Incentives and peer effects in the workplace: On the impact of envy and wage transparency on organizational design

Kragl, Jenny; Bental, Benjamin; Safaynikoo, Peymaneh Article — Published Version Incentives and peer effects in the workplace: On the impact of envy and wage transparency on organizational design Economic Theory Provided in Cooperation with: Springer Nature Suggested Citation: Kragl, Jenny; Bental, Benjamin; Safaynikoo, Peymaneh (2025) : Incentives and peer effects in the workplace: On the impact of envy and wage transparency on organizational design, Economic Theory, ISSN 1432-0479, Springer, Berlin, Heidelberg, Vol. 80, Iss. 1, pp. 87-124, https://doi.org/10.1007/s00199-024-01622-4 This Version is available at: https://hdl.handle.net/10419/323711 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by/4.0/ Economic Theory (2025) 80:87–124 https://doi.org/10.1007/s00199-024-01622-4 RESEARCH ARTICLE Incentives and peer effects in the workplace: On the impact of envy and wage transparency on organizational design Jenny Kragl1·Benjamin Bental2·Peymaneh Safaynikoo1 Received: 25 October 2022 / Accepted: 3 November 2024 / Published online: 20 January 2025 © The Author(s) 2025 Abstract The article is concerned with understanding the impact of social preferences and wage transparencyontheoptimalorganizationaldesignoffirms.Weconsideramoral-hazard environment with envious workers. The integration of workers in one organizational unit yields productive complementarities but also triggers income comparisons and envy. Separating workers rules out social comparison but also precludes productive synergies. Instead, the firm may impose a wage-secrecy policy to keep the latter while avoiding the former. We show that productive synergies and envy are substitutes under unlimited liability when wages are transparent while they become complements when workers earn rents. As a result, firms are much more likely to integrate workers when the latter are protected by limited liability. Furthermore, even when firms can impose wage secrecy, they prefer not to as long as workers are not too envious. In both cases, firms exploit the incentive effect of pay inequality to raise productive efforts and profits. For the same reason, firms may deliberately establish pay inequality by opting for individual performance pay rather than group bonuses. In this sense, transparency This paper extends the third chapter of Peymaneh Safaynikoo’s dissertation at the EBS Universität für Wirtschaft und Recht, Wiesbaden. We are grateful to the co-editor David J. Cooper and two anonymous referees for very helpful comments on previous versions of the paper. We also thank Simon Dato, Mrdjan M. Mladjan, Dana Sisak, and Harvey Upton for valuable remarks and discussions. We are further grateful for feedback received at the Annual Meetings of the Society for Institutional & Organizational Economics (SIOE), the Copenhagen Network of Experimental Economists (CNEE), the Colloquium on Personnel Economics (COPE), the European Association for Research in Industrial Economics (EARIE), the German Economic Association (Verein für Socialpolitik), and the Foundations of Utility and Risk Conference (FUR). BJenny Kragl jenny[email protected] Benjamin Bental [email protected] Peymaneh Safaynikoo peymaneh.saf[email protected] 1EBS Universität für Wirtschaft und Recht, EBS Business School, Rheingaustr. 1, 65375 Oestrich-Winkel, Germany 2Department of Economics, University of Haifa, Haifa, Israel 123 88 J. Kragl et al. and “sunshine laws” may not be in the self-interest of employees, even more so under a positive minimum wage. Keywords Other-regarding preferences ·Incentives ·Organizational design · Integration ·Separation ·Inequality ·Transparency ·Wage secrecy ·Envy ·Team · Synergy JEL Classifications D63 ·D82 ·M52 ·M54 1 Introduction “Envy is the great leveler: if it cannot level things up, it will level them down.” Dorothy Sayers (1949: 771) It is well-established that people compare themselves to others. How such comparisons affect economic outcomes has been examined theoretically, experimentally and empirically, at both the macroand the microeconomic levels. In the current paper, we turn to firms’ optimal organizational structures and their attitude towards wage transparency and study how these are affected by the presence of social preferences. Using an agency model and focusing on envy as one of the most relevant manifestations of such preferences within firms, we specifically consider whether organizations prefer to integrate workers into teams or separate them into different units instead. In the former case, they moreover face the question of whether to enforce a wage-secrecy policy or rather encourage wage transparency. Our results demonstrate that the two issues are interrelated and that the optimal choices concerning these organizational aspects depend specifically on whether or not firms can exploit envy to increase workers’ effort and generate higher profits. We show that, when firms can extract workers’ surplus, they may prefer social distancing even in the presence of productive synergies. In stark contrast, when workers earn informational rents, firms are likely to integrate them into teams and make wages deliberately transparent, thereby generating profitable peer effects arising from envy. Our paper is motivated by three common characteristics of many workplace environments:the presence of socialcomparisons and envy, theprevalenceof wagesecrecy rules, and the existence of peer effects.1That social and income comparisons are ubiquitous in the organizational context is evidenced for example by Card et al. (2012), Cohnetal.(2014),CullenandPerez-Truglia(2022),andDubeet al. (2019). Within this context, it is envy that has been found to be of particular importance (see, e.g., Vecchio 2000,2005; Duffy et al. 2008; Sterling and Labianca 2015; Duffy et al. 2021).2In this respect, the management literature lists both positive and negative consequences of envy for employees and organizations and suggests various organizational responses, 1We present a comprehensive overview of the related literature in Sect.2. 2The meta-analysis by Nunnari and Pozzi (2022) corroborates the empirical relevance of disadvantageousinequality concerns in game-theoretic contexts and experiments (see, e.g., Figure 6). 123 Incentives and peer effects... 89 affecting in particular the social and physical proximity of workers.3Addressing the negative consequences of envy, Obloj and Zenger (2017) note the importance of peerproximity for the formation of reference groups. Invoking the idea of “out of sight, out of mind”, they imply that spatial separation is likely to rule out social comparisons (p. 16). These authors observe that some big pharma firms choose to outsource research projects rather than integrate them in order to avoid demotivational internal comparisons to high-powered incentives that are common in small R&D startups (p. 16). As another method to manage envy in the workplace, Sterling and Labianca (2015) suggest, to “mix things up” (p. 303) by occasionally changing office space and team assignments in an attempt to avoid social comparisons and their manifestations. That envy plays a role also in the academic context is well known (Romero 2022). Sometimes this becomes visible even in terms of organizational consequences. For example, in 1998, Stanford University decided to split its anthropology department into two units as a consequence of long-lasting internal strife. Clearly, the reason for the strife was multifaceted, yet as indicated by the Stanford Magazine, it had “much to do with personality conflicts, [..] and festering disappointments,” which we take the liberty to interpret as one manifestation of social preferences and perhaps envy.4 The second relevant workplace feature, wage secrecy norms, has recently been the subject of extensive research and public debate. The Glassdoor (2017) Global Salary Transparency Survey, conducted in several advanced OECD countries, documents the prevalence of secrecy rules within companies. According to that survey, only about one third of employees say that their company discloses salaries internally. Further evidence on the prominence of wage secrecy around the world is presented by Cullen and Perez-Truglia (2022). In fact, employment contracts frequently stipulate clauses on salary-related confidentiality. In the United States, “between 2017–2018, nearly half of full-time workers reported they were either discouraged or prohibited from discussing wages and salaries” (Sun et al. 2021)).5In the recent past, however, there is indication that some companies actively promote wage transparency out of their own volition.6The University of California too has made the compensation of all its employees public as of 2011.7Another example is the Whole Foods Market, Inc., 3The two possible behavioral responses to envy are discussed, among others, by van de Ven et al. (2009) and Tai et al. (2012). 4See the Stanford Magazine: Divided They Stand at https://stanfordmag.org/contents/divided-they-stand (January/February 2000). One of the coauthors of the current paper can attest to at least three similar incidents he has witnessed where departmental reorganization was clearly driven by interpersonal and envy-driven motives. 5Interestingly, the Glassdoor survey finds that, compared to men, women are more likely to work under a pay secrecy policy and to violate that policy. In addition, French or English workers tend to chat more easily about their salary than Germans. 6See, e.g., https://hbr.org/2016/03/why-keeping-salaries-a-secret-may-hurt-your-company. Promoting wage transparency may either take the form of establishing the “right of workers to talk” or actively publishing salary information. In this respect, an interesting recent study finds that the former approach may not be successful since workers are still hesitant to discuss wages due to traditional norms stipulating a “salary taboo” ( Cullen and Perez-Truglia (2018)). 7For the UC website listing workers’ pay, see https://transparentcalifornia.com/salaries/university-ofcalifornia. Card et al. (2012) have exploited the introduction of wage transparency in the UC system in their analysis of worker satisfaction. 123 90 J. Kragl et al. which has implemented a complete transparency policy.8At the public level, public sector workers in many European countries and federal employees in the United States are paid according to publicly available salary schemes. Moreover, many countries have recently undertaken efforts to implement pay-equality and antidiscrimination laws, thereby indirectly enhancing transparency. Typically, firms are required to report data aggregated along gender and ethnic dimensions. In the United States, so-called “sunshine laws” explicitly prohibit pay-secrecy clauses, albeit only in less than half of thestates.AfurtherexampleisGermanywhichpassedtheRemunerationTransparency Act (2017), entitling employees to inquire about their peers’ average pay. Sweden has a long tradition of maximum transparency, whereby individual tax records have been publicly accessible since 1766. Much more recently, Norway has implemented similar legislation in 2001.9 Finally, peer effects, constituting the third relevant workplace feature, arise when the presence of peers has an impact on worker behavior and productivity. A multitude of field experiments investigates the manifestation of peer effects in various productive environments such as supermarkets, agricultural firms, online labor markets, and the like. They indicate that peer effects tend to increase worker efforts and productivity. Related to the foregoing transparency discussion, these studies also indicate that the emergence of such peer effects depends on the informational environment, specifically the observability of peers’ actions and wages. Accordingly, peer effects may even provide a kind of a “free lunch” for firms, enabling them to exploit the associated social incentives as an alternative to monetary rewards (see the literature review in Sect. 2.1). Notwithstanding the importance and interdependence of all three aforementioned workplace features, the review in Sect.2below testifies that the existing literature does not provide a comprehensive view allowing to jointly analyze all of them. To fill this gap, we provide an integrated analytical framework that embodies all three workplace features and their interaction with firms’ organizational design. Different from the literature, in our setting, the firm can actively choose its organizational and informational structure, thereby affecting whether productive synergies between workers emerge and whether social comparisons arise. This integrated framework allows us to simultaneously consider the effects of firms’ organizational architecture, its internal wage-transparency policies, and provide some insights concerning the normative effects of sunshine laws. The underlying force in our environment is envy. In particular, it is this social preference that drives the emergence of peer effects, the integration or separation decision, and the wage-transparency or -secrecy policy. Formally, we consider a stylized moralhazard environment with two envious workers. Output is generated by the workers’ 8The CEO of Whole Foods Market, Inc. is cited as saying: “I’m challenged [on salaries] all the time. How come you are paying this regional president this much, and I’m making this much?’ I have to say, ‘Because that person is more valuable. If you accomplish what this person has accomplished, I’ll pay you that too.’” See https://hbr.org/2016/03/why-keeping-salaries-a-secret-may-hurt-your-company. 9For the European countries, see https://kompetenz-online.at/2018/05/15/lohntransparenz-iminternationalen-vergleich/. To identify the U.S. states, see the map on https://www.dol.gov/agencies/ wb/equal-pay-protections. Further details may be found in Cullen and Pakzad-Hurson (2023), Footnote 12. See Perez-Truglia (2020) for a short discussion of transparency rules in the Scandinavian countries and Iceland. 123 Incentives and peer effects... 91 non-contractible effort. When workers work jointly in an integrated unit, output is further enhanced through productive synergies. The employer chooses whether to integrate or separate workers, and in the former case, whether to impose a wage-secrecy rule or, on the contrary, make payments public. Workers are motivated by optimally designed individual bonus contracts. In determining the optimal organizational architecture, wage-transparency policy, and contract design, we separately consider two scenarios in which ex-post wages are either constrained by a lower bound or not. The latter case constitutes unlimited worker liability, whereby the employer can extract all informational rents from workers by adjusting the fixed wage accordingly. In the more realistic scenario where workers are protected by limited liability (perhaps arising from wealth constraints, standard wages, minimum wages, etc.), the employer is forced to leave informational rents to the workers. We find that, under unlimited liability where the employer can extract rents from workers, the presence of envy increases employment costs, thereby making productive synergies and envy substitutes.Intuitively, exanteworkersformexpectationsabout the ex-post occurrence of payoff inequity. To induce participation, the employer needs to compensate them by an inequity (envy) premium for the associated disutility stemming from the other-regarding nature of their preferences. In this sense, the workers’ social preferences imply a negative peer effect that counteracts the productive synergies. As a result, if wages are transparent, integrated production will be chosen only if workers are not too envious and productive synergies are sufficiently pronounced. Imposing wage secrecy instead removes the cost associated with social comparisons, making worker integration the optimal choice. In stark contrast, under limited liability, productive synergies and envy become complements as long as workers earn rents. Specifically, when working jointly under wage transparency, workers increase effort to reduce the likelihood of falling behind their co-worker’s wage ex post, a consequence known as the incentive effect of envy. This increased effort is manifested as positive peer effects, providing the employer a “free lunch” in terms of higher productive output and reduced informational rents. However, when envy is intense, workers’ envy premia become so large that rents vanish.It then becomes optimal to impose wage secrecy, if possible, or to separate the workers, if not, also under limited liability. This also explains why employers may deliberately establish pay inequality by opting for individual performance pay rather than group bonuses. On the normative side, we conclude that popular pressures for transparency and “sunshine laws” do not necessarily raise workers’ welfare. In the absence of rents, enforcing transparency may induce firms to separate workers, thereby forgoing gains from positive production externalities and bearing efficiency losses. Alternatively, in the presence of rents, sunshine laws benefit those employers who failed to recognize the profitable incentive effect of wage transparency at the expense of workers.The latter then find themselves placed in settings which trigger social comparisons and envy. Bytheforegoingfindings,ourpaperextendsandprovidesnovelinsightsintothevarious strands of the literature concerning the aforementioned workplace characteristics. In particular, our unified formal theory reveals that envy is potentially a key consideration affecting firms’ organizational and informational design, as has already been indicated by the management literature. However, our model explicitly demonstrates 123 92 J. Kragl et al. that the impact of envy on the foregoing organizational dimensions is not straightforward. Specifically, we are the first to show that whether workers are protected by limited liability is decisive for firms’ optimal organizational architecture and their attitude towards wage transparency. In fact, we show that, under limited liability, firms may deliberately foster income comparisons by organizationally integrating workers and actively promoting wage transparency in order to benefit from both productive synergies as well as intrinsic work incentives arising from envy. These mechanisms provide a new explanation for the emergence of peer effects in the first place and firms’ (potential) active and conscious role in manipulating them. The remainder of the paper is structured as follows. In the following section, we present literature concerning the various aspects of the workplace environment and the model. Section3presents the theoretical environment. In Sect.4, we consider, as a benchmark, the moral-hazard problem under unlimited liability. Specifically, we first analyze the workers’ optimization problem and then derive the optimal incentive contracts under worker integration and separation. Thereafter, we characterize the optimal organizational architecture under wage transparency and then analyze whether the latter policy is optimal. Section5turns to the more realistic scenario where workers are protected by limited liability. In particular, we reconsider the optimal organizational design and discuss the striking differences compared to the unlimited-liability case. In Sect.6, we present several extensions of our model considering the effects of a positive minimum wage, imperfect wage secrecy, and the inclusion of joint performance pay. Moreover, we extend our model to the broader specification of social preferences developed by Charness and Rabin (2002), accommodating inequality aversion (Fehr and Schmidt 1999), social-welfare preferences, and efficiency concerns. Then, in Sect.7, we discuss some of the simplifying features of our model and consider possible manifestations of envy in further social-preference specifications. Finally, the last section concludes and presents some general, societal, and managerial implications. 2 Literature 2.1 Peer Effects in the Workplace While peer effects span various behavioral aspects (see, e.g., Welteke 2015), we focus here on field experiments related to productivity, which is the measure relevant to our study. In this context, a variety of different empirical studies are consistent with our model’s theoretical predictions. For example, Mas and Moretti (2009) used productivity data on supermarket cashiers at a supermarket chain. Their findings indicate the presence of positive peer effects, the extent of which depends on the frequency of interaction in the workplace and, in line with our approach, on observability,in their case of actions. Bandiera et al. (2010) identify workers’ friends within a U.K. agricultural firm and combine this information with each worker’s productivity. In line with our results, they conclude from the data that even in the absence of productivity externalities “firms can exploit social incentives as an alternative to monetary incentives” (p. 417). In the same vein, using German social-security data, Cornelissen et al. (2017) identified peer groups by workers’ occupation and their employer. 123 Incentives and peer effects... 93 Distinguishing between jobs in which mutual observation and judgments are easy and those where such comparisons are more difficult, they found large peer effects on effort, particularly among workers in the former type of occupations. Cornelissen et al. (2017, p. 454) emphasize that it is peer pressure, rather than knowledge spillover, that provides an incentive for workers to increase their efforts. Horton and Zeckhauser (2018) conduct field experiments on Amazon’s online labor market, Mechanical Turk (MTurk). By controlling the informational environment of workers, they could identify peer effects even among workers who did not physically interact. Most relevant for our theoretical environment is their finding that exposing workers to the output of their peers increases their own efforts. This finding led Horton and Zeckhauser (2018, pp. 25, 27) to conclude that “(i)n settings where effort and productivity are tightly coupled and workers can easily monitor each other, peer pressure would seem to provide a kind of free lunch for the firm.” 2.2 Wage transparency Many studies investigate the impact of the informational environment, in particular income transparency, on workers’ wellbeing and behavior (see, e.g., Perez-Truglia 2020). While much of this literature is motivated by “fairness” concerns and the role of wage transparency in alleviating them (see, e.g., the discussion in Charness and Kuhn 2007) many studies report that wage transparency has significant behavioral impact on affected individuals. In fact, there is increasing evidence that making workers aware of the wages of their peers has positive effects on effort. Bamberger and Belogolovsky (2010) found this effect in an experimental setting, using a computer matching game with bonuses paid for success. In that setting, pay secrecy was associated with decreased performance. Huet-Vaughn (2015) designed an experiment on MTurk to show that exposing workers to information about the earnings of others, who perform a similar task at the same piece rate, increased output of the informed group by about 10 percent. Gao et al. (2021) exploit the natural experiment provided by changes in legislation of several U.S. states, passing explicit laws prohibiting wage secrecy clauses (so-called pay-secrecy laws). Using a difference-in-difference approach on a large sample of firm-year observations, they were able to show that (p. 2) “(o)n average, firms headquartered in states that have adopted pay secrecy laws increase their number of patents by 17.7% and increase their number of patent citations by 17.5%, relative to firms headquartered in other states.”10 Focusing on settings with incentive pay, these findings are in line with the positive peer effects identified in our model. In a different setting where wages are fixed and independent of output, Cohn et al. (2014) find that peers exposed to disadvantageous income inequality tend to react by reducing effort. Cullen and Perez-Truglia (2022) also detect effort reductions resulting from horizontal disadvantageous pay differences. A similar effect is found in a field experiment by Breza et al. (2017) and also implicitly by Bennedsen et al. 10 Gao et al. (2021) ascribe the productivity effect of increased transparency to the removal of discriminatory behaviours towards women and ethnic minorities, helping raise the moral and motivation of scientists belonging to these population groups. 123 94 J. Kragl et al. (2020) who exploit a natural experiment. Despite this seeming contradiction to our finding, whereby wage comparisons have positive effort effects, this behavior is nevertheless consistent with our preference specification albeit not with our agency model. Specifically,the foregoingstudies investigatetheeffort effectsofgivenfixed-wagediscrepancies. In contrast to our model, they do not however consider incentive contracts, where worker effort affects final wage payments. The distinct behavioral outcomes are due to this basic difference. Whereas the only way to compensate for disadvantageous fixed-wage inequality is to reduce effort, in our scenario, workers can and will undertake effort to reduce the likelihood of envy to arise. In a very different context, Cullen and Pakzad-Hurson (2023) analyze the effects of wage transparency in a dynamic general-equilibrium bargaining setting. In their empirical application, they find that disadvantageous income inequality eventually leads to increased employment cost (see also Cullen 2023). At the partial-equilibrium level, our agency model also predicts increased employment cost, provided workers receive no rents. 2.3 Social preferences in agency models Our theoretical framework is embedded in the principal-agent literature investigating other-regarding preferences in the firm. In this context, several studies have fruitfully incorporated social-preference features into classical contract-theoretic settings (see Köszegi 2014 for a review of the research in behavioral contract theory). In the moralhazard context, much of that work has revisited the effectiveness of different types of performance pay in the presence of other-regarding preferences, in particular envy or inequity aversion in the sense of Fehr and Schmidt (1999). In these environments, the focus is typically on agency relationships within firms, where workers compare their income with that of co-workers or their boss. The existing studies include work on horizontal and vertical social preferences as well as individual, joint, and relative performance pay. For example, Dur and Glazer (2008) and Englmaier and Wambach (2010) examine optimal incentive contracts when agents care about inequality relative to the principal whereas Demougin et al. (2006) and Neilson and Stowe (2010) focus on mutually inequity averse or envious agents. The impact of the latter preferences in the context of tournaments is analyzed by, e.g., Demougin and Fluet (2003), Grund and Sliwka (2005), and Schöttner (2005). Further studies compare the efficiency of different incentive regimes for other-regarding workers more generally (e.g., Goel and Thakor2006;Bartling 2011). Finally, Itoh(2004) presents acomprehensivemodelthat encompasses a rich set of vertical and horizontal distributional income concerns as well as a variety of contract structures. Overall, this literature indicates that both envy and the joy of outperforming make incentive pay more effective while the opposite is true for compassion. Nevertheless, when workers suffer additional disutility due to their social preferences, it generally becomes more costly to induce participation. In particular, an inequity premium must be paid to compensate workers for the expected disutility from pay inequality. To lower variability in payoffs, principals then typically respond by reducing the optimal incentive pay and, consequently, contracts induce lower effort, thereby reducing output and profit. Altogether, this literature tends to 123 Incentives and peer effects... 101 Fig. 1 Optimal Organizational Architecture under Unlimited Liability (a) without and (b) with Productive Synergies In contrast, productive complementarities per se motivate the employer to induce higher effort. The combined effects of synergy and increased effort shift profits under integrationupwardswhileprofitsunderworkerseparationremain unaffected,as shown in panel (b) for γ=1.2. Still, envy forces the employer to bear the envy-premium costs. Accordingly, as long as the intensity of envy is not too high, integration becomes superior to worker separation. Beyond that critical point (αU(1.2)=0.87), separation dominates as the combined effort and synergy effect is no longer sufficient to overcome the agency cost even though the induced effort is still higher than it is under separation. It is in this sense that the synergy factor γand the workers’ propensity for envy αare substitutes with regard to the optimal organizational design. 4.3.2 Wage secrecy In this subsection we reconsider the optimal organizational architecture when the employer can also choose the organizational policy. The result is formally summarized by the following corollary. Corollary 2 (Optimal Organizational Policy under Unlimited Liability) (i) For γ=0, setting δI=1and δS=1is equivalent to setting δI=0. (ii) For γ>0and α>0, setting δI=1and δS=1strictly dominates setting δI=1and δS=0as well as setting δI=0. (iii) For γ>0and α=0, setting δI=1and δS=1is equivalent to setting δI=1and δS=0. Proof Given the results of Corollary 1, only γ>0 needs to be considered. From equation (7) it is obvious that U(1,1;·,γ)≥U(1,0;·,γ), with strict inequality for α>0.  The Corollary implies that choosing to integrate workers (δI=1) and imposing a secrecy clause (δS=1) becomes (weakly) dominant for any level of envy. Absent social comparisons, integration dominates because it sustains productive complementarities. In the presence of social comparisons wage secrecy then becomes the optimal organizational policy as it rules out any adverse effect of envy. 123 102 J. Kragl et al. Fig. 2 Optimal Organizational Design under Unlimited Liability The result is illustrated for γ=1.2inFig.2. The red curve depicting profits under integration and wage transparency, U(1,0;α, 1.2), and the dashed (dark blue) one representing profits under worker separation, U(0,·; ·,·), are both identical to those shown in panel (b) of Fig.1.With wage secrecy the profit under integration and productive synergy (γ=1.2) is depicted by the dot-dashed (grey-brownish) horizontal line. As the secrecy clause neutralizes the effect of envy it originates at U(1,0;0,1.2)which is, of course, larger than U(0,·; ·,·). Altogether,theabovemayrationalizeempiricalobservationsregardingthetendency of employers to impose wage secrecy despite the questionable legality thereof. In the next section, we reconsider the firm’s optimal organizational design under worker limited liability and verify that the dominance of the wage policy is no longer universally true. 5 The moral-hazard problem under limited liability In this section we analyze the employer’s optimal organizational architecture under the constraint that workers are protected by limited liability, i.e., there exists a lower bound to ex-post wage payments in any state of the world. For simplicity and in line with most of the agency literature we set this lower bound to zero. As it will turn out, this restriction has far-reaching consequences for the optimal incentive contracts and the resulting organizational design. Specifically, we highlight the essential effects on the (non)optimality of worker separation and wage secrecy. 123 Incentives and peer effects... 103 5.1 The employer’s problem The workers’ choice of effort for a given contract (w, b)is unaffected by the introduction of limited liability. Accordingly, their optimal effort eis characterized by the same symmetric Nash-equilibrium described in Sect. 4.1. Analogous to our discussion above we start the analysis of the employer’s problem by assuming that the organizational architecture (δI,δS)is given: max w,b,e2e+δI·γ(e)2−2(w +p(e)b)(II) s.t.b=c(e) (1+δI(1−δS)αp(e))p(e),(IC) w+p(e)b−c(e)−δI(1−δS)α(1−p(e))p(e)b⩾0,(PC) w⩾0,(NNC1) w+b⩾0(NNC2) where (NNC 1)and (NNC 2)ensure that a worker earns a non-negative wage for all possible realizations of his/her signal. Condition (IC)implies that b≥0, and hence (NNC 2)can be disregarded. From (IC),(PC)and (NNC 1)and simplifying, the fixed wage satisfies w=max c(e)+δI(1−δS)α(1−p(e)) −1p(e)c(e) (1+δI(1−δS)αp(e))p(e),0. (8) This implies that either (PC)or (NNC 1)or both must be binding. Note that workers earn a rent when (PC)does not bind. Under separation, (NNC 1)always binds and rents are positive at any effort e>0. Under integration, this also holds for selfish workers but once workers become sufficiently envious, (PC)starts binding. Intuitively, as the workers’ propensity for envy increases, at given effort, also the envy premium increases and eventually exhausts the rent. Substituting wfrom Eq. (8)into(II),the problem becomes: L(δI,δS;α, γ )=max e2e+δIγ(e)2 −2·max c(e)+δI(1−δS)·α(1−p(e))) 1+αp(e) p(e)c(e) p(e), (9) 1 1+δI(1−δS)αp(e)·p(e)c(e) p(e) Remark 1 Consider δI=1 and δS=0. Let αc L(γ ) denote the level of envy at which (NNC 1)and (PC)are just binding and αc U(γ ) denote the level of envy where w=0 when (NNC 1)is not imposed. Then αc L(γ ) < αc U(γ ) for any γ≥0 and for α∈ [αc L(γ ), αc U(γ )]the optimal bonus, wage and effort are jointly determined by (IC), (NNC 1)and (PC)as binding constraints. 123 104 J. Kragl et al. The existence of this interim region follows from the fact that, as long as α< αc L(γ ), the constraint (NNC 1)binds while (PC)does not bind. In this case the profitmaximizing effort is determined by the respective first-order condition associated with (9), whereby the employer is forced to pay rents and to reduce effort relative to the case without worker protection. Moreover, absent worker protection the fixed wage would be strictly negative in that region. This is still true at αc L(γ ), where (NNC 1) still binds and (PC)just becomes binding. Accordingly, when envy rises further to the point αc U(γ ),(NNC 1)just stops binding and wis optimally set to 0. Inside the interval [αc L(γ ), αc U(γ )], bonus, wage, and effort are hence determined solely by the constraints (IC),(PC), (NNC 1),and (NNC 2). Beyond αc U(γ ), optimal effort is again derived from the employer’s first-order condition (9), and the associated fixed wage and bonus are derived from (IC)and (PC)of (II), respectively. Proposition 2 Let δI=1and δS=0. (i) For any 0≤γ, then, as long as α<α c L(γ ), L(1,0;α, γ )is increasing in α, and once α>α c U(γ ),L(1,0;α, γ )is decreasing in α. Proof (i) Consider the following (partial) decomposition of (9): L L(1,0;α, γ )=max e2e+γ(e)2−2p(e)c(e) (1+δ·αp(e))p(e),α<α c L(γ ) L U(1,0;α, γ )=max e2e+γ(e)2 −2c(e)+α(1−p(e)))p(e)c(e) (1+αp(e))p(e),α>α c U(γ ) Since (PC)is not binding in the region α<α c L(γ ), the optimal effort is determined by the first-order condition associated with the maximand and the envelope theorem can be applied, yielding the result. In the region α>α c U(γ ) the function L U(1,0;α, γ ) coincides with U(1,0;α, γ )in (7) and is decreasing in α. The above result shows that - in strict contrast to the case of unlimited liability - under wage transparency employing envious workers in a joint-production setting may be advantageous for the employer. More specifically, as long as (NNC 1)is binding and workers earn rents, the employer exploits the above-mentioned incentive effect of envy to elicit higher productive efforts. Intuitively, inducing effort becomes cheaper because, given any bonus, both workers increase effort in an attempt to avoid being inferior to their peer. As long as rents are positive, this does not lead to an adjustment of the fixed wage. Consequently, as αincreases the employer finds it optimal to raise the bonus and induce an even higher effort. This implies that - again in strict contrast to the case with unlimited liability - the parameters γand αbecome complements, as long as workers earn rents. At some point however, when workers become sufficiently envious (α=αc L(γ )), rents vanish due to the large envy premium. With a further increase in envy (α>α c U(γ )) the limited-liability restriction becomes ineffective and 123 Incentives and peer effects... 105 the employer’s profit coincides with that under unlimited liability, where no constraint on the fixed wage was present in the first place. 5.2 The optimal organizational design To determine the optimal organizational architecture we proceed analogously to the case of unlimited liability. That is, we first analyze the optimal organizational architecture in the common-knowledge case and then determine the optimal organizational policy. As it turns out, unlike in the foregoing section, wage secrecy is no longer a strictly dominant policy if workers are protected by limited liability. Notably, in that case the employer may choose to refrain from imposing a secrecy policy to profitably exploit the peer effect. 5.2.1 Wage transparency The next Corollary 3characterizes the optimal organizational architecture for this case, depending on the workers’ propensity for envy and the synergy factor. Corollary 3 (Optimal Organizational Architecture under Limited Liability) Consider δS=0. Let αL(γ):L(0,·; ·,·)=L1,0;αU,γbe finite. Then (i) αc U(γ)<α L(γ). (ii) For α<α L(γ ),δI=1while, for αL(γ ) < α,δI=0, and at α=αL(γ ) the employer is indifferent between δI=0and δI=1. (iii) αU(γ)<α L(γ).(iv)αL(·)is increasing in γwith αL(0)>0.(v)IfαL(γ)fails to exist, then δI=1is optimal for any α. Proof (i) is an immediate implication of part (i) of Proposition 2. (ii) is analogous to part(i)ofCorollary1, sinceforα>α c U(γ ) thefunctionL U(1,0;α, γ )coincideswith U(1,0;α, γ )in (7). (iii) follows from the fact that L(0,·; ·,·)< U(0,·; ·,·). The proofs for (iv)-(v) are analogous to the respective ones in Corollary 1. By Corollary 3, the profit functions under the two organizational architectures intersect at the critical level αL(γ)of envy when workers are protected by limited liability. According to part (i) of the corollary, integration always dominates worker separation when workers earn rents but even beyond that point. The main point of Corollary 3(iii) is that, for any synergy factor, the employer chooses integration for a larger range of αwhen workers are protected by limited liability as compared to scenarios with unlimited liability. This implies that the optimal organizational architecture critically depends on whether workers are protected by limited liability or not. First, consider the case when there are no productive synergies. Recall that, by Corollary 1(ii), integration is never optimal under unlimited liability. In fact, by 3(iv), when liability is limited the employer finds it optimal to implement integration also when workers are envious. Intuitively, whereas under unlimited liability social comparison is always harmful, in this case joint allocation of workers becomes beneficial. Effort and profitability are increased through the exploitation of work incentives triggered by the workers’ envy. Moreover, in line with the unlimited-liability case, with 123 106 J. Kragl et al. Fig. 3 Optimal Organizational Architecture under Limited Liability (a) without and (b) with Productive Synergies productive synergies, employers find it optimal to induce higher effort and the range of α-values for which integration is chosen is raised even further. Altogether, under limited liability, the employer is likely to deliberately implement integration because this not only allows for productive complementarities but also provokes income comparisons across workers, which in turn strengthen work incentives and raises profit. Figure3illustrates the foregoing results. In both panels the profit under worker separation shown by the dashed (blue) line has shifted downwards by exactly the amount of the workers’ rents as compared to the case of unlimited liability shown in Fig.1.18 In line with Proposition 2profits under integration, shown in solid (red), have kinks at αc L(γ)and αc U(γ)(not marked).19 Thereafter, the curves coincide exactly with those of Fig.1. Again, panel (a) shows the case where there are no productive synergies. Notably, in contrast to Fig.1, profits under integration exceed those under worker separation for sufficiently low intensities of envy (α<α L(0)=2.87). In fact, for the range αc U(0),αL(0)integration remains optimal under limited liability even though profits already decrease in envy. Here, even without the synergy effect, at αL(0)effort under integration is higher than it is under worker separation but profits are eroded by the agency costs. Accordingly, when workers become sufficiently envious α>α L(0)worker separation dominates also under limited liability. With productive synergies, profit under integration shifts upwards due the presence of productive synergy and the higher induced effort (panel (b)). As a result, αc L(γ), αc U(γ)and with them the curve’s kinks shift to the right. Moreover, the intersection of the profit curves under the alternative organizational architectures, αL(γ), shifts to the right as well, so that integration is optimal for higher intensities of envy. A comparison with the case of unlimited liability in Fig.1shows that the presence of limited liability in fact increases the range of α-values for which the employer chooses integration. In particular, as a consequence of the strictly lower profits under separation, the range of 18 Notice that, for the sake of clarity, we adjusted the scale of the y-axis in the figure. 19 The interim regions are given by [αc L(0),αc U(0)]=[0.71,0.74]and [αc L(1.2),αc U(1.2)]= [0.82,0.91], respectively. While effort is increasing in αwithin the interim regions, profits initially continue to increase before they start to decrease once the envy-related costs become dominant. 123 Incentives and peer effects... 107 Fig. 4 Optimal Organizational Design under Limited Liability γ-values for which integration is preferred for any degree of envy is larger than that under unlimited liability (and may potentially become even negative). 5.2.2 Wage secrecy In this section we again reconsider the optimal organizational architecture under limited liability, and moreover determine the optimal organizational policy. Specifically, we analyze under what circumstances imposing a wage-secrecy clause is optimal. The result is summarized by Corollary 4as follows: Corollary 4 (Optimal Organizational Policy under Limited Liability) Let αLS (γ)∈ α:L(1,0;α, γ )=L(1,1;·,γ)∩{α∈R+}. Then (i) αLS (γ)<α L(γ). (ii) For α<α LS(γ ), setting δI=1and δS=0is optimal, for α>α LS(γ ), setting δI=1and δS=1becomes optimal, and, at α=αLS(γ ),δI=1is optimal while the employer is indifferent between δS=0and δS=1. (iii) αLS (γ)is increasing in γ. The proof of Corollary 4is analogous to that of Corollary 3and is thus omitted. Absent productive complementarities, the result coincides with panel (a) of Fig.3. It is only once complementarities arise that wage secrecy becomes relevant as it neutralizes the impact of the workers’ social preferences under integration. The profit generated by the imposition of secrecy, L(1,1;·,γ), is represented for γ=1.2by thedot-dashed(grey-brownish)horizontal lineinFig.4.Accordingly,integrationdominates worker separation, shown by the dashed (blue) line. However, unlike the case where workers are not protected by liability limits, wage secrecy is not always dominant. In particular, as discussed above, with limited liability, envy induces high effort as long as workers receive a rent and even beyond. Clearly, absent envy (α=0), the employer’s optimal profit under secrecy, L(1,1;0,γ), is identical to that under integration without secrecy, L(1,0;0,γ). Notably, as αincreases, wage transparency is more profitable than secrecy. Intuitively, in that case the employer uses transparency to 123 108 J. Kragl et al. deliberately exploit social comparisons and raiseprofits. However, once the propensity for envy becomes sufficiently high (α>α LS (γ)), the envy-premium costs associated with social comparison outweigh the incentive effects on worker motivation, thereby rendering the imposition of wage secrecy the optimal option (in the figure, αLS (1.2)=1.61). Notice that both profits, L(1,0;α, γ )and L(1,1;·,γ),shift upwards as γincreases. As a result, in this setting, αLS (γ)is always finite so that, even for very high values of γ, at some point wage secrecy becomes the preferred policy. 6 Extensions In the sequel, we discuss several extensions to our model. We start by investigating the impact of imposing a positive minimum wage. Then we analyze a scenario where wage secrecy is not fully enforceable. Following that, we consider the inclusion of a groupbonus scheme, whereby the employer jointly pays the workers the same rewards. In the last subsection, we extend the scope of social preferences in line with Charness and Rabin (2002). We show that the gist of our results continues to hold when extending the model in all of these directions. 6.1 Minimum wage In our main analysis, for simplicity we assumed that - when existing - the lower bound for the workers’ wage is set at 0. In this subsection, we present the effects of a strictly positive lower bound as often prevalent under minimum wages or collectively agreed standard wages. Figure5(a) replicates Fig.4, where a zero lower bound ˆw=0is imposed. In the figure below, we have adjusted the horizontal scale in order to allow for a comparison to the case with a positive minimum wage ˆw>0, shown in Fig.5(b). The effects are manifold. Firstly, naturally all profit curves shift down because the firm is forced to pay out higher fixed wages under all organizational designs. Secondly, the range of workers’ envy for which integration is dominant under wage transparency has increased dramatically. Thirdly, if secrecy cannot be implemented, worker separation becomes optimal for larger values of α. And finally, if secrecy is implementable, the range of propensities for envy for which the employer chooses to impose this policy is smaller than it is in the absence of a positive minimum wage. The results emerge from the fact that an increased lower bound on the fixed wage creates rents where none existed before. To mitigate the negative impact of these costs on profits, the employer continues to further exploit the forces unleashed by the existence of envy by inducing higher efforts. Technically speaking, the propensity for envy for which the lower-bound constraint becomes slack, αc L(γ ), is increasing under a positive minimum wage. Furthermore, the value of envy at which the wage under unlimited liability starts to exceed the increased lower bound, αc U(γ ), also increases.20 20 Specifying a 0.09 minimum wage, the interim regions are now given by [αc L(0),αc U(0)]=[1.44,2.40] and [αc L(1.2),αc U(1.2)]=[1.31,1.32], respectively. For both values of γ, these are strictly larger than those with a zero lower bound (see Footnote 19). In general, once the lower bound on the fixed wage 123 Incentives and peer effects... 109 Fig. 5 Optimal Organizational Design with (a) Non-Negative Wages and (b) a Positive Minimum Wage Altogether, the introduction of a positive minimum wage is a double-edged sword. On the one hand, it raises worker welfare by transferring part of the surplus from the employer to the workers via the higher fixed wages. On the other hand, the new emergence of rents causes the employer to react by eliciting higher efforts under integration. As discussed above, the employer achieves this by exploiting the incentive effect of envy under wage transparency. Quite obviously, this stands in conflict with the general policy goals related to transparency. Notably, this conflict is even more prominent under a positive minimum wage since the employer can then utilize the effort-enhancing effect of income comparison for an even larger range of workers’ envy. 6.2 Imperfect wage secrecy In the above analysis we have assumed that wage secrecy is fully enforceable. However, in practice, this may not be always true. Specifically, workers cannot be hindered from revealing (at least some) information about their wage to (at least some of their) colleagues. Moreover, as stated in the introduction, imposing a wage-secrecy policy may in fact be illegal. To take this into account we below discuss the interim scenario arisingunderintegrationwhenwages areimperfectlytransparentorsecret,focusingon the limited-liability scenario. Surprisingly, the following analysis reveals that imperfect secrecy enforcement may be even more prevalent as it is optimal for a broader range of envy intensities than perfect secrecy. We allow for wage-secrecy imperfection (under integration) by adjusting the range of the secrecy indicator, to be δS∈[0,1], reflecting the extent to which secrecy is enforceable. Specifically, a value of δSin the interior of the interval indicates that secrecy can be maintained only with probability δS. Notice that this is observationally equivalent to assuming that secrecy can be enforced with probability 1, but αhas decreased toα=(1−δS)·α. Figure6depicts the situation for γ=1.2 and δS=0.5. The accentuated-dashed (purple) curve L(1,0.5;α, 1.2)displays the profit function becomes sufficiently large, the unlimited liability case is no longer relevant and the interim region is empty. As long as profits remain positive, for α>α c L(γ)effort is set at a level that jointly satisfies the lower bound on the fixed wage, the incentive constraint, and the participation contsraint. 123 110 J. Kragl et al. Fig. 6 Optimal Organizational Design with Limited Liability and Imperfect Wage Secrecy under a partially implementable secrecy policy. For the sake of clarity, we have also included the critical values, now denoted by α(γ,δS), separating the range where it is optimal not to impose (even imperfect) secrecy and the range for which (im)perfect secrecy becomes the optimal option. As is obvious from the above-mentioned observational equivalence, for any δS<1, αLS(γ, δS)<α LS(γ, 1)(for the above parameters, αLS(1.2,0.5)=1.10 whereas αLS (1.2,1)=1.61). That is, somewhat surprisingly, as it becomes harder to enforce secrecy, the employer is inclined to impose it for ever lower propensities of envy. Consequently, as secrecy becomes more enforceable, i.e. δSrises, the upper dashed (purple) profit curve is stretched to the right, thereby becoming flatter. In the limit when δS→1, it converges to the perfect-secrecy case, shown for reference, by the dash-dotted (grey-brownish) horizontal line. Notice that the above sounds paradoxical at first as it implies that firms may have an interest to imperfectly enforce secrecy even when they could perfectly enforce it. Intuitively, analogous to the case where δS=1, the partial success of the secrecy policy allows the employer to benefit from the incentive effect of envy (to a weaker extent) as long as workers are paid rents. Accordingly, for δS<1, profits are rising with αeven beyond the point αLS(γ, δS). As a matter of fact, the range of α-values for which the employer profits from social comparison is consequently even larger under imperfect wage secrecy as compared to perfect secrecy. More precisely, imposing wage secrecy - if imperfect - becomes optimal already for smaller propensities for envy than it does under perfect secrecy. Eventually, rents are exhausted by the inequality premia also under imperfect secrecy, however at a higher level of envy, and profits start decreasing. This has two obvious consequences. First, when envy becomes very intense profits obtained under partial secrecy fall below those that would have emerged under perfect secrecy. Second and more important, in contrast to the latter case where worker separation was always dominated, separating workers (dashed (blue) line) becomes again the optimal organizational architecture if αis sufficiently high (not shown in the figure). 6.3 Group-bonus scheme The above analysis ignores the possibility of joint performance pay under integration. As an extreme case thereof, consider a group-bonus scheme whereby the employer 123 Incentives and peer effects... 117 observe the outcome or just anticipate it. However, there is abundant evidence regarding the striking utility effects of actually observing peer-related pay information (for example, Card et al. 2012, Perez-Truglia 2020). Our simplifying assumption that only ex-post observed wage differences matter reflects precisely this evidence, thereby allowing us to capture the relevance of the informational environment regarding wage-transparency policies. Another possibility is that workers do form anticipations about their peers’ possible pay but have consistent biases concerning either the probability of a disadvantageous wage differential or its size. The effect of a downward bias in either is similar to that of imperfect secrecy and thereby observationally equivalent to reduced envy. Accordingly, our results in Sect. 6.2, as illustrated in Fig.6, would carry over to such environments,therebybroadeningthescopeofthepositiveeffectsofsocialpreferences on firm profits. Due to our focus on the firm’s architectural and contractual design, we disregard potential social comparisons across firms. However, in some cases wage transparency transcends not only firm boundaries but also national borders. Notice that such published information does not lead to other-regarding effort incentives in the sense of our model. In particular, this informational diffusion is exogenous to organizations and workers other than those belonging to its originator (e.g., the UC system) and bears no resemblance to our setting (see Bental and Kragl (2021) for an analysis of the role of social comparison within a societal framework).31 Finally, our paper concerns horizontal income comparisons arising between workers rather than vertical comparisons between workers and their boss. Moreover, we focus solely on ex-ante identical workers who may experience ex-post income differences. Beyond providing analytical clarity, this setting is likely to apply to lateral comparison situations. This is not to say that ex-post income differences resulting from ex-ante distinctions do not affect envious workers. However, the extent to which such ex-ante differences, e.g., in ability, productivity levels, or life circumstances, affect utility where other-regarding preferences are concerned, goes beyond the scope of this paper (see our companion paper, Bental and Kragl (2024), for an analysis of the role of envy in the face of worker heterogeneity). 7.2 Envy in other types of social preferences Notwithstanding the undoubted importance of envy in employment relationships, many experimental settings and the meta-analysis by Nunnari and Pozzi (2022), though, show that people may in general behave benevolently towards one another. Prominent examples are ultimatum and dictator games in allocational situations where individuals often tend to display compassion to co-players and preferences towards equality. Significant effort has been devoted to rationalize such behavior patterns by various formal preference specifications. In line with the literature review of Cooper and Kagel (2016), in this subsection, we briefly and informally discuss the relevance 31 Thereisaparallelliteratureconcerning theroleofsocialpreferencesinthecontextofgeneral-equilibrium theory (see, e.g., Caucutt 2001; Sobel 2005; Bosmans 2007; Kilenthong and Madeir 2017; Fleurbaey et al. 2024; Thomson 2024). 123 118 J. Kragl et al. and possible implications of some further leading specifications beyond the models by Charness and Rabin (2002) and Fehr and Schmidt (1999) analyzed in Sect. 6.4. Thereby we focus on those alternative formulations that may be relevant to our economicenvironment and research question.In particular, we discusswhether theyadmit envy among workers and whether this is a dominant factor. We disregard reciprocity and intentions, which are also considered by many preference specifications, since there is no direct give-and-take relationship between the workers in our setting. AnotherimportantformulationofequalityconcernsispresentedbyBoltonandOckenfels (2000) whose model encompasses equity, reciprocity and competition (ERC) in the context of social preferences. In their specification (p. 171), people are sensitive to their share relative to the equal share of the total pecuniary payout, whereby any deviation from that share induces disutility. In their specific example (p. 173), that part of the preference specification is quadratic, implying symmetry between upward and downward deviations of the same absolute magnitude from the equal share. Applying this specification to the CR-environment would imply that envy and compassion are equally weighted, (in the CR notation ρ=−σ) enhancing the inequality premium but mitigating the incentive effect. As Figs.7and 8show, this combination has no particular effect on our conclusions. Rabin (1993) exemplifies an early attempt to formulate social preferences accounting for fairness, altruistic behavior, and reciprocity. In Rabin’s formulation (p. 1287) individuals considerthe“kindness”ofco-playerstowardstheminthe contextofallocational choices. In particular, an individual’s utility depends on the perceived deviation of the other person’s notional allocation from an equal split. Utility is reduced if that person is deemed to be “unkind” (allocating to himself more than the equitable amount). A favorable deviation, on the other hand, is utility-enhancing. The utility’s negative reaction to the perception of “unkind” behavior is akin to the presence of envy. The positive impact of “kind” behavior would be similar to the “competitive” attitudes discussed in Sect. 6.4.32 Levine (1998) rationalizes experimental outcomes of ultimatum and the final round of centipede games. The preference specification (p. 597) allows persons to be “altruistic” or “spiteful” towards co-players, whereby the utility also depends on whether the other players in turn are altruistic or spiteful towards them. A spiteful (altruistic) person’s utility is negatively (positively) affected by the utility of the other parties. Again referring to the CR-model, such preferences would entail increased (reduced) inequality-premium costs and an intensified (mitigated) incentive effect. Finally, the focus of Andreoni and Miller (2002)isonaltruistic behavior. The paper shows that axioms of revealed preferences can be applied to rationalize such behavior. In fact, the authors estimate a CES utility function which depends on own payoff and that of the other person. Depending on the elasticity of substitution between the two arguments and the cost associated with transferring resources to the other person, the model is consistent with altruistic sharing but also with perfectly selfish behavior. Notably, Andreoni and Miller (2002) found that a significant minority of 32 Rabin’s model has been extended by Dufwenberg and Kirchsteiger (2004) to a dynamic repeated game setting where it becomes crucial how beliefs on others’ future intention-based reciprocity are updated. 123 Incentives and peer effects... 119 subjects behave “jealously”, whereby these subjects intentionally erode the value of the transferred resources to reduce disadvantageous inequality. 8 Conclusion With this study, we contribute to literature concerning the presence of envy, the role of wage transparency, and the importance of peer effects in the workplace. We provide a formal theory that integrates these aspects into a unified analytical framework. Taking envy to be the driving force, we investigate its impact on firms’ optimal organizational design and their attitude towards wage transparency within a moral-hazard framework. Our analysis shows that transparency may prove to be a double-edged sword. In fact,itmayeventuallyturnagainstthe employeesandbenefit the employerinstead, and even more so under a positive minimum wage. Specifically, our results of Sect.4.3 may rationalize observations regarding the tendency of employers to impose wage secrecy, despiteitsquestionablelegality. This occurs because payinequalityraisesagencycosts when workers are not protected by limited liability. By contrast, in Sect. 5.2,weshow that the popular pressure for transparency (“sunshine laws”) may not be necessarily in the self-interest of employees. In fact, the main concern of sunshine laws is to reduce pay inequality and discrimination as well as enforce government accountability. Yet they also generate social comparisons and thus affect organizational design. In our setting, when workers earn rents, transparency triggers pay comparisons and generates envy, thereby raising workers’ intrinsic work incentives and efforts. It is the latter that are manifested as positive peer effects and provide a “free lunch” to firms. On the other hand, when workers do not earn rents, forced transparency and the associated envy-related agency costs generate negative peer effects and may induce employers to separate workers even at the expense of productive synergies. Regarding the organizational consequences, we find that, under unlimited worker liability, agency costs generated by wage comparisons turn out to be of primary concern. To avoid these costs, firms may choose to forgo productive synergies and separate workers into independent productive units. In contrast, worker integration becomes often optimal when workers are protected by limited liability and may thus earn rents. By deliberately placing workers jointly in one productive unit, firms trigger pay comparisons and provoke envy to raise profits. Notably, with wage transparency, integration remains optimal even when rents are dissipated unless envy becomes sufficiently intense, thereby making the costs resulting from social comparisons dominant. In extensions, we show that, following the same rationale, firms may opt for individual performance pay rather than group bonuses when workers earn rents. However, as just noted, when workers are highly sensitive to inequality, firms abandon wage transparency and impose secrecy in integrated settings. Interestingly, when wage secrecy is not fully enforceable, firms turn out to be more tolerant regarding worker envy and, accordingly, prefer worker integration over separation for higher intensities of social preferences. We also discuss the impact of a minimum wage, showing that integration becomes then more likely because the limited-liability scenario is more likely to apply. Our results are thus in line with the prominent evidence on the presence of positive peer effects amongst workers at the lower end of the wage scale. We further 123 120 J. Kragl et al. investigate a broad class of social preferences using the specification of Charness and Rabin (2002), including inequality aversion, competitiveness, and social-welfare preferences. We demonstrate that our results extend to a large range of empirically relevant parameter combinations, whereby competitive preferences strengthen the impact of envy further while the less likely specifications representing compassion and altruism mitigate its effect. Finally, our model may be used to evaluate popular “new-work” environments and therecentlywidespread use of remotework.Thereisevidence thatworkingfromhome reduces interpersonal contacts among coworkers. In the sense of our discussion, this may or may not lower productive synergies, yet it is likely to reduce the extent of social comparisons. However, it seems that after a drastic increase of firms’ use of remote work during the Covid-19 pandemic, employers now strive to get workers physically back to the workplace. This “natural experiment” may provide some insights into the interrelationships of synergies, social comparisons, peer effects, effort, and output. Appendix Group-bonus scheme Consider a bonus scheme whereby both workers obtain a bonus B1if one of them emits the signal s=1 and a bonus B2if both do. Taking the effort choice of worker j,ej, as given, worker i’s participation constraint becomes: w+p(ei)1−p(ej)+p(ej)(1−p(ei))B1+p(ei)pejB2−c(ei)≥0 (A.PC) The associated incentive constraint is: p(ei)1−2p(ej)B1+p(ei)pejB2−c(ei)=0(A.IC) Absent any constraints on the payment scheme, the employer sets e1=e2and solves: UGB =max e,b,B2e+γe2−2p(e)(1−p(e)) B1−2p2(e)B2 s.t. (A.PC) (A.IC) (A.I) With condition (A.PC)binding, the employer chooses to induce the first-best effort level, e∗∗, and any pair of (B1,B2)that satisfies (A.IC)at e∗∗ is consistent with this choice. 123 Incentives and peer effects... 121 Suppose now that workers are protected by limited liability. Focusing again on the symmetric case, the employer faces the following problem: LGB =max e,b,B2e+γe2−2p(e)(1−p(e)) B1−2p2(e)B2 s.t. (A.PC) (A.IC) w, B1,B2≥0 (A.II) Taking into account that at the optimum under limited liability the employer is forced to set w∗=0 and that condition (A.PC)is not binding, the problem (A.II) turns into: GB =max e,b,B ⎧ ⎨ ⎩ 2e+γe2−2p(e)(1−p(e)) B1−2p2(e)B2 +λp(e)(1−2p(e))b+p(e)p(e)B2−c(e) +μB1B1+μB2B2 ⎫ ⎬ ⎭,(A.III) where λ,μB1and μB2are non-negative multipliers associated with (A.IC)and the non-negativity constraints on B1and B2. Focusing on the latter, we obtain: −2p(e)(1−p(e)) +λp(e)(1−2p(e))+μB1=0 −2p2(e)+λp(e)p(e)+μB2=0 (A.mult) We will next rule out the case where both B1and B2are strictly positive as well as the case that B1>0 and B2=0. Supposethatbothbonuspaymentsarestrictlypositive.Inthatcase,μb1=μB2=0, by the second row of (A.mult)implying λ=p(e) p(e). Substituting this in the first row leads to −p(e)=0,a contradiction for e>0. Suppose next that B1>0butB2=0. In this case, μB1=0,implying λ= 2p(e)(1−p(e)) p(e)(1−2p(e)). From the second row of (A.mult)we then obtain 2 p3(e) 1−2p(e)+ μB2=0. Since, for B1>0,constraint (A.IC)implies that 1 −2p(e)>0, this contradicts the requirement that μB2>0. As a result, the only remaining case is B1=0 and B2>0. From (A.IC)we obtain: B2=c(e) p(e)p(e)(A.B) Finally, the problem (A.I)becomes: GB =max e,B2e+γe2−2p(e)c(e) p(e)(A.IV) 123 122 J. Kragl et al. Comparing this problem to problem (II) shows that the employer induces exactly the same effort as under perfect wage secrecy and obtains the same profit. Notice that there the individual bonus is adjusted to accommodate the fact that it is paid less often. Funding Open Access funding enabled and organized by Projekt DEAL. Open Access ThisarticleislicensedunderaCreativeCommonsAttribution4.0InternationalLicense,which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. 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