important, and that the trait itself (i.e., narcissistic rivalry) can explain best why some leaders display abusive supervision and others not. This somewhat contradicts the threatened egotism theory and trait activation theory in so far as here the situational trigger (follower behavior) was not relevant to the supervisor's behavior. In sum, we conclude that in the case of leaders who are high in narcissistic rivalry, whether or not their followers show supervisor-directed deviance is of relatively little importance as these leaders are highly prone to treating others badly, irrespective of how others behave. That is, they need little or nothing to trigger their negative behavior.

Practical Implications
Our findings also have notable implications for organizations. Given the negative outcomes of abusive supervision (Schyns & Schilling, 2013), it is important to take measures to prevent such behavior. As our study shows that leaders high in narcissistic rivalry are particularly likely to engage in abusive supervision, organizations should be cautious when hiring or promoting such leaders. In addition, organizations could train leaders high in narcissistic rivalry to display more supportive leader behaviors (e.g., Gonzalez-Morales et al., 2018), or provide coaching to help them develop their leadership skills (Kets de Vries, 2014). As narcissists seldom see reasons to change their destructive behavior, organizations should focus on self-relevant reasons for doing so (e.g., implications for performance ratings) to incentivize narcissistic leaders to take their followers' well-being into account. Leaders high in narcissistic rivalry should be made aware that healthy and productive followers reflect better on them. This should help them understand that abusive supervision does not contribute to their desired grandiose self-view. Instead, for selfish reasons, they should refrain from displaying abusive supervision and commit to ethical leadership practices. In addition, as leaders high in narcissistic rivalry strive for status (Grapsas et al., 2019), they should be made aware that productive and healthy followers can also be a means for boosting their status in organizations that uphold communal values and do not tolerate aggression.
Furthermore, we found, at least in one study that leaders high in narcissistic rivalry are prone to perceiving selfesteem threats, and that perceived self-esteem threats can translate into abusive supervision intentions (see Study 2). Therefore, firms should develop interventions aiming to mitigate perceived self-esteem threats. For instance, Grapsas et al. (2019) proposed that individuals should be trained to be less attentive to cues that hinder the pursuit of status. Accordingly, leaders high in narcissistic rivalry could be trained to focus less on followers' negative evaluations that might evoke perceptions of self-esteem threat. Instead, they should learn to direct their attention to their followers' positive aspects. In addition, leaders high in narcissistic rivalry could be taught to critically reflect on their followers' actual negative evaluations and reappraise them as learning experiences and opportunities to improve their status (Grapsas et al., 2019).

Limitations and Suggestions for Future Research
Whereas a strength of this research is that we conducted two studies with different research methodologies, there are also some limitations. In Study 1, we enhanced the external generalizability of our findings by examining actual leader-follower dyads in the workplace. One drawback of Study 1 is that we assessed our focal variables cross-sectionally, limiting the causal conclusions that can be drawn from these findings. Therefore, future longitudinal field studies are needed to show the process in the field. Another interesting approach would be to conduct diary studies using event sampling methods (Lopes et al., 2004;Ohly et al., 2010). These could capture the short-term dynamics of abusive supervision as a direct reaction to single episodes of supervisordirected deviance and self-esteem threat.
Finally, as participation in our study was voluntary, we cannot rule out the possibility of self-selection bias. It is possible that leader-follower dyads with positive relationships were more likely than others to participate in our study. Indeed, the variance of followers' supervisor-directed deviance was relatively low across the whole sample with a "high" value set at 1.20. This indicates that there was a floor effect, and in particular, that followers who did not behave in deviant ways participated in our study. For future research, we would recommend selecting participants differently to ensure more variance in followers' supervisor-directed deviance. For instance, HR departments could invite random leader-follower dyads to participate in research studies to ensure more variance in follower behaviors.
In Study 2, we randomly assigned participants to one of three experimental vignettes describing low, medium, or high supervisor-directed deviance. However, our manipulation check showed that participants rated the medium and high supervisor-directed deviance experimental vignettes as equally deviant. In the medium supervisordirected deviance condition, the follower was described as someone who sometimes shows deviant behaviors toward the leader; whereas in the high supervisor-directed deviance condition, the follower was described as someone who often showed these behaviors toward the leader. Thus, it seems that as soon as a follower is described as someone who shows supervisor-directed deviance to some extent (irrespectively if this is sometimes or often), the follower is perceived as deviant and also as more deviant than a follower who never shows supervisor-directed deviance (low supervisor-directed deviance condition). Consequently, we grouped the medium and high supervisor-directed deviance conditions for our analyses. For our results, we consider the lack of differentiation between the medium and high supervisor-directed deviance groups as less problematic, as we found an indirect effect of leaders' narcissistic rivalry on abusive supervision intentions via perceived self-esteem threat in all conditions (low, and medium/high). This finding also aligns with the results of Study 1, in which, similarly, followers' supervisor-directed deviance did not moderate the indirect effect of leaders' narcissistic rivalry on abusive supervision via perceived self-esteem threat.
In our study, participants first read the supervisor-directed deviance vignettes and were subsequently asked about perceived self-esteem threat and about their abusive supervision intentions. With this design, we were able to ensure that supervisor-directed deviance preceded our mediator (i.e., self-esteem threat) and dependent variable (i.e., abusive supervision intentions). However, we are cautious about making claims about the causal ordering of our mediator and dependent variable. Future research could therefore implement experimental causal-chain designs to establish a causal ordering (Spencer et al., 2005). Furthermore, in Study 2, we chose a between-subjects design to keep participants' workload low. However, this approach did not allow us to make comparisons concerning the same person. To overcome this restriction, future studies could implement within-person designs (Aguinis & Bradley, 2014). This would offer an opportunity to examine how different forms of supervisor-directed deviance affect abusive supervision intentions within the same individual.
According to trait activation theory (Tett & Burnett, 2003;Tett & Guterman, 2000), threatened egotism theory (Baumeister et al., 1996;Bushman & Baumeister, 1998), and the NARC (Back et al., 2013), individuals high in narcissistic rivalry are assumed to be particularly likely to aggress when their grandiose, but fragile self-views are threatened. However, contrary to our expectations, our studies showed that followers' supervisor-directed deviance did not trigger self-esteem threat in leaders high in narcissistic rivalry and lead to abusive supervision. Instead, leaders high in narcissistic rivalry were prone to showing abusive supervision irrespective of their followers' behavior. Therefore, future research could examine whether other follower behaviors may threaten the grandiose self-esteem of leaders high in narcissistic rivalry and thus increase the likelihood of abusive supervision. For instance, prior research assumed that narcissists are more likely to aggress when threatened in public than in private (Ferriday et al., 2011). Individuals high in narcissism want to be admired by others and being challenged in public could threaten their positive self-image. Accordingly, we advise future researchers to differentiate between private vs public ego-threatening follower behaviors, because the latter might be even more threatening to leaders high in narcissistic rivalry, and thus lead to more abusive supervision.
Furthermore, it has been proposed that narcissists are particularly likely to aggress when threatened in status-related (and less when threatened in affiliation-related) aspects, as when being confronted with a competitor who could damage the narcissist's reputation (Grapsas et al., 2019). Thus, it could be that leaders high in narcissistic rivalry might be particularly prone to show aggression toward followers who outperform them and thus undermine their status.

Conclusion
In sum, our findings show that narcissistic rivalry is the maladaptive dimension of leader narcissism, while leaders' narcissistic admiration seems to be the brighter narcissism dimension. Across the two studies, we found that leaders' narcissistic rivalry, but not their narcissistic admiration, was consistently positively associated with follower-reported abusive supervision and abusive supervision intentions. Furthermore, leaders high in narcissistic rivalry showed tendencies toward abusive supervision, irrespective of followers' supervisor-directed deviance, and that only in part could leaders' perceived self-esteem threats explain why leaders high in narcissistic rivalry displayed abusive supervision intentions.
Funding Open Access funding enabled and organized by Projekt DEAL.

Conflict of interest
The authors declare that they have no conflict of interest.
Informed Consent Informed consent was obtained from all individual participants included in the studies.
Research Involving Human Participants and/or Animals All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards.
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