Abuse of authority and collusion in organizations

European Journal of Political Economy Vol. 21 (2005) 385 – 405 www.elsevier.com/locate/ejpe

Abuse of authority and collusion in organizations Kouroche VafaR * LAEP, Universite´ Paris 1-Panthe´on Sorbonne, Maison des Sciences Economiques, 106-112 Boulevard de l’Hoˆpital, 75647, Paris Cedex 13, France, and IZA, Bonn, Germany Received 16 September 2002; received in revised form 23 June 2004; accepted 6 July 2004 Available online 8 December 2004

Abstract I investigate an agency relationship with moral hazard where a principal relies on a supervisor to obtain verifiable information about an agent’s output. The supervisor’s discretionary power allows him to engage in unofficial activities, namely collusion and abuse of authority. Collusion occurs when the supervisor receives a bribe from the agent to conceal information whereas abuse of authority occurs when instead the supervisor asks the agent for a tribute to reveal information. I characterize the optimal incentive contracts in this environment and study how collusion and abuse of authority interact. Compared with the presence of a single form of unofficial activity, the presence of multiple forms of unofficial activity is never harmless and is more severely harmful. I also identify the condition under which the presence of multiple forms of unofficial activity entails cost super-additivity. D 2004 Elsevier B.V. All rights reserved. JEL classification: D82; L20; M12 Keywords: Moral hazard; Hierarchy; Abuse of authority; Collusion

1. Introduction Social science research on organizations has shown that hierarchies are exposed to multiple forms of unofficial activity.1 Yet, the principal–supervisor–agent literature to date has only investigated a single form of unofficial activity, namely collusion between the * Tel.: +33 1 45 79 26 21. E-mail address: [email protected]. 1 For example, Edwards (1979), Crozier and Friedberg (1980), Johnson and Libecap (1989), Husbands (1992), among others. 0176-2680/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ejpoleco.2004.07.006

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supervisor and the agent.2 In the standard model of this literature, the supervisor and the agent may form a coalition in order to withhold information to the detriment of the principal. I extend this model by allowing the supervisor to engage in both collusion and abuse of authority. Including abuse of authority in the analysis of multi-level hierarchies is an important step towards a better understanding of the functioning of these organizations. Indeed, abuse of authority is one of the most widespread and harmful forms of unofficial activity in hierarchies. Anecdotal evidence on minor forms of abuse of authority abounds. There is also a great deal of evidence on severe forms of abuse of authority such as sexual harassment.3 In a comprehensive study conducted by the United States Merit Systems Protection Board in 1989, 42% of women and 15% of men reported that they had been sexually harassed on the job (Flynn, 1991). Similar results have been obtained by Timmerman and Bajema (1999) in their investigation of sexual harassment in Northwest European countries.4 For the analysis, I consider a three-level hierarchy with hard (i.e., verifiable) information in the tradition of Tirole (1986, 1992). In such an environment, information can only be concealed but not forged.5 More formally, I investigate a principal–supervisor–agent hierarchy with moral hazard where hard information about the output produced by the agent is obtained through supervision. The role of the supervisor is therefore to produce a verifiable report on the agent’s output. Since the supervision technology is imperfect, the supervisor obtains information only with a certain probability. The informed supervisor then has the discretion to conceal information and pretend that he has not observed anything. This allows him to engage either in collusion or abuse of authority. When supervision reveals evidence that the agent has produced a low output, the supervisor may collude with the agent and, in exchange for a bribe, conceal his information from the principal. When instead supervision reveals evidence that a high output has been produced, the supervisor may abuse his authority by asking the agent for a tribute to reveal the information he has obtained.6 I characterize the optimal contracts in this environment. To investigate the additional modifications that the presence of two forms of unofficial activity introduces in the organization, I characterize the optimal contracts in the cases where only a single form of unofficial activity may take place and in the case where both forms are feasible. I first show that, in the moral hazard environment considered here, when only collusion may occur in the organization, it can be costlessly deterred, and is hence harmless. I next 2

Tirole (1992) and Laffont and Rochet (1997) provide extensive surveys of the literature on collusion. See also Edwards (1979) and Johnson and Libecap (1989) for evidence on other forms of abuse of authority in organizations. 4 Sexual harassment falls into two categories: quid pro quo harassment and hostile work environment harassment. Quid pro quo harassment, as the name implies, occurs when an employee must submit to unwelcome sexual advances as part of his or her employment (for example, sexual favors in return for increase in pay). Hostile work environment harassment occurs when an employee is subject to sexual misconduct (be it physical actions by another or others, or verbal sexual comments or innuendos), which creates a work environment so intolerable that a breasonable personQ would not be able to work under those conditions. The present paper is concerned with quid pro quo sexual harassment. 5 A different strand of literature investigates organizations where information is soft—that is, forgeable—and where collusion takes place under asymmetric information (e.g., Laffont and Martimort, 1997; Faure-Grimaud et al., 2003). 6 The paper’s terminology is borrowed from the sociological literature (see, for example, Breton, 1995). In this literature, bauthorityQ is used to describe a superior control over his subordinate. 3

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find that when abuse of authority is the only possible form of unofficial activity, it is not systematically costly to deter it. Abuse of authority is harmful only when the supervision technology is sufficiently inefficient. Therefore, though abuse of authority is not systematically harmful, it is more harmful than collusion. I then consider both forms of unofficial activity and show that, compared with the case where only a single form of unofficial activity is possible, the presence of multiple forms of unofficial activity increases both the scope and the intensity of the efficiency loss sustained by the organization. Indeed, preventing unofficial activities becomes systematically costly in this case and reduces more severely the efficiency of the organization. In other words, compared with the presence of a single form of unofficial activity, the presence of multiple forms of unofficial activity is never harmless and is more intensively harmful. This is because the possibility of abuse of authority makes collusion deterrence costly. Collusion is not harmless anymore. There thus exist negative interactions between unofficial activities. Finally, I identify the condition under which the cost of preventing both forms of unofficial activity is larger than the sum of the costs of preventing a single form of unofficial activity. That is, I identify the condition under which the presence of multiple forms of unofficial activity entails cost super-additivity. It has recently been shown that collusion can be costlessly prevented in a large class of circumstances with adverse selection and risk neutral players (e.g., Kessler, 2000; Che and Kim, 2004). In the light of these findings, Che and Kim (2004) question the relevance of the prevailing concerns about collusion in theoretical models and identify several environmental characteristics that may make collusion noxious, such as, for example, players’ risk aversion. As mentioned above, I show that collusion may also be harmless in a moral hazard setting with risk neutral players—though for reasons other than those in adverse selection models—and I identify another cause for collusion noxiousness, namely the presence of other forms of unofficial activity. Although unofficial activities can take many forms, principal–supervisor–agent models have rarely considered other forms of unofficial activity beside collusion.7 There is however a burgeoning literature that investigates optimal contracting in the presence of two forms of unofficial activity. VafaR (1994, 2002) investigates collusion and abuse of authority in a similar environment to the one considered here. However, since in his models there is no uncertainty in production, collusion and abuse of authority do not interact. Collusion is costless to deter even in the presence of abuse of authority.8 Hindriks et al. (1999) and Marjit et al. (2000) analyze extortion and collusion in the context, very different from mine, of tax evasion. They investigate a hierarchy composed of a government, a tax inspector, and a taxpayer in which the tax inspector may either collude with the taxpayer or extort money from him. Since in their models the taxpayer is not a member of the organization, and is hence not paid by the government, these authors 7

Other forms of unofficial activity than collusion have been studied by economists. For example, Milgrom (1988) and Shleifer and Vishny (1989) consider respectively influence activities and managerial entrenchment in firms. Unlike these authors, I am concerned with unofficial activities taking place in a principal–supervisor–agent organization with hard information. 8 The possibility of multiple types of unofficial activity is also considered by VafaR (2004a) who studies a principal–supervisor–agent organization exposed to multiple types of collusion.

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are concerned with external unofficial activities while I focus on internal unofficial activities. Moreover, these authors consider an environment where the supervisor’s information is soft while I am concerned with a hard information environment in the tradition of Tirole (1986, 1992).9 The plan of the paper is as follows. The model is presented in Section 2. Section 3 characterizes the optimal incentive contracts in the absence of unofficial activities. Sections 4 and 5 characterize the optimal incentive contracts respectively when a single form of unofficial activity is possible and when two forms of unofficial activity are possible. Section 6 concludes the paper. All proofs are in Appendix A.

2. The model I consider a hierarchical organization under moral hazard consisting of three risk neutral players: a principal (it), a supervisor (he) and an agent (she). The organization has the following characteristics. 2.1. Production technology The agent, who is in charge of the production task, has the choice between two effort levels, ea{0, 1}; i.e., she may either shirk (e=0) or work (e=1). Neither the principal nor the supervisor can observe the agent’s effort level. The production technology is such that if the agent decides to work, she produces a high output x HN0 with probability pa(0, 1) and a low output x Lu0 with probability 1
p. If instead the agent decides to shirk, she produces x L. 2.2. Supervision technology The principal can obtain hard information, or, equivalently, hard evidence (i.e., verifiable) about the output produced by the agent only through supervision. The agent and the principal are unable—due, for example, to a lack of time or expertise—to perform the supervisory task. The principal therefore relies on the supervisor whose role is to make a verifiable report on the agent’s output. Evidence obtained on output is private information to the supervisor, but, once revealed, it is verifiable.10 For the sake of simplicity, I assume that supervision is costless. Since the supervision technology is imperfect, the supervisor obtains private evidence about output only with probability pa(0, 1). The supervisor’s report, r, thus belongs to I={x L, F, x H}, where r=F indicates that supervision has been inconclusive. Given that the private information (evidence) obtained by the supervisor is hard, it can be concealed but not forged. That is, it is not possible for the informed supervisor to misreport the low output as high output or the high output as low output. 9

Lambert-Mogiliansky (1997) also studies extortion and collusion in the context, different from the present, of public procurement. 10 This means that evidence is verifiable only by the person(s) to whom the supervisor reveals it. Evidence is publicly verifiable only when the supervisor produces a report.

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2.3. Payoffs The agent’s and the supervisor’s utility functions are respectively, U A(w, e)=w
ce and U (s)=s, where w and s are the transfers received from the principal and cN0 is the agent’s disutility of effort. The agent’s reservation utility is u. For simplicity and without loss of generality, the supervisor’s reservation utility is normalized to zero. I assume that x H is large enough for it to be in the principal’s interest to engage in production. The principal must therefore elicit the production effort level e=1 for its organization to be valuable. The principal’s utility function is then U P(w, s)=px H
C(w, s), where C(w, s)=p[p(w H+ s H)+(1
p)(w L+s L)]+(1
p)(w F+s F) is the expected cost of production and supervision. S

2.4. Contracts Since hard information about the output is exclusively obtained through supervision, contracts are contingent on the supervisor’s report. The principal offers a contract (w L, w F , w H) to the agent, where w L and w H are the wages he receives when r=x L and r=x H, respectively, and w F is the wage he receives when r=F. Similarly, the principal offers a contract (s L, s F, s H) to the supervisor. The agent and the supervisor are protected by limited liability. I simply assume that the principal cannot impose negative wages on them. 2.5. Unofficial activities Given that the supervision technology is imperfect, the supervisor has discretion to conceal information from the principal. The supervisor’s discretion allows him to engage in two forms of unofficial activity. I assume that, when engaging in unofficial activities, the supervisor unofficially shows (but does not give) the private evidence he has obtained to the agent. In other words, unofficial activities take place under symmetric information about evidence between the supervisor and the agent. When supervision reveals evidence that the agent has produced a low output, the supervisor may collude with the agent and, in exchange for a bribe, report r=F to the principal. The agent then receives w F and pays the promised bribe to the supervisor. When instead supervision reveals evidence that a high output has been produced, the supervisor may abuse his authority and threaten the agent with an uninformative report, r=F, in case she refuses to comply and to pay him a tribute. If the agent decides to comply, the supervisor reports r=x H. The agent then receives w H and pays the promised tribute to the supervisor. Concerning unofficial activities, I make the following assumptions. 2.5.1. Observability Unofficial activities are only observable to the involved parties. 2.5.2. Side transfer technology Following the literature on collusion, I assume that the technology used to transfer bribes and tributes, which I refer to as side transfer technology, is less efficient than the official transfer technology (i.e., the transfer technology used by the principal to pay its employees). Formally, unofficial income can be transferred to the supervisor at a rate

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ka(0, 1). That is, the side transfer creates a deadweight loss. A side transfer of size t is then only worth kt to the supervisor. There are therefore transaction costs connected to side contracting. The transaction costs of side contracting reflect the fact that unofficial activities are costly to organize. These transaction costs can also reflect the non-monetary nature of bribes and tributes.11 Observe that if k=0, the side transfer technology is totally inefficient, and thus unofficial activities do not occur. Finally, note that the technology of the organization is fully characterized by the vector (p, p, k). 2.5.3. Unofficial bargaining In concert with Tirole (1992) and others, I assume that the supervisor has all the bargaining power when engaging in unofficial activities. 2.5.4. Unofficial commitments An essential feature of unofficial activities is that they involve unofficial commitments (i.e., threats and promises). When the agent and the supervisor collude, the agent promises to pay a bribe to the supervisor after the supervisor has reported r=F. When the supervisor abuses his authority and the agent complies, she promises to pay the demanded tribute to the supervisor after he has reported r=x H. The agent will pay the promised bribe or tribute only if the supervisor’s threat of punishing her, that is, of seeking revenge, in case she does not keep her promise is credible. Following Baliga and Sjo¨stro¨m (1998, p. 204, footnote 6) and others, I make the standard assumption that the supervisor has access to a mechanism for punishing the agent in case she does not pay him the promised bribe or tribute, and the punishment is severe enough to make the agent’s strategy not to keep her promise unprofitable. As just explained, the agent will keep her promise only if the supervisor’s threat of using this mechanism is credible. Similarly, the agent will comply to the supervisor’s abuse of authority only if the supervisor’s threat of punishing her, that is, of seeking revenge by reporting r=F instead of r=x H, in case she refuses to comply is credible. To sum up, abuse of authority is possible only if the supervisor’s threats of punishing the agent by reporting r=F instead of r=x H in case she does not comply and of punishing her by using the just mentioned mechanism if she complies but finally refuses to pay the promised tribute once the supervisor has reported r=x H are credible. Likewise, collusion is possible only if the supervisor’s threat of punishing the agent by using the above mechanism if she refuses to pay the promised bribe once the supervisor has reported r=F is credible. Given that these unofficial commitments cannot be enforced by a third party, they have to be enforced by various mechanisms. Like the existing literature on unofficial activities in organizations—more particularly Tirole (1986, 1992) and VafaR (2002)—I do not explicitly model the mechanism that guarantees the credibility of the above discussed unofficial commitments. Findings in experimental economics and evidence derived from case studies of abuse of authority in hierarchies show that both reputational and non-monetary mechanisms sustain the

11

See Tirole (1992) for a discussion of different kinds of transaction costs.

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credibility of commitments even in one-shot interactions (e.g., Fehr and Ga¨chter, 1999, 2000; Bosman et al., 2001; Bosman and van Winden, 2002).12 I therefore take these findings and evidence as the starting point of my modelling. Following the existing literature, I assume that several possible mechanisms ensure the credibility of the supervisor’s and the agent’s unofficial commitments, namely emotions, reputation, and reciprocity.13 For example, if it is common knowledge that the supervisor incurs a prohibitive psychological or emotional cost, due to frustration or anger, when he does not carry out his threats or when he does not reciprocate what he perceives as a hurtful action, the agent both complies when the supervisor abuses his authority by threatening her with reporting r=F instead of r=x H and keeps her promise to pay a bribe or a tribute to the supervisor in the collusion and abuse of authority subgames (i.e., unofficial subgames). Commitments in the unofficial subgames are then credible due to the commonly known vindictive or aggressive psychological profile of the supervisor.14 As argued by Shavell and Spier (2002, p. 8): bA plausible emotional motivation provides a reason to believe that a threat might be credible without a binding commitment. Suppose that a threatener will become angry with the victim if his demand is rejected, and thus enjoy carrying out his threat, whereas the threatener will not be angry (and possibly will be favorably disposed toward the victim) if the victim pays him. If this is so and the victim understands that, the threatener’s psychological makeup will itself lead him to carry out his threat if and only if he is not paid, so that his threat will be credible.Q Similarly, if the supervisor has developed a reputation for being vindictive—that is, as just explained, for incurring a prohibitive psychological or emotional cost if he does not carry out threats—commitments in unofficial subgames are credible.15 The psychological or emotional paradigm can then be viewed as an extreme case of a reputation model in which the prior probability of the supervisor being vindictive is equal to one. Note that the discussion suggests that a single form of reputation or emotion guarantees the credibility of both threats and promises in the unofficial subgames. This means that no extra assumption is needed to also study abuse of authority in principal– supervisor–agent organizations. There is therefore no reason to rule out the possibility of abuse of authority once the possibility of collusion is allowed. 2.6. Timing The timing is as follows: (1) The principal offers a contract (w L, w F , w H) to the agent and a contract (s L, s F, s H) to the supervisor. (2) The agent and the supervisor decide whether to accept or refuse the contract. If either refuses, the game ends and they both get their reservation utility. If instead contracts are accepted, the game continues as follows. (3) Supervision takes place and the agent decides whether to work or to shirk. (4) If (i) 12

See also Hirshleifer (1987, 2001), Frank (1988) and Loewenstein (1996). For a detailed discussion of these mechanisms, see VafaR (2002). 14 For models where emotions may offset material incentives so as to make some behaviors credible, see, for example, Huang and Wu (1992) and Yaniv (2001). 15 As discussed in VafaR (2002), further evidence in support of the assumption that long term as well as nonmonetary devices sustain the credibility of the supervisor’s threat can be derived from case studies of sexual harassment. 13

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supervision reveals evidence that the agent has produced a low output, the agent and the supervisor decide whether or not to collude; (ii) supervision reveals evidence that a high output has been produced, the supervisor decides whether or not to abuse his authority. (5) The supervisor produces a report. (6) Transfers and side transfers take place. I look for a Subgame Perfect Equilibrium of this game.

3. Optimal contracts in the absence of unofficial activities As a benchmark, let me consider the case where unofficial activities are not possible (i.e., k=0). The agent’s incentive compatibility constraint is then, p[pw H+(1
p)w L]+ (1
p)w F
czpw L+(1
p)w F , or equivalently, c ð1Þ wH
wL z : pp This equation makes the agent prefer to exert effort in equilibrium.16 The agent’s contract must also satisfy her participation constraint, p½pwH þ ð1
pÞwL  þ ð1
pÞwF
cz
u:

ð2Þ

Given that the agent and the supervisor are protected by limited liability, wL z0; wF z0; wH z0; sL z0; sF z0; sH z0:

ð3Þ


Since supervision is costless,
the supervisor accepts any contract sL ; sF ; sH aR3þ . That is, any contract sL ; sF ; sH aR3þ is individually rational. In order to provide incentives to the supervisor to reveal the information he has obtained, the principal must also set s Lzs F and s Hzs F.17 Given that the optimal contract offered to the supervisor in this case and in the subsequent cases satisfies these constraints, I will systematically disregard them. When unofficial activities are not possible, the program of the organization can thus be written as 
½P 0  min p p wH þ sH Þ þ ð1
pÞ wL þ sL Þ þ ð1
pÞ wF þ sF wL ;wF ;wH ;sL ;sF ;sH

s.t. Eqs. (1), (2) and (3). Proposition 1 summarizes the set of solutions to this program. Proposition 1. If unofficial activities are not possible, the optimal contracts are such that w F a[0, u/(1
p)], w L a[0, u/p
(1
p)w F /p], w H = (c+ u)/(pp)
(1
p)w F / (pp)
(1
p)w L /p, and (s L , s F , s H )=(0, 0, 0). The expected cost of production and supervision is C 0 =c+u. The proposition states that, in the absence of unofficial activities, the principal does not need to provide rents to obtain information. I now study if this result still holds when the supervisor may engage in unofficial activities. 16 17

I assume that the agent chooses to work when she is indifferent. I assume that the supervisor reports truthfully when he is indifferent.

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4. Optimal contracts in the presence of a single form of unofficial activity In this section, I study the cases where the supervisor may only engage in a single form of unofficial activity. I respectively consider the case where only collusion is possible and the case where the supervisor may only engage in abuse of authority. 4.1. Collusion In an organization where only collusion is possible, the supervisor and the agent may collude when supervision reveals evidence that a low output has been produced. This takes place either when the agent shirks or when she works hard but is unlucky. In both of these cases, the agent promises to pay a bribe to the supervisor if he accepts to conceal information and report r=F instead of r=x L. If collusion occurs and the agent pays the promised bribe, her utility is w F
b if she has shirked, and w F
b
c if she has worked but has been unlucky, where b is the bribe offered to the supervisor. If instead collusion does not occur, the agent’s utility is w L if she has shirked, and w L
c if she has worked but has been unlucky. The agent is thus ready to form a coalition with the supervisor if w F
bzw L, that is, if bVw F
w L. The maximum bribe, b M, the agent is willing to offer for an uninformative report is therefore b Muw F
w L, where w F
w L is the stake of collusion. If the principal sets w Fbw L, the stake of collusion is destroyed, and hence collusion does not take place. If instead the principal sets w Fzw L, given that the supervisor has all the bargaining power, he can extract b M from the agent. I make the standard assumption that the supervisor does not engage in unofficial activities when he is indifferent. Collusion between the supervisor and the agent will hence not occur if the supervisor’s utility from making a truthful report, s L, exceeds his utility from concealing information, s F+kb M, that is, if
sL zsF þ k wF
wL ; ð4Þ This constraint is the no-collusion constraint. It expresses that collusion can be prevented either by creating incentive payments for the supervisor or by destroying its stake, that is, by setting w F=w L.18 Clearly, collusion can be costlessly prevented if the principal sets w Fbw L or, from the no-collusion constraint, w F=w L. In other words, all collusion-free contracts of Proposition 1 verifying w FVw L are collusion-proof. Therefore: Proposition 2. When collusion is the only possible form of unofficial activity, it does not affect the efficiency of the organization. In the next section I show that collusion is not harmless anymore when the supervisor may also engage in abuse of authority. Observe that a similar result as that of Proposition 2 is proven in Vafaı¨ (1994, 2002). However, the reason behind the result there is different from the one here. Indeed, collusion is there harmless because p=1, and hence the supervisor’s wage s L does not enter 18

Note that in the environment considered here, there is no loss of generality in restricting attention to contracts that deter collusion.

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the objective function. This wage can then be set so large as to deter collusion without affecting the efficiency of the organization. I am not of course claiming that collusion is systematically costless to prevent. My result suggests that, unlike in certain adverse selection hierarchies with risk neutral members, collusion, when the only possible form of unofficial activity, may be completely harmless in a moral hazard setting while, as will be shown below, abuse of authority is not always costless to prevent in such a setting. As discussed in VafaR (2002), collusion can also be harmless in risk neutral adverse selection organizations. Indeed, recent papers show that the harmfulness of collusion is very dependent on the environment in which collusion may occur (e.g., Olsen and Torsvik, 1998; Kessler, 2000). These papers prove that if the standard adverse selection model of collusion with risk neutral players is slightly modified, collusion becomes harmless or even beneficial.19 4.2. Abuse of authority In the case where abuse of authority is the only possible form of unofficial activity, the supervisor may abuse his authority when supervision reveals evidence that the agent has produced a high output. The supervisor then threatens the agent with an uninformative report if she refuses to comply and to pay him a tribute. The agent’s utility is w H
t
c if she complies to the supervisor’s abuse of authority and pays the demanded tribute, denoted t, and w F
c if she does not comply. The agent therefore complies and pays a tribute for information revelation if w H
t
czw F
c, that is, if tVw H
w F. Since the supervisor can extract the maximum amount of t Muw H
w F from the agent, his utilities corresponding respectively to abusing and not his authority are s H+kt M and s H. The supervisor thus engages in abuse of authority whenever he has a stake in it, that is, whenever t MN0.20

19 For instance, Kessler (2000) proves that collusion becomes costless to deter if the timing of the observation of the supervisor in the standard collusion model with adverse selection is modified. 20 Note that, as discussed above, if no mechanism exists to ensure the credibility of the supervisor’s threats, or equivalently, of the agent’s promises and the supervisor’s threat, unofficial activities will not occur. In the subgame where the supervisor may engage in abuse of authority, the supervisor threatens to report r=F instead of r=x H in case the agent refuses to comply to his abuse of authority, and to punish the agent (i.e., to inflict a decisive loss on her) if she complies but decides not pay the demanded tribute once the supervisor has reported r=x H. If no mechanism sustains these threats, the supervisor reports r=x H if the agent refuses to comply, and does not punish the agent if she complies but decides not to pay the promised tribute. The agent’s utilities associated respectively with complying and paying a tribute and complying but deciding not to pay a tribute are then w H
t M
c and w H
c. Therefore, if the agent complies she will not pay a tribute. Applying backward induction, the agent has then the choice between complying but deciding not to pay the demanded tribute and not complying. Since these two choices yield the same utility, w H
c, the agent does not comply to the supervisor’s abuse of authority. The supervisor’s utility is then s H whether he engages or not in abuse of authority, and hence this form of unofficial activity does not occur. As explained, a single mechanism sustains the credibility of the supervisor’s threat of punishing the agent if she does not pay the promised bribe or tribute, respectively, in the collusion and the abuse of authority subgames. Therefore, in the absence of a mechanism, collusion also does not take place. This is because, anticipating that the supervisor will not punish her, the agent will not pay the promised bribe to the supervisor after he has reported r=F instead of r=x L. Since the supervisor’s utility is then s F if he colludes with the agent and s L if he does not, he will not collude with the agent.

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Accordingly, when the supervisor may engage in abuse of authority, the agent’s incentive compatibility constraint is, p[p(w H
t M)+(1
p)w L]+(1
p)w F
czpw L+ (1
p)w F , or equivalently, c ð5Þ wF
wL z : pp Similarly, the agent’s participation constraint is p[p(w H
t M)+(1
p)w L]+(1
p)w F
czu, or equivalently, u: ð6Þ ½1
pð1
pÞwF þ pð1
pÞwL zc þ
Since abuse of authority takes place as long as t MN0, the principal also faces the following constraint, ð7Þ wH
wF z0: When only abuse of authority is possible, the program of the organization is therefore  A 
P p p wH þ sH Þ þ ð1
pÞ wL þ sL Þ þ ð1
pÞ wF þ sF min wL ;wF ;wH ;sL ;sF ;sH

s.t. Eqs. (3), (5), (6) and (7). Define p˜ uc/(c+pu). The solution to this program is summarized in Proposition 3. Proposition 3. The organization where only abuse of authority is possible has the following properties: (1) For pVp˜, the optimal contracts are (w L , w F, w H )=(0, c/(pp), c/(pp)) and (s L , s F , s H )=(0, 0, 0). Abuse of authority reduces the efficiency of the organization. The expected cost of production and supervision is C A =[1
p(1
p)]c/(pp). (2) For pNp˜, the optimal contracts are such that w L a[0, [ppu
(1
p)c]/(pp)], w F =w H =(c+u)/[1
p(1
p)]
p(1
p)w L /[1
p(1
p)], and (s L , s F , s H )=(0, 0, 0). Abuse of authority does not affect the efficiency of the organization. The expected cost of production and supervision is C 0 . The principal has the choice between tolerating and deterring abuse of authority. Recall that the supervisor engages in abuse of authority whenever w HNw F . Since the expected cost of production and supervision is increasing in w H, it is clearly optimal for the principal to deter abuse of authority by setting w H=w F , that is, by destroying its stake, rather than tolerating it by instead setting w HNw F .21 21

Preventing abuse of authority is also optimal in the case where supervision is costly (and, for simplicity, attention is restricted on pure strategies). In this case, the supervisor has the choice between two unobservable supervision effort levels, e Sa{0, 1}. At the zero-effort level supervision reveals nothing. Since the supervision technology is imperfect, at the one-effort level supervision reveals evidence on the output with probability pa(0, 1). Clearly, the principal wants to implement e S=1. The supervisor’s incentive compatibility constraint is then p[p(s H+kt M)+(1
p)s L]+(1
p)s F
nzs F, or equivalently, p(s H+k(w H
w F))+(1
p)s L
s Fzn/p, where n is the disutility of supervision effort. Given that the supervisor is protected by limited liability and his reservation utility is normalized to zero, his participation constraint is in this case clearly redundant. If the principal sets w HNw F , and hence tolerates abuse of authority, the agent receives a bglobalQ transfer (i.e., a wage packet) out of which she partly or totally bpaysQ the supervisor. In other words, the principal pays the supervisor, partially or totally, via the agent. It is then the agent’s tribute which contributes to satisfying the supervisor’s incentive compatibility constraint. The principal is better off tolerating abuse of authority whenever this alternative remuneration system is less costly than the traditional one (i.e., paying the supervisor directly). Since the side transfer technology is less efficient than the official one (i.e., kb1), it is not optimal to tolerate abuse of authority.

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There are fewer instruments available to deter abuse of authority than to deter collusion. Indeed, unlike collusion, abuse of authority cannot be deterred by an incentive policy, that is, a policy which creates incentive payments for the supervisor to reveal his information. An incentive policy is ineffective against abuse of authority because when the supervisor engages in this form of unofficial activity he does not have to trade-off a low wage (i.e., a wage associated with an uninformative report) plus a tribute, and a high wage (i.e., a wage associated with an informative report), since he can get both a tribute and a high wage. As expressed above, the only available policy against abuse of authority is a policy which destroys its stake, that is, which reduces the supervisor’s discretion. When adopting this policy, the principal makes the incentive payments to the agent less sensitive to the supervisor’s report. The principal then offers a flat wage to the agent whenever r p x L. That is, the principal sets w H=w F . Proposition 3 also states that, unlike collusion, abuse of authority cannot always be costlessly deterred. This form of unofficial activity affects the efficiency of the organization whenever the supervision technology is sufficiently inefficient (i.e., pVp˜ ). In this case, the agent receives a rent. However, when pNp˜ , abuse of authority is harmless.22 Abuse of authority is thus sometimes harmless in the case where the supervisor may only engage in this form of unofficial activity. In the next section, I show that when the organization is exposed to both collusion and abuse of authority, unofficial activities are never harmless.23 Before proceeding, it is important to observe that the assumption of the agent’s limited liability plays an essential role in the results of Proposition 3.24 Indeed, as shown in the proof of this proposition, relaxing the assumption of the agent’s limited liability results in abuse of authority becoming harmless. This is because the principal can then systemati22

Observe that the principal can also prevent abuse of authority by setting w Fzw H. Indeed, if w Fzw H, the supervisor does not engage in abuse of authority since he has no stake in it. The agent’s incentive compatibility and participation constraints are thus constraints (1) and (2). Abuse of authority can then be costlessly deterred when pzp˜ . For example, note that for pzp˜ the optimal contract (w L, w F , w H)=(0, u/(1
p), c/(pp)) of program [ P 0] satisfies w Fzw H. Therefore, as is the case for the optimal pair of contracts of case 2 of Proposition 3, for pNp˜ the pair of contracts (w L, w F , w H)=(0, u/(1
p), c/(pp)) and (s L, s F, s H)=(0, 0, 0) of program [ P 0] costlessly deters abuse of authority. It is straightforward to verify that for pVp˜ , the only optimal pair of contracts against abuse of authority is that of Proposition 3, and hence satisfies w Hzw F. 23 Notice that I do not account for the possibility of the agent appealing to the principal or lodging a complaint against her superior. Indeed, the agent cannot prove her allegations if she decides to lodge a complaint against the supervisor since abuse of authority cannot be observed and the information provided by the supervisor is the only available information. This accords with empirical evidence that lodging a complaint is often ineffective. For example, in the case of sexual harassment, Husbands (1992, p. 556) writes: bA complaint may encounter a number of practical obstacles in litigating a sexual harassment case. In pursuing any type of civil case in the countries surveyed, the burden of proofs falls on the complainant alleging the harassment. . .the proposition asserted by the complainant may be difficult to prove in a sexual harassment case. Most propositions for tangible job benefits in exchange for sexual favors are not made with witnesses present, so it may often be the complainant’s word against the alleged harasser’s.Q He then notes: bThere is evidence that a great deal of sexual harassment goes unreported.Q (p. 538). As observed by Roberts and Mann (1996, p. 270): b. . .most cases of sexual harassment still go unreported: as many as 95% of all such incidents may not be brought to light.Q On this issue, see also Peirce et al. (1998). 24 This assumption systematically plays an essential role in models of unofficial activities in organizations.

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cally set w L so low as to keep the agent at her reservation utility level. Unlike collusion, abuse of authority is harmless only in the absence of the agent’s limited liability.

5. Optimal contracts in the presence of multiple forms of unofficial activity I now turn to the case where both collusion and abuse of authority are possible. Constraint (4) must be added into program [ PA] when looking for the optimal contracts in an organization where both collusion and abuse of authority are possible. Let [ P CA] denote this new program. Proposition 4 then summarizes the solution to [ P CA]. Proposition 4. The organization where both collusion and abuse of authority are possible has the following properties: (1) For pVp˜, the optimal contracts are (w L , w F, w H )=(0, c/(pp), c/(pp)) and (s L , s F , s H )=(kc/(pp), 0, 0). The expected cost of production and supervision is C 1CA =[1
p(1
p)(1
k)]c/(pp). (2) For pNp˜, the optimal contracts are (w L , w F, w H )=([ppu
(1
p)c]/(pp), (pu+c)/p, (pu+c)/p) and (s L , s F , s H )=(kc/(pp), 0, 0). The expected cost of production and supervision is C 2CA =u+[(1
p)k+p]c/p. (3) Compared with the case where only abuse of authority may occur, the presence of multiple forms of unofficial activity increases both the scope and the intensity of the efficiency loss sustained by the organization. As in the previous section, it is optimal to prevent abuse of authority by setting w H=w F .25 However, unlike in the absence of abuse of authority, collusion is now harmful. The intuition for this is as follows. When collusion is the only unofficial activity that may occur, there are two policies available to deter it. Indeed, as explained in Section 4, in the absence of abuse of authority, collusion can be deterred either by creating incentive payments for the supervisor or by destroying its stake, that is, by setting w F V w L—or equivalently, by eliminating the gap between w F and w L or by specifying a negative gap between these two wages. When both forms of unofficial activity may take place, this second policy is not available anymore. As established above, the possibility of abuse of authority modifies the agent’s incentive compatibility constraint which becomes w F
w Lzc/(pp). The possibility of abuse of authority thus makes it impossible for the principal to deter collusion by setting w F V w L. The only available policy for preventing collusion is then to create incentive payments for the supervisor, that is, to set s L=k(w F
w L)N0 (since optimally s F=0). The presence of abuse of authority therefore makes collusion costly to deter, that is, negatively affects the deterrence of collusion. Collusion is not harmless anymore. Preventing collusion has then a cost, p(1
p)s L where s L=kc/(pp), that is, (1
p)kc/p. Indeed,

25

As can easily be verified, no pair of contracts ((w L, w F , w H),(s L, s F, s H)) satisfying w Fzw H can deter unofficial activities at a strictly lower cost than the contracts of Proposition 4.

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comparing the expected costs in Propositions 3 and 4, one has both C 1CA
C A and C 2CA
C 0 equal to (1
p)kc/p.26 Compared with the case where only abuse of authority is possible, the presence of both collusion and abuse of authority has two important consequences. First, it increases the scope of the efficiency loss sustained by the organization. In other words, while the sole presence of abuse of authority only reduces the efficiency of the organization when pVp˜ , the presence of both abuse of authority and collusion also reduces the efficiency of the organization when pNp˜ . Unofficial activities are now always harmful. As explained, this is because deterring collusion has now a cost, (1
p)kc/p. This additional cost reduces the efficiency of the organization when pNp˜ . Second, as it is easy to verify, the expected cost of production and supervision increases when the supervisor may engage in both collusion and abuse of authority. That is, C CANC A and C CANC 0.27 The presence of multiple forms of unofficial activity thus also increases the intensity of the efficiency loss sustained by the organization. Again, this is because preventing collusion is now costly. This extra cost systematically increases the loss sustained by the hierarchy. One then has that when pVp˜ , both the supervisor and the agent receive a rent, whereas when pNp˜ , only the supervisor receives a rent. To summarize the discussion, unofficial activities negatively interact.28 As noted in the previous section, recent studies of collusion in hierarchies have shown that this form of unofficial activity does not systematically reduce the efficiency of organizations. I have found that this is also the case with abuse of authority. This form of unofficial activity is not systematically harmful when employees are protected by limited liability and is harmless in the absence of the agent’s limited liability. Things are however different when the organization is exposed to multiple forms of unofficial activity. Indeed, as shown in the Proof of Proposition 4, when the agent is not protected by limited liability, she is systematically kept at her reservation utility level while the supervisor receives a rent. As above, deterring collusion has a cost, (1
p)kc/p. Therefore, when both collusion and abuse of authority may occur, unofficial activities are always harmful even in the absence of the agent’s limited liability. This is another illustration of the fact that, unlike the 26

In the environment considered here, it is possible and optimal to simultaneously deter both forms of unofficial activity. This may not be systematically the case in alternative environments. Indeed, in the very different context of crime and punishment, Marjit and Shi (1998) show that it may even be impossible to deter a single form of unofficial activity. They present a model that synthesizes the classical and the strategic approaches to crime and punishment. Unlike me, they consider external collusion, that is, collusion between a member of an organization (the law enforcing agent) and an outsider (the criminal). In my model, the supervisor and the agent are both members of the same organization, and hence both receive their wages from the same principal. My model is thus one of internal collusion in the tradition of Tirole (1986, 1992). 27 A 0 More precisely, one has C CA ˜ , and C CA ˜. 1 NC for pVp 2 NC for pNp 28 It is important to note that my implicit assumption that the principal is honest is innocuous. The principal may act dishonestly to the detriment of the agent whenever supervision reveals the evidence that the agent has produced a high output and the supervisor shows (but does not give) the evidence to the principal. To avoid paying a high wage, w H, to the agent, the principal may then give a bribe to the supervisor to report r=F. In this case, the agent receives w F. This is clearly equivalent to a renegotiation of the supervisor’s contract. Given that abuse of authority is optimally deterred by setting w H=w F , deterring abuse of authority also prevents the principal from acting dishonestly to the detriment of the agent. For more on this issue, see VafaR (2004b).

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presence of a single form of unofficial activity, the presence of multiple forms of unofficial activity systematically reduces the efficiency of organizations. As explained, this is because there are negative interactions between unofficial activities. One can then state: Corollary 1. Compared with the presence of a single form of unofficial activity, the presence of multiple forms of unofficial activity is never harmless and is more severely harmful. Another interesting point is to study if the cost of preventing both forms of unofficial activity, C CA, is larger than the sum of the costs of preventing a single form of unofficial activity, C A+C 0. Formally, one must verify if C 1CAzC 0+C A when pVp˜ , and if C 2CAz2C 0 when pNp˜ . In words, it is interesting to investigate if the presence of multiple forms of unofficial activity entails cost super-additivity. The following corollary identifies the condition under which this is the case. Define p˜ukc/[(1+k)c+u]. One then has: Corollary 2. For pVp˜ , the presence of multiple forms of unofficial activity entails cost super-additivity. The intuition for this result is based on the observation that the above cost comparisons boil down to (1
p)kc/pzC 0. The left-hand side of this inequality is the extra expected cost of collusion deterrence in an organization with both collusion and abuse of authority whereas the right-hand side is the expected cost of an organization where only collusion may occur. Given that the additional expected cost of collusion deterrence increases as p decreases while the expected cost C 0 is a constant, one has that when p is relatively small (i.e. pVp˜), the presence of multiple forms of unofficial activity entails cost superadditivity. The opposite holds for p relatively large.

6. Conclusion Recently, investigations of optimal incentive contracts in principal–supervisor–agent hierarchies have accounted for the possibility of collusion between the supervisor and the agent. In this paper, I have extended the analysis of these hierarchies by allowing the supervisor to engage in both collusion and abuse of authority. I have characterized the optimal incentive contracts in such an environment, and have analyzed how collusion and abuse of authority interact. I have found that, while in the absence of abuse of authority collusion is harmless, this is not true anymore when both forms of unofficial activity are possible. I have also shown that, compared with the cases where a single form of unofficial activity may occur, the presence of collusion and abuse of authority increases both the scope and the intensity of the efficiency loss sustained by the organization. Finally, I have proved that the presence of multiple forms of unofficial activity may entail cost super-additivity. The approach taken in this paper should be considered a first step in the study of the interaction between abuse of authority and collusion in organizations. Since in many real world situations evidence is not verifiable, and thus can be forged, an important extension is to investigate collusion and abuse of authority in a moral hazard hierarchy with soft

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information. Another interesting extension is to relax the simplifying assumptions of a binary effort decision and of the existence of an effort target to account for more complex environments. Finally, this paper has dealt exclusively with moral hazard. The study of unofficial activities in an adverse selection environment is also an important topic for future research.

Acknowledgments Many thanks to two anonymous referees for helpful comments.

Appendix A

Proof of Proposition 1. Before turning to the derivation of the optimal incentive contracts in the different scenarios, it is straightforward to see that, in each of these scenarios, the principal sets s F as low as allowed by the limited liability constraints, that is, s F=0. This is because an uninformative report is undesirable from the principal’s point of view.
As explained in the text, any contract sL ; sF ; sH aR3þ is individually rational. Given that the expected cost of production and supervision is increasing in s L, s H, and reducing these wages does not make constraints more severe, the principal sets s L and s H as low as allowed by the limited liability constraints, that is, s L=s H=0. Rewriting the agent’s incentive and participation constraints respectively as w Hzc/ (pp)+w L and w Hz(c+u)/(pp)
(1
p)w F /(pp)
(1
p)w L/p, one has two constraints on w H (plus the limited liability constraints). To find which of the incentive compatibility constraint and the participation constraint is more restrictive, one must compare c/(pp)+w L with (c+u)/(pp)
(1
p)w F /(pp)
(1
p)w L/p. One has that the incentive compatibility constraint is more restrictive than the participation constraint if c/(pp)+w Lz(c+u)/ (pp)
(1
p)w F/(pp)
(1
p)w L/p, that is, if w Lzu/p
(1
p)w F /p. The converse is true if w LVu/p
(1
p)w F /p. Therefore, (1) If w Lzu/p
(1
p)w F /p, the relevant constraint is the agent’s incentive compatibility constraint. Since limited liability requires w Lz0, one must then have w FVu/ (1
p). Note that setting w FNu/(1
p) is clearly not optimal. Given that the objective function is increasing in w H, w L, and reducing these wages does not make constraints more severe, the principal sets w H and w L, respectively, as low as allowed by the agent’s incentive compatibility constraint and constraint w Lzu/ p
(1
p)w F /p. That is, w H=c/(pp)+w L and w L=u/p
(1
p)w F /p. Substituting w L=u/p
(1
p)w F /p into the agent’s incentive compatibility constraint then yields w H=(c+pu)/(pp)
(1
p)w F /p. Since limited liability requires w Hz0, one must have w FV(c+pu)/[(1
p)p]. One obviously has min{u/(1
p), (c+pu)/[(1
p)p]}=u/ (1
p ). Finally, substituting w L =u /p
(1
p )w F /p and w H =(c+pu )/ (pp)
(1
p)w F /p into the objective function of program [ P 0], one obtains the

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new objective function c+u. One must then minimize this function under the constraint w Fa[0, u/(1
p)]. Since w F does not enter the new objective function, the set of solutions to this program is w Fa[0, u/(1
p)], w H =(c+pu)/ (pp)
(1
p)w F /p, and w L=u/p
(1
p)w F /p. (2) If w LVu/p
(1
p)w F /p, the relevant constraint is the agent’s participation constraint. As above, one must have w FVu/(1
p). Given that the objective function is increasing in w H, and reducing this wage does not make constraints more severe, the agent’s participation constraint binds. One then has w H=(c+u)/ (pp)
(1
p)w F /(pp)
(1
p)w L/p. Since limited liability requires w Hz0, one must have w LV(c+u)/[ p(1
p)]
(1
p)w F /[ p(1
p)]. Similarly, one must have w Lz0, and hence w FV(c+u)/(1
p). One now has two constraints on w L: w LVu/ p
(1
p)w F /p and w LV(c+u)/[ p(1
p)]
(1
p)w F /[ p(1
p)]. One has min{u/ p
(1
p)w F /p, (c+u)/[ p(1
p)]
(1
p)w F /[ p(1
p)]}=u/p
(1
p)w F /p if w FV(c+pu)/[(1
p)p]. As derived above, given that limited liability requires w FVu/(1
p) and one has u/(1
p)b(c+pu)/[(1
p)p], the relevant constraint on w L is w LVu/p
(1
p)w F /p. Substituting w H=(c+u)/(pp)
(1
p)w F/(pp)
(1
p)w L/p into the objective function of program [ P 0], one obtains the new objective function c+u. One must then minimize this function under the constraints w La[0, u/ p
(1
p)w F/p] and w Fa[0, u/(1
p)]. Given that w L and w F do not enter the new objective function, the set of solutions to the principal’s program is w Fa[0, u/ (1
p)], w La[0, u/p
(1
p)w F /p], and w H=(c+u)/(pp)
(1
p)w F/(pp)
(1
p)w L/ p. Since it includes the above set of solutions, this set of solutions is the optimal set of solutions to program [ P 0]. The expected cost of production and supervision is then C 0=c+u. 5 Proof of Proposition 3. Given that the expected cost of production and supervision is increasing in w H, that one must have w Hzw F and that reducing w H does not make constraints more severe, it is optimal for the principal to set w H=w F. The agent’s incentive compatibility and participation constraints can be respectively rewritten as w Fzc/(pp)+w L and w Fz(c+u)/[1
p(1
p)]
p(1
p)w L/[1
p(1
p)]. To find which of these two constraints is more restrictive, one must compare c/(pp)+w L with (c+u)/[1
p(1
p)]
p(1
p)w L/[1
p(1
p)]. One has that the agent’s incentive compatibility constraint is more restrictive if w Lz[ppu
(1
p)c]/(pp). The converse is true if w L V[ppu
(1
p )c]/(pp). Since limited liability requires w L z0 and one has [ppu
(1
p)c]/(pp)V0 if pVp˜ uc/(c+pu), the agent’s incentive compatibility constraint is always the relevant constraint when pVp˜ . Given that the objective function is increasing in w F , and reducing this wage does not make constraints more severe, in this case the agent’s incentive compatibility constraint binds. One thus has w F=c/(pp)+w L. Clearly, the wage w L must then be set as low as allowed by the limited liability constraint, that is, w L=0, and hence w F=c/(pp) (=w H). When instead pNp˜ , two cases must be distinguished. (a) If the principal sets w Lz[ppu
(1
p)c]/(pp), the agent’s incentive compatibility constraint is the relevant constraint. From the same reasoning as above, one then has w F=c/(pp)+w L. Substituting w F=c/(pp)+w L into the objective function of program

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[ PA], one obtains the new objective function [1
p(1
p)]c/(pp)+w L. One must then minimize this function under the constraint w Lz[ppu
(1
p)c]/(pp). Since the objective function is increasing in w L, and reducing this wage does not make constraints more severe, it is optimal to set w L as low as allowed by the constraint, that is, w L=[ppu
(1
p)c]/(pp). One thus has w F=(pu+c)/p (=w H). (b) If the principal sets w LV[ppu
(1
p)c]/(pp), the agent’s participation constraint is the relevant constraint. Since limited liability requires w Fz0, one must then have (c+u)/[1
p(1
p)]
p(1
p)w L/[1
p(1
p)]z0, that is, w LV(c+u)/[ p(1
p)]. Given that one must also have w LV[ppu
(1
p)c]/(pp), one has w LVmin{[ppu
(1
p)c]/ (pp),(c+u)/[ p(1
p)]}=[ppu
(1
p)c]/(pp). From the above reasoning, one has that the agent’s participation constraint binds. Substituting w F=(c+u)/[1
p(1
p)]
p(1
p)w L/[1
p(1
p)] into the objective function of program [ PA], one obtains the new objective function c+u. This new objective function must then be minimized under the constraint w La[0, [ppu
(1
p)c]/(pp)]. Given that w L does not enter this function, any w La[0, [ppu
(1
p)c]/(pp)] is solution to this program. Since it includes the solution to case (a), the set of solutions to case (b) is the optimal set of solutions to program [ PA] for pNp˜ . As in the previous proof, the principal sets the supervisor’s wages s L and s H as low as allowed by the limited liability constraints, that is, s L=s H=0. The expected cost of production and supervision is then C A=[1
p(1
p)]c/(pp) if pVp˜ and C 0 otherwise. Before turning to the Proof of Proposition 4, observe that abuse of authority is harmless in the case where the agent is not protected by limited liability. The reason behind this is that the principal can then always set w L so low as to keep the agent at her reservation utility level. Clearly, in the absence of limited liability, the principal can systematically set w LV[ppu
(1
p)c]/(pp) where ½pp
u
ð1
pÞc=ð ppÞaR. As explained above, the relevant constraint is then the agent’s participation constraint and this constraint binds. One thus has w F=w H=(c+u)/[1
p(1
p)]
p(1
p)w L/[1
p(1
p)], s L=s H=0, and the expected cost of production and supervision is C 0. 5 Proof of Proposition 4. As in the preceding proof, one has s H=0 and w H=w F. Given that the expected cost of production and supervision is increasing in s L, and reducing this wage does not make constraints more severe, the no-collusion constraint binds. That is, s L=k(w F
w L). Since one must have s Lz0, one then has w F
w Lz0. This constraint is less restrictive than the agent’s incentive compatibility constraint, and hence can be ignored. As in the previous proof, one must compare the agent’s participation constraint with her incentive compatibility constraint. Following the lines of the Proof of Proposition 3, one has that when pVp˜ , the agent’s incentive compatibility constraint is the relevant constraint and this constraint binds. Substituting w F=c/(pp)+w L into the no-collusion constraint then yields s L=kc/(pp). Finally, from the same reasoning as in the previous proof, when pVp˜ one has w L=0 and w H=w F=c/(pp). Again, as in the Proof of Proposition 3, two cases must be considered when pNp˜ . (a) Following the lines of the preceding proof, if the principal sets w Lz[ppu
(1
p)c]/(pp), the agent’s incentive compatibility constraint is the

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403

relevant constraint. As explained above, this constraint binds, and hence one has s L=kc/(pp). Then, from the same reasoning as in the Proof of Proposition 3, one has w L=[ppu
(1
p)c]/(pp) and w F=(pu+c)/p (=w H). (b) If instead the principal sets w LV[ppu
(1
p)c]/(pp), the agent’s participation constraint is the relevant constraint. As in the previous proof, one has that this constraint binds. One must then substitute w F=(c+u)/[1
p(1
p)]
p(1
p)w L/ [1
p(1
p)] into s L=k(w F
w L). This yields s L=k(c+u)/[1
p(1
p)]
kw L/ [1
p(1
p)]. Given that limited liability requires w Fz0 and s Lz0, one must then h a v e ( c+ u ) / [ 1
p ( 1
p) ]
p ( 1
p) w L / [ 1
p ( 1
p) ] z0 a n d k ( c+ u ) / [1
p (1
p)]
kw L /[1
p (1
p)]z0. That is, w L Vmin{(c+u ) / [ p (1
p)], c+u}=(c+u)/[ p(1
p)]. Since one must also have w LV[ppu
(1
p)c]/(pp), one has w LVmin{[ppu
(1
p)c]/(pp), (c+u)/[ p(1
p)]}=[ppu
(1
p)c]/(pp). Substituting w F=(c+u)/[1
p(1
p)]
p(1
p)w L /[1
p(1
p)] and s L=k(c+u)/ [1
p(1
p)]
kw L/[1
p(1
p)] into the objective function of program [ P CA], one obtains the new objective function [1
p (1
p)(1
k )](c+u )/[1
p (1
p)]
pk (1
p)w L / [1
p(1
p)]. This new objective function must be minimized under the constraint w La[0, [ppu
(1
p)c]/(pp)]. Given that this objective function is decreasing in w L, it is optimal to set w L=[ppu
(1
p)c]/(pp). One therefore has w F=(pu+c)/p (=w H) and s L=kc/ (pp). Since cases (a) and (b) yield the same result, the expected cost of production and supervision is C 1CA=[1
p(1
p)(1
k)]c/(pp) if pVp˜ and C 2CA=u+[(1
p)k+p]c/p otherwise. As is straightforward to verify, one has C 1CANC A when pVp˜ , and C 2CANC 0 when pNp˜ . This proves the third result of Proposition 4. Before turning to the Proof of Corollary 2, observe that even in the absence of the agent’s limited liability unofficial activities are always harmful. Indeed, as can easily be verified, dropping the assumption of limited liability and following the above reasoning, one has wL ¼ ½ppu
ð1
pÞc=ð ppÞaR, w F=(pu+c)/p (=w H), and s L=kc/ (pp). In the absence of the agent’s limited liability, the expected cost of production and supervision is then always C 2CA. Since one clearly has C 2CANC 0, the presence of multiple forms of unofficial activity thus systematically reduces the efficiency of the organization. 5 Proof of Corollary 2. To see if the presence of multiple forms of unofficial activity entails cost super-additivity, one must check if C 1CAzC 0+C A when pVp˜ ; and if C 2CAz2C 0 when pNp˜ . One has both C 1CAzC 0+C A and C 2CAz2C 0 when pVp˜ ukc/[(1+k)c+u]. 5

References Baliga, S., Sjo¨stro¨m, T., 1998. Decentralization and collusion. Journal of Economic Theory 83, 196 – 232. Bosman, R., van Winden, F., 2002. Emotional hazard in a power-to-take experiment. Economic Journal 112, 147 – 169. Bosman, R., Sonnemans, J., Zeelenberg, M., 2001. Emotions, rejections, and cooling off in the ultimatum game. Working paper, CREED/Department of Economics, University of Amsterdam.

404

K. VafaR / European Journal of Political Economy 21 (2005) 385–405

Breton, A., 1995. Organizational hierarchies and bureaucracies: an integrative essay. European Journal of Political Economy 11, 411 – 440. Che, Y.-K., Kim, J., 2004. Collusion-proof implementation of optimal mechanisms. Working paper, Department of Economics, University of Wisconsin-Madison. Crozier, M., Friedberg, E., 1980. Actors and Systems: The Politics of Collective Action. The University of Chicago Press, Chicago. Edwards, R., 1979. Contested Terrain. Basic Books, New York. Faure-Grimaud, A., Laffont, J.-J., Martimort, D., 2003. Collusion, delegation and supervision with soft information. Review of Economic Studies 70, 253 – 280. Fehr, E., G7chter, S., 1999. Cooperation and punishment in public goods experiments. Working Paper, Institute for Empirical Research in Economics, University of Zurich. Fehr, E., G7chter, S., 2000. Fairness and retaliation: the economics of reciprocity. Journal of Economic Perspectives 14, 159 – 181. Flynn, K., 1991. Preventive medicine for sexual harassment. Personnel 68, 17. Frank, R., 1988. Passions within reason: the strategic role of the emotions. W.W. Norton, New York. Hindriks, J., Keen, M., Muthoo, A., 1999. Corruption, extortion and evasion. Journal of Public Economics 74, 395 – 430. Hirshleifer, J., 1987. On the emotions as guarantors of threats and promises. In: Dupre´, J. (Ed.), The Latest on the Best: Essays in Evolution and Optimality. MIT Press, Cambridge, pp. 307 – 326. Hirshleifer, J., 2001. Game-theoretic interpretations of commitment. In: Nesse, R.M. (Ed.), Evolution and the Capacity for Commitment. Russell Sage Press, New York, pp. 77 – 93. Huang, P.H., Wu, H.-M., 1992. Emotional responses in litigation. International Review of Law and Economics 12, 31 – 44. Husbands, R., 1992. Sexual harassment law in employment: an international perspective. International Labour Review 131, 535 – 559. Johnson, R.N., Libecap, G.D., 1989. Bureaucratic rules, supervisor behavior, and the effect on salaries in the federal government. Journal of Law, Economics, and Organization 5, 53 – 82. Kessler, A.S., 2000. On monitoring and collusion in hierarchies. Journal of Economic Theory 91, 280 – 291. Laffont, J.-J., Martimort, D., 1997. Collusion under asymmetric information. Econometrica 65, 875 – 911. Laffont, J.-J., Rochet, J.-C., 1997. Collusion in organizations. Scandinavian Journal of Economics 99, 485 – 495. Lambert-Mogiliansky, A., 1997. Regulatory blackmail in procurement relationships. Cepremap, Paris. Working Paper 9701. Loewenstein, G.F., 1996. Out of control: visceral influences on behavior. Organizational Behavior and Human Decision Processes 65, 272 – 292. Marjit, S., Shi, H., 1998. On controlling crime with corrupt officials. Journal of Economic Behavior and Organization 34, 163 – 172. Marjit, S., Mukherjee, V., Mukherjee, A., 2000. Harassment, corruption and tax policy. European Journal of Political Economy 16, 75 – 94. Milgrom, P., 1988. Employment contracts, influence activities, and efficient organization design. Journal of Political Economy 96, 42 – 60. Olsen, T.E., Torsvik, G., 1998. Collusion and renegotiation in hierarchies: a case of beneficial corruption. International Economic Review 39, 413 – 438. Peirce, E., Smolinski, C.A., Rosen, B., 1998. Why sexual harassment complaints fall on deaf ears. Academy of Management Executive 12, 41 – 54. Roberts, B.S., Mann, R.A., 1996. Sexual harassment in the workplace: a primer. Akron Law Review 29, 269 – 276. Shavell, S., Spier, K.E., 2002. Threats without binding commitment. B.E. Journals in Economic Analysis and Policy, Topics in Economic Analysis and Policy 2, Article 2. Shleifer, A., Vishny, R., 1989. Management entrenchment: the case of manager-specific investments. Journal of Financial Economics 25, 123 – 139. Timmerman, G., Bajema, C., 1999. Sexual harassment in northwest Europe. European Journal of Women’s Studies 6, 419 – 439.

K. VafaR / European Journal of Political Economy 21 (2005) 385–405

405

Tirole, J., 1986. Hierarchies and bureaucracies: on the role of collusion in organizations. Journal of Law, Economics, and Organization 2, 181 – 214. Tirole, J., 1992. Collusion and the theory of organizations. In: Laffont, J.-J. (Ed.), Advances in Economic Theory, vol. 2. Cambridge University Press, Cambridge, pp. 151 – 206. VafaR, K., 1994. Collusion and blackmail in hierarchies. Universite´ Paris 1-Panthe´on Sorbonne. Working Paper. VafaR, K., 2002. Preventing abuse of authority in hierarchies. International Journal of Industrial Organization 20, 1143 – 1166. VafaR, K., 2004a. Collusion and organization design. Economica (in press). VafaR, K., 2004b. Opportunism in organizations. Universite´ Paris 1-Panthe´on Sorbonne. Working Paper. Yaniv, G., 2001. Revenge, tax informing, and the optimal bounty. Journal of Public Economic Theory 3, 225 – 233.