In a three-tier hierarchy agency model I study optimal contracts to induce the board of directors to efficiently monitor the CEO. I find that next to type of compensation
(fixed or bonus), monitoring cost and potential reputation damage of the board determine the monitoring decision. Optimal firm value can be realised under both fixed and bonus pay, if the cost of monitoring is low enough relative to the board’s potential reputation damage of false reporting. The possibility of setting a bonus for the board increases the sustainable level of monitoring cost. This provides support for the optimal contracting view that bonuses may be optimal under certain firm-specific circumstances. However, the required level of CEO contribution to firm value to receive a bonus must be higher for the CEO than for the board to make the board’s bonus effective. Furthermore, the sustainable level of the bonus for the board is limited by the expected severity of reputation damage. As long as the monitoring cost is low enough relative to the expected reputation damage, optimal contracts are also sustainable under the threat of collusion. However, if the expected severity of reputation damage is low, CEO incentives need to be decreased to deter collusion between the board and the CEO. This necessarily leads to lower than optimal firm value.

1.
Introduction
In this thesis I will add to the Principal-Supervisor-Agent (PSA) theory by incorporating the busyness of directors (Fich and Shivdasani (2006)) and their reputation concern (Fama and Jensen (1983)) in the PSA model. I model shareholders, the board of directors and the CEO and incorporate the cost of monitoring for the board and the reputation effect of false reporting. In this model I analyse how shareholders can optimally set contracts and analyse the influence of director busyness and reputation concern on the optimal contract. I will also take into account the possibility of collusion between the board and the CEO and how shareholders can deter it. Studying collusion is interesting as it can be seen as a form of the managerial power approach. In my model shareholders are not able to directly contract with the CEO but need to contract with the board. Next the board on its turn contracts with the CEO. Analysing whether fixed or bonus pay is optimal is relevant looking at the different ways board members are rewarded in different countries and the debate in the literature.
Compensation of executives and directors of public companies is part of a heated public as well as academic debate. In the Netherlands there has recently been a lot of discussion on the compensation of the executives of the big banks ABN AMRO and
ING 1 . The discussion is around the level and the form of director and executive compensation. From the organisational economics perspective director compensation should be structured in a way to make directors effective monitors of executives. That monitoring is not always effective is shown by the financial scandals at for example
WorldCom and Enron. Here directors were also held responsible and agreed to pay fines of over $10 million out of their own pocket 2 .
Although the discussion in the public domain is not always based on solid understanding of incentive theory, the discussion seems to be relevant since there is also not a clear answer to these issues from the economic literature. The issues around compensation and monitoring of executives are studied in the domain of corporate governance. Hermalin (2013: 734) defines corporate governance as: “Primarily the study of what happens when investors seek to protect themselves against mismanagement, misallocation and misappropriation of their investment by those
1 See for example: De Jong, Laura. Zijn de bankiers losgezogen van de werkelijkheid?, De Volkskrant,
30 maart 2015 (available online)
2 See for example: Taub, Stephen. Former Enron Directors Will Pay $13M, CFO.com, 11 January 2015
2

who control the corporations in which they wish to invest”. Boards of directors seem to be a solution to the corporate governance problem. Hermalin and Weisbach (2003) conclude that since corporate boards are usually larger than required by law and that they are also used in situations where not required by law, boards must be part of a market solution to an agency problem. Therefore, in this thesis I take the existence of the board as given rather than analysing the reason for its existence. The question then is how to contract with the board and the CEO efficiently. Broadly speaking there are two views on CEO and director contracting. The first one is called the ‘optimal contracting approach’, which acknowledges executive compensation as an efficient way to solve the agency problem between shareholders and managers. Hermalin
(2013) provides an overview of the organisational economics literature on corporate governance. Differences in compensation and board structure can be a result of inherent differences between firms. This can make it optimal to choose different compensation packages for executives and the board as well as making different choices in board structure and compensation at different organisations. In this view the empirically observed differences may resemble optimal contract structures as the result of inherent firm specifics. Bryan et al. (2002) empirically find that compensation of board members is structured to mitigate agency problems, in line with the optimal contracting approach. I find evidence for the optimal contracting approach by identifying specific circumstances under which fixed pay or bonus pay are optimal to induce effective monitoring. In my model, whether fixed or bonus pay is optimal depends on the monitoring cost.
The other view is the ‘managerial power approach’, stating that executive compensation itself is part of the agency problem. For example, Bertrand and
Mullaiathan (2001) find that CEO compensation is generally more linked to random events, or ‘luck’, than to actual performance. They indicate this as evidence of the managerial power approach, because effectively resolving the agency problem would require a strong link between factors managers can influence and their compensation.
Bebchuk et al. (2010) find that options awarded to CEOs as well as directors are designed to provide ‘lucky’ grants. That means options were awarded at the most favourable time of the month. This timing is a result of deliberate choices of the firm, not merely of procedures. Bebchuk et al. (2010) also provide evidence that there is a link between the luck of the CEO and that of the directors, including independent directors. Furthermore, they find that a majority of independent directors on the board
3

is only effective if they do not receive lucky grants themselves. Hahn and Lasfer
(2010) show that broadly speaking in European countries compensation of nonexecutive directors is fixed whereas in the USA oftentimes there are performance incentives. It is thus not obvious from the start which one of the two is most efficient and some more insight in the mechanisms could help to provide explanations.
There is some discussion on whether boards in their current form are effective monitors or not. For example, an OECD article (Kirkpatrick (2009)) concludes that the financial crisis can for a large part be blamed on non-functioning corporate governance leading to excessive risk-taking . Barton and Wiseman (2015) find that most directors do not have a proper understanding of the strategy of the company they are supposed to monitor. They conclude that part of the solution is to reward directors more and (more importantly) change the compensation structure to more long-term variable compensation. This is necessary to have directors act more like owners and make sure they spend enough time on their monitoring tasks. It seems that directors face an opportunity cost. Typically they are part of more than one board and have to divide their time and effort between the different positions they have. Besides that,
Fama and Jensen (1983) also find that most outside directors are CEOs of other firms or have a senior executive position at another firm. Most likely, part of their compensation as executive is variable and thus dependent on their effort. This may drag away their attention from outside board positions. However, Conyon and Read
(2006) find from a theoretical model that executives are expected to spend more time on directorships than is optimal for their home firm 3 . Empirically, Fich and
Shivdasani (2006) find that busy boards are related to weaker corporate governance.
Directors with over three outside directorships are classified as ‘busy’. This could be evidence that directors with many directorships do not put enough effort in the different jobs or are not able to do this. Another way of seeing this is that board members engage in a form of collusion with management. Busy board members prefer to spend the lowest possible amount of effort in monitoring management. The board members are then prone to collusion with management to provide shareholders favourable messages about management effort and abilities. On the other hand, Fama and Jensen (1983) propose that the board has incentives to monitor because they care about their reputation as good monitors. I find that the level of monitoring cost
3 Being the firm where they have an executive position
4

relative to the potential reputation damage of the board determines the monitoring decision of the board, with and without the possibility of collusion.
Hermalin and Weisbach (2003) identify the general need for increasing formal theory on boards of directors. This is partly driven by the fact that there is a large empirical issue in the inherent heterogeneity of governance solutions. For example, research focusing on the number of directors is often focused on the relationship between the number of directors and firm performance (e.g. Yermack (1996)). However, to interpret the results one must assume that the inherent differences between firms do not in itself determine the optimal number of directors. If the optimal number of directors is dependent on firm specific characteristics we cannot interpret these results. Theoretical work may help overcome empirical difficulties by providing new models and empirically testable hypotheses. Optimal contracting and the possibility of collusion can be theoretically studied in Principal-Supervisor-Agent (PSA) models.
Tirole (1986) was the first to model collusion within a PSA model. Hermalin (2013) identifies the need for better modelling of corporate governance in hierarchical structure instead of the standard principal-agent model. When modelling this threetier hierarchy he argues that one cannot analyse these models without evaluating the possibility for collusion between two of the actors in the model. Different authors that
I will discuss in the next section have further developed this line of theory.
2.
Theoretical background
Hahn and Lasfer (2010) analyse the corporate governance guidelines in many different countries. Broadly speaking they find three main roles for the board of directors: the agency/control role, the strategic and policy support role and the resource acquirer role. As is common in agency models and following Hermalin’s
(2013) definition of corporate governance, the focus of my thesis is on the agency/control role of the board. On the agency/control role of the board roughly two lines of thought have been developed throughout the literature.
The first line of thought consists of scholars advocating that non-executive directors should be as independent as possible and therefore should receive a fixed wage unrelated to firm performance. One of the reasons for this is the belief that strong links between share price and director wealth will give incentives to collude with management, for example to ‘cook the books’. There are several arguments proposed in the literature why incentives would not be necessary. According to Fama and
5

Jensen (1983) the fact that board members have a reputation concern would induce them to be effective monitors. The argument here is that board members care about their task as monitor and when they do not do their job well this would jeopardise not only the current board membership but also other (future) board positions. The board’s reputation concern thus incentivises it to monitor effectively. There is empirical support for the reputation effect in Fich and Shivdasani (2007). They find that outside directors that are in a board of a company subject to a financial fraud lawsuit experience a significant decline in their number of other board positions. The effect of losing directorships (the reputation effect) is larger if the director bears a larger responsibility for financial monitoring and larger if the allegations are more severe. The effect is only found to be significant for board positions other than the board position for the firm that is sued for financial fraud. Finally, Fich and
Shivdasani (2007) find that overall this also reduces the welfare of directors serving a firm accused of financial fraud.
Hirshleifer and Thakor (1994 and 1998) argue that the market for takeovers provides a mechanism for external control on the board of directors. In their models the shareholders delegate contracting of the manager to the board and rely on the market for external takeovers to discipline board members. However, they conclude that this mechanism is a rather costly way of correcting for agency failures. Graziano and
Luporini (2003) also find evidence that relying on the takeover market may be a costly way of disciplining board members. They model board efficiency and find that the board has an incentive to keep a bad CEO under high pressure of the takeover market to defend their own seat. Barton and Wiseman’s (2015) qualitative conclusion that most directors do not have sufficient knowledge about their company’s strategy also makes the point that the reputation concern and market for takeovers might not be sufficient to induce efficient monitoring levels.
The second line of scholars argues that non-executive directors should be incentivised to make sure their interests are aligned with the shareholders (e.g. Shen (2005)). The latter of course makes sense from an agency perspective as without (strong) reputation concern it is questionable that the director would care about shareholder interests intrinsically. Shen (2005) argues that also for non-executive directors strong incentives are necessary to make directors engaged in governing the firm and be independent challengers of the executives. Jensen (1989:6) finds that “the idea that outside directors with little or no equity stake in the company could effectively
6

monitor and discipline the managers who select them has proven hollow at best”. The idea that proper incentives are necessary for the board of directors may also be supported by social and psychological reasons. Main, O’Reily and Wade (1995) provide a discussion by looking at the social psychology of the board of directors as a group. Norms of reciprocity, authority and similarity and liking may influence director decisions rather than financial rationale and shareholder interests. Incentives may help to re-align director and shareholder interests. Bebchuk and Fried (2003) state that the design of compensation packages for the board must also partly exhibit the same agency problem as the design of manager compensation and thus may not be the solution on itself. We thus need more insight in how these incentives would work out theoretically to be able to say more on the effects of incentives and fixed wages on the effectiveness of board monitoring in general.
The most relevant theoretical work in this field is built on Principal-Supervisor-Agent
(PSA) models. Mookherjee (2013) provides a good overview of the literature. The standard PSA framework is concerned with the allocation of decision-making authority between principal and manager. There exist two extreme forms. The first one is where the principal retains all control and sets all contracts. In the second one, the principal delegates all the decision power to the supervisor/monitor. In the first setting the principal basically treats the monitor as a supervising technology. He merely buys the information and sets optimal contracts based on it. This is basically
Tirole (1986), who concludes that in this setting a centralised hierarchy can always do at least as good as delegation. In the case of delegation and inability to monitor sidepayments the firm is prone to collusion, which makes delegation more expensive.
Centralisation however, may also be prone to collusion. Recently, several authors analyse the need for delegation of contracting to a supervisor in the general PSA model, examples are Strausz (1997a and 1997b), Baliga (1999), Fraure-Grimaud et al.
(2003), Vafaï (205) and Celik (2009). Fraure-Grimaud et al. (2003) conclude that whenever there are information asymmetries left between supervisor and agent, delegation to a supervisor makes sense. Warther (1998) assumes there is a reason for delegating contracting to the board (supervisor) instead of evaluating whether this is the best option. Warther (1998) states that it is widely accepted that the diffuse ownership of public corporations creates free-ridership in terms of monitoring from the side of shareholders rendering effective managerial oversight impossible.
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From the PSA literature Kumar and Sivaramakrishnan (2008) is most related to my paper. They also model contracts in a setting where the shareholders delegate contracting decisions to the board. The model includes both adverse selection and moral hazard. Their focus is on the independence of board members. They find that independence of directors and incentive pay can be substitutes. The difference between my work and theirs is that they do not consider collusion between the board and management and do not evaluate the effect of monitoring cost. Giebe and Gürtler
(2012) model different supervisor types, but do not consider collusion. In their model the two types are either neutral or altruistic towards the agent. Here the optimal contract entails paying the supervisor a flat wage independent of type and evaluation of the agent’s effort. This result only holds when the possibility of a neutral supervisor is sufficiently large. The agent does not know the supervisor’s type and thus needs to be incentivised by the neutral supervisor type, as the lenient supervisor will always report favourably. If the probability of a neutral supervisor is large enough, leniency is accepted rather than eliminated and both receive a flat wage.
Laffont and Rochet (1997) stress that naturally you expect a collusive reaction from agents to protect their rents in the PSA model. This means that when analysing such models, collusion needs to be taken into account. Thiele (2013) finds in a moral hazard environment with subjective performance evaluation, that under the threat of collusion incentives of the supervisor need to be increased and incentives of the agent reduced. If both the supervisor and the agent are sufficiently patient then there will not be collusion. This model consists of an infinitely repeated game that is stable as long as collusion can be deterred. Collusion is profitable whenever the one-time game for the agent is better than continuing the relationship. To deter collusion the total rent paid to supervisor and agent needs to be increased, while the one-time gain for the agent needs to be reduced. Optimally the incentives of the supervisor then increase and the incentives of the agent decrease. From the above it follows that the optimal type of compensation in the PSA model is not a-priori clear and may depend on the factors considered. Therefore, I need to look at the factors that determine the effectiveness of boards.
Zattoni and Cuomo (2010) find that the key determinants for the effectiveness of nonexecutive board members are: the degree of independence, the level of knowledge and skills and the economic incentives to behave properly. Fich and Shivdasani (2006) add the importance of busy directors and find that boards dominated by busy directors
8

are generally associated with weaker corporate governance. These boards have lower market-to-book values, are less likely to remove the CEO and have abnormal returns related to the removal of a busy board member. Beasley (1996) studies the likelihood of financial statement fraud in relationship to outside directors. One of his findings is that the likelihood of financial statement fraud decreases with less busy board members. Core et al. (1999) finds that CEO compensation is generally higher when board members are considered as busy. Ferris et al. (2003) do not find evidence for the ‘busyness hypothesis’ that too many board positions lead to less effective monitoring. To the contrary, they find that when a busy director joins the board of a company, that company experiences significantly higher abnormal returns. However,
Fich and Shivdasani (2006) argue that Ferris et al. (2003) do not use the proper econometric specifications to identify the true effect. Since empirical work does not provide conclusive evidence of the effect of busy directors this makes it interesting to study it in a theoretical setting that might lead to empirically testable hypotheses.
Moreover, incorporating other key factors for board effectiveness gives a comprehensive model that can give further clarification on the seemingly contradictory empirical results.
3.
The model
I will first discuss the basic model, second the assumptions and finally summarise with the timing of the model.
3.1
Basic model
The players are: the shareholder (S and she), the board member (B and it) and the manager (M and he). The reservation utility of B and M is equal to 0.
M is the productive player and M’s contribution to firm value Φ = 𝛿 𝑗
+ 𝑒
𝑀
. Here 𝛿 𝑗 represents the ability of M, with 𝑗 ∈ {ℎ, 𝑙}, 𝛿 ℎ
> 𝛿 𝑙
= 0 and Pr(𝑗 = ℎ) =
1
2
. The 𝛿 𝑗
is private knowledge to M at the start of the game. Next, 𝑒
𝑀
≥ 0 represents effort of M.
M dislikes exerting effort with his cost of effort being 𝐶(𝑒
𝑀
) =
1
2 𝑒
𝑀
2 , which is public knowledge. The monetary payment to M is specified in the contract Κ {𝛼 𝑗
𝑀
, 𝛽
𝑀
, ℛ̃} offered by B to M, where 𝛼 𝑗
𝑀
is a fixed payment and the bonus (if 𝛽
𝑀
> 0 ) is paid by
S under the condition that ℛ ≥ ℛ̃ with ℛ̃ ϵ ℝ + set by B. Then 𝑤
𝑀
= 𝛼 𝑗
𝑀
+ 𝛽
𝑀
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represents the total wage payment that S makes to M. After observing 𝑒
𝐵
but before choosing 𝑒
𝑀
, M can also offer side-contract Γ (𝑇, ℛ̂) to B to send a preferable report
ℛ̂ to S in exchange for payment of T . M has full bargaining power in side-contracting.
Once M and B agree on Γ they will stick to it. The payoff for M then is:
𝑈
𝑀
= 𝛼 𝑗
𝑀
+ 𝛽
𝑀
−
1
2 𝑒
𝑀
2 − 𝑇
The task of B is to contract and supervise M. B provides a report ℛ ϵ ℝ + that represents a statement on Φ , but not necessarily its true value. The information provided in ℛ is soft and non-verifiable by a third party and thus cheap talk. B first proposes a contract Κ {𝛼 𝑗
𝑀
, 𝛽
𝑀
, ℛ̃} and if not vetoed by S, it offers Κ to a randomly drawn M from the available pool. B also incurs a penalty each time it does not propose a contract that is acceptable to Κ , which ensures that an acceptable contract will be offered. For simplicity, I assume that B has full bargaining power in contracting with M. To observe Φ , B must monitor. To monitor B incurs a cost of monitoring effort: 𝐶(𝑒
𝐵
) = 𝑐𝑒
𝐵
, with 𝑒
𝐵
ϵ {0,1} and 𝑐 ϵ (0, 𝛿 ℎ
+
1
2
) 4 . The monitoring cost c is public knowledge. If B is indifferent between 𝑒
𝐵
= 1 and 𝑒
𝐵
= 0 it chooses 𝑒
𝐵
= 1 . There is also a probability 𝜋 ϵ (0, 1) that Φ is revealed publicly after all efforts are realised and payments made. If Φ is revealed it is completely informative and B incurs reputation damage of 𝜂|ℛ − Φ| if ℛ ≠ Φ . The parameter 𝜂 > 0 represents the harm of a bad reputation in this world. Both 𝜋 and 𝜂 are common knowledge. The monetary payment to B is specified in the contract 𝜒 {𝛼
𝐵
, 𝛽
𝐵
, ℛ̅} , with 𝛼
𝐵
representing a fixed payment and 𝛽
𝐵
a bonus paid if ℛ ≥ ℛ̅ with ℛ̅ 𝜖 ℝ + .
Then B’s total wage payment 𝑤
𝐵
= 𝛼
𝐵
+ 𝛽
𝐵
and B’s payoff is:
𝑈
𝐵
= 𝛼
𝐵
+ 𝛽
𝐵
+ Τ − 𝑐𝑒
𝐵
− 𝜋𝜂|ℛ − Φ|
The shareholder is the residual claimant to the value of the firm: 𝑉 = 𝛿 𝑗
+ 𝑒
𝑀
+ 𝜀 , with 𝜀 representing a random shock uniformly distributed over [−𝑥, 𝑥] and x large enough to make publicly observed V uninformative for Φ . S is also the first player to make a decision by offering 𝜒 {𝛼
𝐵
, 𝛽
𝐵
, ℛ̅} to B. If B does not accept 𝜒 then S incurs a large positive cost and the game ends, which ensures that S will always offer an acceptable contract to B. S can choose fixed pay by setting 𝛽
𝐵
= 0 or for bonus pay
4 In the equilibrium outcome of the model in propositions 4.2 and 5.2 it will be clear that if this assumption does not hold, monitoring is never profitable. Following the literature I assume there must be profit in monitoring, hence this assumption
10

by setting 𝛽
𝐵
> 0 . If indifferent between the two, S chooses for 𝛽
𝐵
= 0 . For simplicity, I assume that S has full bargaining power in contracting with B.
Furthermore, she can also veto any contract Κ that B proposes to offer to M. S then maximises the following utility function:
𝑈
𝑆
= 𝛿 𝑗
+ 𝑒
𝑀
+ 𝜀 − 𝑤
𝐵
− 𝑤
𝑀
Both 𝜒 and Κ are public knowledge once agreed upon and legally enforceable. S makes all wage payments but will not pay if she detects Τ > 0 or 𝑒
𝐵
= 0 .
3.2
Motivation of assumptions
My model consists of a three-level hierarchy organisation to represent the common structure of public companies and follow the Principal-Supervisor-Agent (PSA literature 5 . Apart from the fact that I follow the approach in the literature, modelling shareholders, the board and management as one player each is also intuitive.
Shareholder preferences are similar, they care about the value of the firm and minimising wage payments. The preferences of the board of directors can be seen as the result of an internal process of alignment between the different independent board members. In the end the board will have to come up with one contract offer to the manager, so this also makes sense intuitively. Finally, when thinking of the manager as the CEO it is straightforward to model the manager as one player.
In this thesis I analyse optimal contracts for the board of directors and make assumptions accordingly. From the literature discussed in section 2, I find that key factors in determining board of director effectiveness are the degree of independence, the level of knowledge and skills, the economic incentives to behave properly, the busyness of directors and their reputation concern. First, I take the point of view of the board of directors as the non-executives and thus outside directors. This means I will not explicitly model the independence of directors, instead I think of the board of directors as representing the independent (non-executive) directors. Second, the knowledge of B depends on what level 𝑒
𝐵
it chooses. If 𝑒
𝐵
= 1 then it perfectly observes Φ , otherwise it only knows what it can anticipate. Third, incentives are an important part of my model. S can set bonus pay (incentive pay) by setting 𝛽
𝐵
> 0 for
ℛ ≥ ℛ̅ . This means that B gets a bonus for ensuring a good report and, if the report is
5 For examples see Strausz (1997a,b), Baliga (1999), Fraure-Grimaud, et al. (2003), Kumar and
Sivaramakrishnan (2008), Celik (2009) and Tichem (2013)
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honest, this means high manager contribution to firm value. Fourth, I model busyness of directors by incorporating a cost of monitoring. I leave c as a parameter drawn from a distribution to evaluate the effect of the busyness of the board on optimal contracts and collusion. More busy directors will have a higher cost of monitoring. In the model this is represented by a world where c is higher .
Another important point to make is that it could be that c is too high to induce any monitoring effort from the board. This could relate to situations where the board is too busy to be able to monitor effectively. Fifth, I model the reputation concern of the board. False reporting may lead to reputation damage in the model if the true contribution of M to V is revealed publicly. This may happen because of criminal investigation into fraud or for example by journalists or analysts doing research. The potential damage is dependent on how far from the truth B’s report is: |ℛ − Φ| , which incorporates that a small deviation from the truth will not cause much damage but big deviations will. That Φ is potentially revealed only after all efforts are realised and payments made reflects the fact that fraud and bad monitoring are usually only detected years later or take a long time to prove in the legal system. Furthermore, the severity of damage 𝜂 represents the importance of reputation in the world considered. If punishment for false reporting or the consequences in terms of loosing directorships is higher then 𝜂 is higher. This will lead to a loss of both income and status, decreasing board member utility as discussed in section two. The probability that the true values are revealed ( 𝜋 ) may depend on the quality of the legal system and transparency of reporting. The assumptions that 𝐶(𝑒
𝐵
) , 𝐶(𝑒
𝑀
), 𝜋 and 𝜂 are common knowledge are made for simplicity.
From the model it is clear that S does not directly contract with B. I assume that it is impossible for S to fulfil the monitoring function and contract with M. Here I thus follow Warther (1998) in assuming that there exists a free-rider problem among shareholders making it impossible for them to monitor effectively. Therefore, S needs to delegate contracting and monitoring of M to B. For the same reason I assume collusion between S and B or M is impossible. However, S is able to veto any contract from B to M that does not maximise her utility. This is a way of preventing collusion and possible because contracts are public knowledge. In reality the shareholders meeting can also vote against a contract if they think it will not maximise firm value. The reason for assuming that S chooses fixed compensation if
12

indifferent is that offering a contract with bonus compensation makes the contract more complicated which could result in a higher cost to S in reality. Furthermore, paying a bonus in reality may lead to some uncertainty for B, which in case of (even slight) risk-aversion would require a higher payment. B is potentially valuable to S since 𝜀 ensures that V is uninformative for Φ . The shock 𝜀 can be thought of to include the effect of the economy, market as well as all other influences on firm value outside the range of control and influence of the manager.
The manager observes 𝑒
𝐵
before making his own effort decision. M knows for example if B has been present enough times at meetings to have judgement on M’s ability and effort. The assumption that M has full bargaining power in sidecontracting reflects the large influence of M documented in the literature.
I assume that both M and B will keep their promise once a side-contract has been agreed upon. The justification is that side-contracts may resemble favours the manager grants to the board members, for example inviting them to other board positions, increasing their expense possibilities and/or giving them good recommendations. This may require a monetary amount from the manager or could be seen as effort the manager needs to exert to provide favours to the board, which both reduce manager utility. The enforceability then results from an implicit contract based on the relationship. We can think of this as an infinitely repeated game where shirking on promises brakes up the relationship. I assume that the value of keeping the promise and maintaining the relationship is always higher than breaking the promise for a onetime gain. This means that both M and B will always keep their promises once a sidecontract is agreed upon. This assumption is made to focus on whether collusion is profitable rather than whether it is stable.
3.3
Timing
The following summarises and shows the timing of the model:
1.
S offers a contract 𝜒 {𝛼
𝐵
, 𝛽
𝐵
, ℛ̅} to B
2.
B chooses to accept 𝜒 or not, if B does not accept the game ends and S incurs a large positive cost
3.
B proposes contract Κ {𝛼 𝑗
𝑀
, 𝛽
𝑀
, ℛ̃}
4.
S may veto Κ and if S does so, B incurs a negligible but positive cost and the game returns to stage 2
13

5.
If S does not veto Κ , then it is offered to a randomly drawn M from the available pool
6.
M chooses to accept the contract or not. If M does not accept the game returns to stage 4
7.
B chooses effort 𝑒
𝐵
8.
M observes 𝑒
𝐵
and may choose to offer side-contract Γ (𝑇, ℛ̂) to B
9.
B chooses to accept Γ or not. If B does not accept the game continues without side-contract
10.
M chooses 𝑒
𝑀
11.
If 𝑒
𝐵
= 1 then B observes Φ
12.
B sends the report ℛ to S
13.
Payments 𝑤
𝐵
and 𝑤
𝑀
and possibly T are made and V is realised
14.
Φ is revealed publicly with probability 𝜋 and conditional on Φ becoming public, B incurs additional disutility of 𝜂|ℛ − Φ|
15.
Game ends
In section 4 and section 5 I analyse which type of contract(s) would be optimal for S to offer to B. The focus of the analysis will be on the impact of the busyness of B on the optimal contract structure for S and the influence on the optimal contract of the threat of collusion between B and M. To find the optimal contract I will first analyse the optimal contract when collusion is not possible in section 4. Second, I will check whether this contract is prone to collusion and how this could be solved in section 5.
4.
Optimal contracting without collusion
In this section I will assume that collusion is not possible and thus effectively 𝑇 = 0 throughout. Under this condition I will show that as long as the monitoring cost is not too high, S can induce truthful reporting resulting in first best effort levels. However, if the monitoring cost is too high relative to the potential reputation damage truthful reporting cannot be induced and the outcome is lower than optimal for S. I proceed by backward induction.
4.1
Choice of the report
The last decision of the game is when B chooses the report ℛ . Two effects influence this decision. First, the reputation effect incentivises B to set ℛ to minimise |ℛ − Φ| .
14

Second , if S offers a bonus for ℛ ≥ ℛ̅ this incentivises B to set ℛ ≥ ℛ̅ . B’s monitoring decision will thus depend on both 𝐸 [Φ] and ℛ̅ .
Lemma 4.1
Consider an equilibrium, then irrespective of 𝑒
𝐵
:
 If ℛ̅ ≤ 𝐸[Φ] B reports ℛ = 𝐸[Φ]
 If ℛ̅ > 𝐸[Φ] : 𝑤ℎ𝑒𝑛 { 𝛽
𝐵 𝛽
𝐵
≤ 𝐸[𝜋𝜂|ℛ̅ − Φ|] − 𝐸[𝜋𝜂|𝐸[Φ] − Φ|] 𝐵 𝑟𝑒𝑝𝑜𝑟𝑡s ℛ = 𝐸[Φ]
> 𝐸[𝜋𝜂|ℛ̅ − Φ|] − 𝐸[𝜋𝜂|𝐸[Φ] − Φ|] 𝐵 𝑟𝑒𝑝𝑜𝑟𝑡𝑠 ℛ = ℛ̅
Proof: Note first that, in this stage the monitoring decision has already been made and the cost of monitoring is thus irrelevant.
If ℛ̅ ≤ 𝐸[Φ] , B will report 𝐸[Φ] to minimise the reputation damage to 0. This is independent of whether pay is offered in fixed of bonus form, because as long as ℛ̅ ≤
𝐸[Φ] , B can always combine reporting the 𝐸[Φ] and ℛ ≥ ℛ̅ to receive the bonus.
If ℛ̅ > 𝐸[Φ] then B chooses to report ℛ = 𝐸[Φ] if 𝛼
𝐵
− 𝐸[𝜋𝜂|𝐸[Φ] − Φ|] ≥ 𝛼
𝐵
+ 𝛽
𝐵
− 𝐸[𝜋𝜂|ℛ̅ − Φ|] which reduces to 𝛽
𝐵
≤ 𝐸[𝜋𝜂|ℛ̅ − Φ|] − 𝐸[𝜋𝜂|𝐸[Φ] − Φ|] . This means B reports ℛ = ℛ̅ if 𝛽
𝐵
> 𝐸[𝜋𝜂|ℛ̅ − Φ|] − 𝐸[𝜋𝜂|𝐸[Φ] − Φ|] 
I will refer to the situation where B reports ℛ = 𝐸[Φ] , given 𝐸[Φ] , as the situation where B reports honestly .
With honest reporting B thus reports its best guess of the true value instead of reporting favourably to M ( ℛ ≥ ℛ̅ ) to receive the bonus, irrespective of 𝐸[Φ] . Please note that if 𝑒
𝐵
= 1 , then B observes the true value ( Φ ) and does not have to guess. This means that if 𝑒
𝐵
= 1 then 𝐸[Φ] = Φ and
𝐸[𝜋𝜂|ℛ̅ − Φ|] − 𝐸[𝜋𝜂|𝐸[Φ] − Φ|] = 𝜋𝜂|ℛ̅ − Φ| .
Lemma 4.1 shows that if in the reporting stage ℛ̅ > 𝐸[Φ] , B chooses between reporting honestly or favourably to M to receive the bonus. This choice depends on the level of the bonus relative to the difference in potential reputation damage between reporting ℛ = ℛ̅ and ℛ = 𝐸[Φ] . The latter shows that this decision will also depend on ℛ̅ . However, even honest reporting does not necessarily result in a ℛ = Φ .
This is because if 𝑒
𝐵
= 0 , B may not exactly know which type of M accepted the contract and what effort was exerted and thus cannot be sure to report the true value.
Lemma 4.1 shows that the probability that B reports honestly decreases in the level of
15

the bonus 𝛽
𝐵
, and increases in the difference in expected reputation damage between reporting honestly and favourably.
4.2
Manager effort choice
Before B chooses ℛ , M chooses 𝑒
𝑀
. The level of 𝑒
𝑀
depends on the compensation offered to M, which is necessary to offset his cost of effort. However, M also anticipates the reporting decision of B and thus ℛ̅ also influences his effort choice. M knows ℛ̅ as it is part of the contract between S and B and the contracts are public knowledge. M will accept the contract Κ if it leads to 𝐸[𝑈
𝑀
] ≥ 0 (Participation
Constraint), as his reservation utility is 0 by assumption. Whether M accepts Κ may also dependent on its type h or l . I will come back to this in lemma 4.6. To aid the analysis I define Φ as the minimum 𝐸[Φ] such that B will choose ℛ ≥ ℛ̃ .
Lemma 4.2 𝑒 ∗
𝑀
Given an equilibrium, effort choices of M are given by 𝑒 ∗
𝑀 𝑒 ∗
𝑀
= 0 , if 𝑒
𝐵
= 0 or 𝛽
𝑀
<
1
2
2 or 𝛽
𝐵
> 𝐸[𝜋𝜂|ℛ̅ − Φ||𝑒
𝐵
̃ }
, 𝜒]
:
= 𝑒
𝑀
̃ − 𝛿 𝑗
, if 𝑒
𝐵
= 1 , 𝛽
𝑀
≥
1
2
2 , 𝛽
𝐵
≤ 𝐸[𝜋𝜂|ℛ̅ − Φ||𝑒
𝐵
= 0]
Proof: If 𝛽
𝑀
= 0 then 𝑒 ∗
𝑀
= 0 . If 𝑒
𝐵
= 0 , M knows that B does not observe 𝑒
𝑀
+ 𝛿 𝑗
.
In this case exerting effort does not influence whether M receives the bonus. Exerting effort then only decreases 𝑈
𝑀
and 𝑒 ∗
𝑀
= 0 . If 𝛽
𝐵
> 𝐸[𝜋𝜂|ℛ̅ − Φ||𝑒
𝐵
, 𝜒] then the bonus is always better than monitoring even though this implies incurring reputation damage. This means that B will then not monitor and M’s level of effort does not influence his chance on receiving his bonus, therefore 𝑒 ∗
𝑀
= 0 .
If M observes 𝑒
𝐵
= 1 it is optimal for him to exert effort only if this increases his pay.
M also knows that S will only pay 𝛽
𝑀
if ℛ ≥ ℛ̃ . Given 𝛽
𝑀
, M therefore prefers to set the lowest possible 𝑒
𝑀
to realise a level of Φ that ensures B has the incentive to report
ℛ ≥ ℛ̃ . M thus sets 𝑒 ∗
𝑀
̃ − 𝛿 𝑗
. The optimal effort choice then depends on the conditions as given in lemma 4.2 and is given by 𝑒
𝑀
̃ } 
16

Lemma 4.2 shows that a bonus for B also influences 𝑒 ∗
𝑀
. Furthermore, the choice of 𝑒
𝑀
depends on 𝑒
𝐵
, ℛ̃ and 𝛽
𝑀
. The level of ℛ̅ that S will set may also influence the effort choice in case a bonus is offered to B. Next, I define 𝜆 = lim 𝑥→0 𝑥 .
Lemma 4.3
Consider an equilibrium where 𝑒 ∗
𝑀
= 𝑒 ̃ , then:
 𝑒
𝑀 𝑗
, if 𝛽
𝐵
= 0 or ℛ̃ > ℛ̅
 𝑒
𝑀 𝑗
− 𝛽
𝐵 𝜋𝜂
+ 𝜆 if 𝛽
𝐵
> 0 and ℛ̃ ≤ ℛ̅
Proof: If 𝛽
𝐵
= 0 it follows from lemma 4.1 that always ℛ = 𝐸[Φ] and thus Φ .
Therefore, M will choose 𝑒
𝑀 𝑗
, given that 𝑒 ∗
𝑀
= 𝑒 ̃ . If 𝛽
𝐵
> 0 it follows from lemma 4.1 that B reports ℛ = Φ if Φ ≥ ℛ̅ or if both Φ < ℛ̅ and 𝛽
𝐵
≤ 𝜋𝜂|ℛ̅ − Φ| .
This means that if ℛ̃ > ℛ̅ and 𝑒 ∗
𝑀
̃ it always holds that B chooses ℛ = Φ . It follows from lemma 4.2 that then 𝑒
𝑀 𝑗
. If ℛ̃ ≤ ℛ̅ then a level Φ < ℛ̅ is sustainable for M if 𝛽
𝐵
> 𝜋𝜂|ℛ̅ − Φ| . Because Φ = 𝑒
𝑀
+ 𝛿 𝑗
, this leads to the condition 𝛽
𝐵
> 𝜋𝜂|ℛ̅ − 𝑒
𝑀
− 𝛿 𝑗
| . Rewriting gives 𝑒
𝑀 𝑗
− 𝛽
𝐵 . This means 𝜋𝜂 that 𝑒
𝑀 𝑗
− 𝛽
𝐵 𝜋𝜂
+ 𝜆 , but constraint to the level of 𝛽
𝑀
and 𝛽
𝐵 𝜋𝜂
≥ 𝜆 . If 𝛽
𝐵 𝜋𝜂
< 𝜆 then it is not possible for M to induce B to report ℛ̅ > Φ , which should be always possible by assumption. This means that under these conditions M decreases effort by 𝛽
𝐵 𝜋𝜂
− 𝜆 to make B just better off reporting ℛ̅ > Φ 

Lemma 4.3 shows that depending on ℛ̃ relative to ℛ̅ , M’s optimal effort level may decrease if 𝛽
𝐵
> 0 . Because M knows that B has an incentive to report favourably if 𝛽
𝐵
> 0 , he can reduce his effort to a level that B just prefers reporting favourably to reporting honestly.
4.3
Board monitoring choice
The monitoring choice of B represents a trade-off between benefits and costs of monitoring. The benefit of monitoring is the possibility to report the truth to minimise
17

potential reputation loss. The cost of monitoring is represented by the cost of monitoring effort, reducing B’s utility. The monitoring decision is also influenced by the wage that B expects to receive under 𝑒
𝐵
= 1 and 𝑒
𝐵
= 0 .
Lemma 4.4
Consider an equilibrium, then B will monitor if: 𝑐 ≤ 𝑤
𝐵
(𝑒
𝐵
= 0, ℛ,∙) − 𝑤
𝐵
(𝑒
𝐵
= 1, ℛ,∙) + 𝐸[𝜋𝜂|ℛ − Φ||𝑒
𝐵
= 0]
− 𝐸[𝜋𝜂|ℛ − Φ||𝑒
𝐵
= 1]
Proof: In general B will monitor if 𝐸[𝑈
𝐵
(𝑒
𝐵
= 1, ℛ, Κ, 𝜒)] ≥ 𝐸[𝑈
𝐵
(𝑒
𝐵
=
0, ℛ, Κ, 𝜒)] . Taking into account that B incurs monitoring cost 𝑐 if it monitors and 0 otherwise gives the condition in lemma 4.4 

Lemma 4.4 shows that B will monitor if the monitoring cost is low enough compared to the differences in wage and expected reputation damage between 𝑒
𝐵
= 0 and 𝑒
𝐵
=
1 . Note that if 𝛽
𝐵
= 0 then 𝑤
𝐵
(𝑒
𝐵
= 0, ℛ,∙) − 𝑤
𝐵
(𝑒
𝐵
= 1, ℛ,∙) = 0 .
From lemma 4.4 it also follows that if 0 ≤ 𝛽
𝐵
≤ 𝛿 ℎ
and B is able to contract such that it screens out one type M irrespective of 𝑒
𝐵
it will never monitor, because by assumption 𝑐 > 0 .
4.4
Optimal contracts
Before B chooses 𝑒
𝐵
it will offer contract Κ {𝛼 𝑗
𝑀
, 𝛽
𝑀
, ℛ̃} to M. After I show how B sets Κ , I can move to the first stage of the game where S offers contract 𝜒 {𝛼
𝐵
, 𝛽
𝐵
, ℛ̅} to B. Finally, I can summarise the contracts and provide the equilibrium outcome of the game.
The types of contract that B can offer are limited by the veto power of S. I define Φ ∗ as the optimal level (Φ|π, η, 𝛿 ℎ
, 𝑐) for S.
Lemma 4.5
S will veto any contract Κ {𝛼 𝑗
𝑀
, 𝛽
𝑀
, ℛ̃} that will not result in 𝐸[𝑈 ∗
𝑆
|𝜒]
Proof: Given the values of 𝑐, 𝜋, 𝜂 and 𝛿 ℎ
, S writes the contract 𝜒 {𝛼
𝐵
, 𝛽
𝐵
, ℛ̅} that induces the optimal 𝐸[𝑈
𝑆
] = 𝐸[𝑈 ∗
𝑆
] given that B writes the contract Κ {𝛼 𝑗
𝑀
, 𝛽
𝑀
, ℛ̃}
18

that induces Φ ∗ at the lowest cost. Since S has veto power over the contract
Κ {𝛼 𝑗
𝑀
, 𝛽
𝑀
, ℛ̃} she use her veto power to cancel any Κ that will not result in 𝐸[𝑈 ∗
𝑆
|𝜒] 

Lemma 4.5 shows that B’s choice of Κ {𝛼 𝑗
𝑀
, 𝛽
𝑀
, ℛ̃} is restricted by S’ veto. B must offer an efficient contract Κ to M otherwise S will veto it and B incurs a small but positive cost. This means that after accepting 𝜒 , it is always better for B to offer a contract that is not vetoed by S. Next, I will show that B can also make sure that the high ability manager self-selects by offering the right type of contract.
Lemma 4.6
Consider an equilibrium, then self-selection of M occurs only if M believes that B will choose 𝑒
𝐵
= 1 after M accepts contract Κ :
 If 𝛽
𝐵
= 0 or ℛ̃ > ℛ̅ by:
1
2
(ℛ̃ − 𝛿 ℎ
)
2
≤ 𝛽
𝑀
<
1
2
ℛ̃ 2 and 𝛼 𝑙
𝑀
< 0
 If 𝛽
𝐵
> 0 and ℛ̃ ≤ ℛ̅ by:
1
2
(ℛ̅ − 𝛿 ℎ
− 𝛽
𝐵 𝜋𝜂
)
2
≤ 𝛽
𝑀
<
1
2
(ℛ̅ − 𝛽
𝐵 𝜋𝜂
) 2 and 𝛼 𝑙
𝑀
< 0
Proof: If in the contracting stage M believes that B will pick 𝑒
𝐵
= 1 then B can set 𝛽
𝑀
such that only type 𝛿 ℎ
will accept. Using lemma 4.2 and 4.3, if 𝛽
𝐵
= 0 or ℛ̃ > ℛ̅ ,
B should then set
1
2
(ℛ̅ − 𝛿 ℎ
) 2 ≤ 𝛽
𝑀
<
1
2
ℛ̅ 2 . If 𝛽
𝐵
> 0 and ℛ̃ ≤ ℛ̅ then B should set:
1
2
(ℛ̅ − 𝛿 ℎ
− 𝛽
𝐵 𝜋𝜂
)
2
≤ 𝛽
𝑀
<
1
2
(ℛ̅ − 𝛽
𝐵 𝜋𝜂
) 2 .
In these cases the bonus is high enough for the 𝛿 ℎ
manager to exert optimal effort and low enough for the 𝛿 𝑙
manager to make it inefficient to exert enough effort to make sure B reports ℛ̅ . If M is then of type 𝛿 𝑙
he anticipates that B will observe Φ = 0 and combining this with 𝛼 𝑙 𝑚
< 0 makes accepting the contract worse than his outside option. If M believes that B will pick 𝑒
𝐵
= 0 he anticipates that B will not observe 𝑒
𝑀
+ 𝛿 𝑗
. In this case also the low ability manager always has an incentive to accept the contract as long as the participation constraint is satisfied. B can never deter the low ability type in this situation since it cannot make a credible promise to not pay the bonus if M does not ensure ℛ̃ 
Lemma 4.6 shows that B can only deter the lower ability manager if M believes that B will monitor. Monitoring while setting a bonus for M thus has two important effects, only the high ability M will accept the contract and he will also exert effort. How B
19

should set Κ if it wants to deter the low ability M also depends on whether B gets a bonus or not.
Lemma 4.7
The optimal level of Φ for S is:
Φ ∗ = δ h
+ 1 if 𝐸[U
𝑆
|𝑒
𝐵
= 1,∙ ] ≥ 𝐸[U
𝑆
|𝑒
𝐵
= 0,∙ ]
𝐸[Φ ∗ ] =
1
2
δ h
if 𝐸[U
𝑆
|𝑒
𝐵
= 1,∙ ] < 𝐸[U
𝑆
|𝑒
𝐵
= 0,∙ ]
Proof: S wants to maximise E[𝑈
𝑆
|π, η, 𝛿 ℎ
, 𝑐] . If 𝐸[U
𝑆
|𝑒
𝐵
= 1,∙ ] < 𝐸[U
𝑆
|𝑒
𝐵
= 0,∙ ] then inducing monitoring is not efficient for S. This means that optimally 𝑒
𝐵
= 𝑒
𝑀
=
0 and thus the highest attainable value of Φ = δ h
with Pr[ Φ = δ h
] =
1
2
.
If 𝐸[U
𝑆
|𝑒
𝐵
= 1,∙ ] ≥ 𝐸[U
𝑆
|𝑒
𝐵
= 0,∙ ] , inducing monitoring is efficient. Then the δ j that maximises the equation is δ h
since δ l
= 0 and S does not incur additional costs of setting δ h
instead of δ l
. Differentiating shows that MB( e
M
) = 1 and MC( e
M
) = e
M
.
Thus MB = MC if e
M
= 1 
Lemma 4.7 shows the optimal levels of manager contribution to firm value given the other parameters. Now I can define the contract that B will offer that is clearly constraint to the condition in lemma 4.5.
Lemma 4.8
Consider an equilibrium, then B will offer Κ {𝛼 𝑗
𝑀
, 𝛽
𝑀
, ℛ̃} to M as follows:
Κ {0,0,0} , if (𝑈
𝐵
| 𝜒, 𝑒
𝐵
= 0) > (𝑈
𝐵
| 𝜒, 𝑒
𝐵
= 1)
Κ {𝛼 𝑙
𝑀
< 0 & 𝛼 ℎ
𝑀
= 0,
1
2
, δ h
+ 1} if (𝑈
𝐵
| 𝜒, 𝑒
𝐵
= 1) ≥ (𝑈
𝐵
| 𝜒, 𝑒
𝐵
= 0)
Proof: Lemma 4.5 shows that B cannot offer a contract that does not result in
𝐸[𝑈 ∗
𝑆
|𝜒] , because it will be vetoed by S. Then if 𝐸[U
𝑆
|𝑒
𝐵
= 1,∙ ] < 𝐸[U
𝑆
|𝑒
𝐵
= 0,∙ ] , S will offer a contract 𝜒 such that (𝑈
𝐵
| 𝜒, 𝑒
𝐵
= 0) > (𝑈
𝐵
| 𝜒, 𝑒
𝐵
= 1) . In this case
𝐸[Φ ∗ ] =
1
2
δ h
, which does not require wage payment nor incentives for M and thus
Κ {0,0,0} 6 .
6 In fact any ℛ̃ ϵ ℝ + would be sufficient if 𝛽
𝑀
= 0 , I assume that if this is the case B will set ℛ̃ = 0 .
20

If 𝐸[U
𝑆
|𝑒
𝐵
= 1,∙ ] ≥ 𝐸[U
𝑆
|𝑒
𝐵
= 0,∙ ] then S will offer a contract 𝜒 such that
(𝑈
𝐵
| 𝜒, 𝑒
𝐵
= 1) ≥ (𝑈
𝐵
| 𝜒, 𝑒
𝐵
= 0) . This means that Φ ∗ = δ h
+ 1 and the optimal contract for M depends on ℛ̅ . Any contract that does not realise 𝐸[𝑈
𝑆
∗ |𝜒] will be vetoed. From lemma 4.3 and lemma 4.6 it then follows that B will offer Κ {𝛼 𝑙
𝑀
<
0 & 𝛼 ℎ
𝑀
= 0,
1
2
, δ h
+ 1 } 
Lemma 4.8 shows that B will offer a contract such that M exerts optimal effort given that S has set the right level ℛ̅ to make sure M does. The above makes clear that S needs to induce B to monitor to make sure she reaches maximum utility. If B monitors, from lemma 4.5 and lemma 4.8 we know that B also can and will offer a contract that induces Φ ∗ . Next, I can how S optimally sets 𝜒 . Since S is the first player to make a move in the game she can take the decisions of the other two players into account when setting 𝜒 {𝛼
𝐵
, 𝛽
𝐵
, ℛ̅} . Lemma 4.3 and 4.8 show that that while S does not directly contract with M she still influences M’s effort choice trough her choice of ℛ̅ .
Lemma 4.9
If ℛ̅ ≥ ℛ̃ then 𝛽
𝐵
is ineffective in incentivising B to monitor
Proof: If ℛ̅ ≥ ℛ̃ and 𝛽
𝐵
> 0 , the E[𝑈
𝐵
(ℛ = ℛ̅,∙ )] = 𝛼
𝐵
+ 𝛽
𝐵
− 𝑐 − 𝜋𝜂|ℛ − Φ| . It follows from lemma 4.3 that Φ = ℛ̅ − 𝛽
𝐵 𝜋𝜂
+ 𝜆 . Combining these gives
E[𝑈
𝐵
(ℛ = ℛ̅,∙ )] = 𝛼
𝐵
+ 𝛽
𝐵
− 𝑐 − 𝜋𝜂 (ℛ − ℛ̅ + 𝛽
𝐵 𝜋𝜂
− 𝜆) = 𝛼
𝐵
− 𝑐 − 𝜋𝜂(ℛ − ℛ̅ − 𝜆) . This shows that 𝛽
𝐵
is completely offset by an increase in expected reputation damage due to lower 𝑒
𝑀


Lemma 4.9 shows that if S sets a bonus she must also ensure ℛ̅ < ℛ̃ to make the bonus effective. To do so she must set ℛ̅ < Φ ∗ if 𝛽
𝐵
> 0 .
Lemma 4.10
Consider an equilibrium, then S can realise Φ ∗ = δ h
+ 1 if 𝑐 ≤
1
2 𝜋𝜂δ h
+ 𝛽
𝐵
and 𝛽
𝐵
≤ 𝜋𝜂(1 − 𝜆) by setting ℛ̅ < Φ ∗
21

Proof: From lemma 4.7 it follows that S will only reach its maximum utility if B monitors. Therefore, S must make sure that the monitoring condition in lemma 4.4 holds. From lemma 4.1 it follows that to make a bonus effective it must be that B does not receive the bonus if 𝑒
𝐵
= 0 and from lemma 4.9 that ℛ̅ < Φ ∗ . Lemma 4.1 shows that if 𝛽
𝐵
≤ 𝐸[𝜋𝜂|ℛ̅ − Φ|] − 𝐸[𝜋𝜂|𝐸[Φ] − Φ|] then B reports ℛ = 𝐸[Φ] . Then if S sets ℛ̅ > 𝐸[Φ|𝑒
𝐵
= 0] and 𝛽
𝐵
≤ 𝐸[𝜋𝜂|ℛ̅ − Φ||𝑒
𝐵
= 0] − 𝐸[𝜋𝜂|𝐸[Φ] − Φ||𝑒
𝐵
= 0] ,
B will not receive the bonus if 𝑒
𝐵
= 0 . The 𝐸[𝜋𝜂|ℛ − Φ||𝑒
𝐵
= 0] depends on the realisation of Φ . From lemma 4.2 we know that if 𝑒
𝐵
= 0 then 𝑒
𝑀
= 0 . Lemma 4.6 shows that the realisation of δ j
depends on the belief of M about 𝑒
𝐵
in the contracting stage. In equilibrium M’s beliefs must be consistent. Therefore I assume M believes 𝑒
𝐵
= 0 here and check if this is consistent later. The 𝐸[𝜋𝜂|ℛ − Φ||𝑒
𝐵
= 0] =
1
2
𝜋𝜂|ℛ − 𝛿 ℎ
| +
1
2 𝜋𝜂|ℛ − 𝛿 𝑙
| =
1
2 𝜋𝜂 (|ℛ − 𝛿 ℎ
| + ℛ) . Using the latter, 𝐸[𝜋𝜂|ℛ̅ −
Φ||𝑒
𝐵
= 0] =
1
2 𝜋𝜂 (|ℛ̅ − 𝛿 ℎ
| + ℛ̅) and 𝐸[𝜋𝜂|𝐸[Φ] − Φ|] =
1
2 𝜋𝜂𝛿 ℎ
. Given the monitoring condition S prefers 𝐸[𝜋𝜂|ℛ̅ − Φ||𝑒
𝐵
= 0] as high as possible which is if
ℛ̅ = δ h
+ 1 − 𝜆 .
This is because combining lemma 4.8 and 4.9 shows that a level
ℛ̅ ≥ Φ ∗ makes the bonus ineffective. Then 𝐸[𝜋𝜂|ℛ̅ − Φ||𝑒
𝐵
= 0] = 𝜋𝜂(1 − 𝜆 +
1
2
δ h
) and it must be that 𝛽
𝐵
≤ 𝜋𝜂(1 − 𝜆) to make sure ℛ = 𝐸[Φ] if 𝑒
𝐵
= 0 . Under this condition 𝐸[𝜋𝜂|ℛ − Φ||𝑒
𝐵
= 0] =
1
2 𝜋𝜂𝛿 ℎ
. Next, I need to know
𝐸[𝜋𝜂|ℛ − Φ||𝑒
𝐵
= 1] . Given that ℛ̃ = Φ ∗ > ℛ̅ , lemma 4.1 tells B will report ℛ̅ =
Φ ∗ and thus 𝐸[𝜋𝜂|ℛ − Φ||𝑒
𝐵
= 1] = 0 . Solving the monitoring condition than leaves 𝑐 ≤
1
2 𝜋𝜂δ h
+ 𝛽
𝐵

Lemma 4.10 shows that the first best effort levels are realisable if the cost of monitoring effort is low enough relative to the expected reputation damage. The first best effort levels can be realised for a larger set of values of c if S chooses 0 < 𝛽
𝐵
≤ 𝜋𝜂(1 − 𝜆) over 𝛽
𝐵
= 0 . However, this effect is limited because for 𝛽
𝐵
> 𝜋𝜂(1 − 𝜆) ,
B will choose to report ℛ ≥ ℛ̅ irrespective of 𝑒
𝐵
. Please note that δ h
basically represents the difference in ability of managers since δ l
= 0 . The probability that B will monitor thus decreases in the monitoring cost, but increases in the probability
22

that Φ is observed, the magnitude of reputation damage 𝜂 and difference in managerial ability δ h
.
Proposition 4.1
In equilibrium the realisation of Φ ∗ depends on c:
 If 𝑐 ≤
1
2 𝜋𝜂δ h
, 𝛽
𝐵
= 0 is sufficient to realise Φ ∗ = δ h
+ 1
 If
1
2 𝜋𝜂δ h
< 𝑐 ≤
1
2 𝜋𝜂δ h
+ 𝜋𝜂(1 − 𝜆) then 0 < 𝛽
𝐵
≤ 𝜋𝜂(1 − 𝜆) is required to realise Φ ∗ = δ h
+ 1
 If 𝑐 >
1
2 𝜋𝜂δ h
+ 𝜋𝜂(1 − 𝜆) then 𝐸[Φ ∗ ] =
1
2
δ h
Proof: Follows directly from lemma 4.10 

From proposition 4.1 it follows that if the monitoring cost is low enough, S can realise the first best effort levels with fixed pay for B. If the monitoring cost is higher, the optimal effort levels can still be realised, but this requires a bonus payment. If the cost of monitoring is too high then optimal effort levels cannot be realised.
Proposition 4.2
The equilibrium outcome of the game is:
 If 𝑐 ≤
1
2 𝜋𝜂δ h
given by: o 𝜒 {𝑐, 0, 0} 𝑎𝑛𝑑 Κ {𝛼 𝑙
𝑀
< 0 & 𝛼 ℎ
𝑀
= 0,
1
2
, δ h
+ 1} o 𝐸[𝑈
𝑆
] = 𝛿 ℎ
+
1
2
− 𝑐
 If
1
2 𝜋𝜂δ h
< 𝑐 ≤
1
2 𝜋𝜂δ h
+ 𝜋𝜂(1 − 𝜆) given by: o 𝜒 {
1
2 𝜋𝜂δ h
, 𝑐 −
1
2 𝜋𝜂δ h
, δ h
+ 1 − 𝜆 } 𝑎𝑛𝑑 Κ {𝛼 𝑙
𝑀
< 0 & 𝛼 ℎ
𝑀
= 0,
1
2
, δ h
+ 1} o 𝐸[𝑈
𝑆
] = 𝛿 ℎ
+
1
2
− 𝑐
 If 𝑐 >
1
2 𝜋𝜂δ h
+ 𝜋𝜂(1 − 𝜆) given by: o 𝜒 {
1
2 𝜋𝜂𝛿 ℎ
, 0,0} and Κ {0,0,0} o 𝐸[𝑈
𝑆
] = 𝛿 ℎ
(1−𝜋𝜂)
2
Proof: From proposition 4.1 it follows that 𝛽
𝐵
= 0 is sufficient to realise Φ ∗ = δ h
+
1 if 𝑐 ≤
1
2 𝜋𝜂δ h
. The latter condition satisfies the monitoring condition in lemma 4.4.
23

Then lemma 4.8 gives that Κ {𝛼 𝑙
𝑀
< 0 & 𝛼 ℎ
𝑀
= 0,
1
2
, δ h
+ 1} . The level of ℛ̅ does not matter for B as with 𝛽
𝐵
= 0 there is no need for ℛ̅ . The level of ℛ̅ also does not matter for M as lemma 4.3 shows that 𝑒
𝑀 𝑗
with 𝛽
𝐵
= 0 . Then any ℛ̅ 𝜖 ℝ + is sufficient 7 . Then given K, ̃ = 1 . The 𝑈
𝑆
= 𝛿 𝑗
+ 𝑒
𝑀
+ 𝜀 − 𝑤
𝐵
− 𝑤
𝑀
, with E[ 𝜀] = 0 .
Solving for the results above results in 𝐸[𝑈
𝑆
] = 𝛿 ℎ
+
1
2
− 𝑐 .
If 𝑐 >
1
2 𝜋𝜂δ h
, lemma 4.10 shows that 𝛽
𝐵
≤ 𝜋𝜂(1 − 𝜆) can increase the opportunity for realising Φ ∗ = δ h
+ 1 . The maximally sustainable cost of effort is then 𝑐 ≤
1
2 𝜋𝜂δ h
+ 𝜋𝜂(1 − 𝜆) . As by assumption S prefers fixed pay if possible, a bonus will only be used if
1
2 𝜋𝜂δ h
< 𝑐 ≤
1
2 𝜋𝜂δ h
+ 𝜋𝜂(1 − 𝜆) . Since S prefers 𝛽
𝐵
= 0 she will choose the lowest possible level of the bonus, which is 𝛽
𝐵
= 𝑐 −
1
2 𝜋𝜂δ h
. Then she needs to by make sure B’s participation constraint is satisfied by setting 𝛼
𝐵
=
1
2 𝜋𝜂δ h
.
Finally S then optimally sets ℛ̅ = δ h
+ 1 − 𝜆 , as follows from lemma 4.10. Lemma
4.8 then again gives Κ and 𝐸[𝑈
𝑆
] is the same as before.
If 𝑐 >
1
2 𝜋𝜂δ h
+ 𝜋𝜂(1 − 𝜆) then always (𝑈
𝐵
| 𝜒, 𝑒
𝐵
= 0) > (𝑈
𝐵
| 𝜒, 𝑒
𝐵
= 1) and S is best off not to incentivise B to monitor. However, B still faces expected reputation loss 𝐸[𝜋𝜂|ℛ − Φ||𝑒
𝐵
= 0] =
1
2 𝜋𝜂𝛿 ℎ
. This means that S needs to offer 𝛼
𝐵
=
1
2 𝜋𝜂δ h to offset this cost. With 𝛽
𝐵
= 0 the level of ℛ̅ then again is irrelevant and can be any
ℛ̅ 𝜖 ℝ + . Lemma 4.8 states that B will offer Κ {0, 0,0} . It follows that 𝐸[𝑈
𝑆
] = 𝛿 ℎ
(1−𝜋𝜂)

2
Proposition 4.2 shows that S cannot incentivise B if the monitoring cost is too high relative to the expected reputation damage. S then relies on the shock and probability of a high ability manager accepting the contract. The probability of monitoring thus decreases in the monitoring cost, but increases in the probability that Φ is observed, the magnitude of reputation damage 𝜂 and the difference in managerial ability 𝛿 ℎ
.
From proposition 4.2 we can see that for values of c that are sufficiently low, fixed pay for B is sufficient to realise the optimal result for S. Furthermore, the same level of 𝐸[𝑈
𝑆
] can be reached under a larger set of values of c when including a bonus payment. Whether bonus or fixed pay for the board is observed thus depends on the
7
Similar to the contract of M, if any ℛ̅ ϵ ℝ + is sufficient, I assume that S sets ℛ̅ = 0 .
24

value of c relative to the expected reputation damage. S can still earn a positive utility even if monitoring cost is too high to induce monitoring given that 𝛿 ℎ
(1 − 𝜋𝜂) > 0 or the shock is sufficiently positive. However, she then relies on a positive shock and the probability of a high ability manager accepting the contract. This shows that even without effort a high ability manager can still create value for the firm. Moreover, even if no high ability manager joins the firm, investment in the firm can still create value depending on the shock. With the shock representing everything outside the influence of the manager, this may resemble a situation in which investment in the firm only creates value because of positive outside factors. This could for example be that the firm is in a good market by luck or economic conditions are so good that even without CEO contribution it still represents economic value. From the analysis also follows the hypothesis that if the monitoring cost is too high to induce monitoring effort we should observe reservation utility wage payments to M, but still positive payment for B. The latter is caused by the fact that S has to compensate B for the expected reputation damage if it does not monitor. Since M provides no additional value by exerting effort, wage payment is lower than if effort can be induced. While S is worse off in this situation, B and M are equally well off in both situations. This is the result of S being able to extract all rents from B and M under the optimal contract without collusion if monitoring can be induced.
5.
Optimal contracting under the threat of collusion
Now that I have established the optimal contracts without collusion the next step is to show optimal contracts under the threat of collusion. In the model collusion means that M can offer B a side-contract Γ (𝑇, ℛ̂) to pay B a fee T to choose ℛ ≥ ℛ̂ irrespective of 𝐸[Φ] . The optimal contracts derived in section 4 will be the basis for evaluating the decision of M to offer this bribe. As discussed in section 3, I only consider collusion between B and M. I find that the optimal contract derived in section 4 is prone to collusion if the potential reputation damage is low. S can deter collusion by lowering the manager’s wage, but this necessarily leads to a lower than optimal level of effort. Finally, the possibility of collusion does not depend on the level and type of compensation of B.
5.1
Incentives and opportunities for the manager to bribe the board
25

I will start this section with the incentives M has to bribe B and continue with the analysis of circumstances under which M is able to bribe B. From proposition 4.2 it follows that 𝑈
𝑀
= 0 under the optimal contracts and if : 𝑐 >
1
2 𝜋𝜂δ h
+ 𝜋𝜂(1 − 𝜆) there is no possibility for collusion. In the latter case M does not receive a positive wage payment and thus has no opportunity to bribe B. Collusion is thus restricted to situations where 𝑐 ≤
1
2 𝜋𝜂δ h
+ 𝜋𝜂(1 − 𝜆) . Intuitively, if the monitoring cost is high this means that a board member is very busy and CEO and board do not meet often.
Then there may not be much opportunity to organise collusion or not sufficient trust to make it stable. In this case we may not observe collusion. Alternatively, if monitoring cost is very high, the board will not monitor effectively anyways and bribing may not be necessary. In the equilibrium of the model S knows exactly when
B will monitor and thus makes sure to only pay M a positive wage if B will monitor.
I define 𝑇̂ as the level of T that makes B indifferent between adhering to the optimal contract and sending ℛ ≥ ℛ̂ irrespective of 𝐸[Φ] . Since B will adhere to the contract if indifferent, M needs to pay B an amount higher than 𝑇̂ .
Lemma 5.1
If 𝑐 ≤
1
2 𝜋𝜂(δ h
+ 𝜆) M will bribe B to report ℛ = ℛ̃ irrespective of 𝐸[Φ] as long as 𝑤
𝑀
−
1
2 𝑒 2
𝑀
> 𝑇̂
Proof: First, if ℛ ≠ Φ ∗ under the optimal contract then S will detect collusion and make no payments. Then it will always hold that the optimal ℛ̂ = ℛ̃ = Φ ∗ . Given that
𝑈
𝑀
= 0 under optimal contracts, reducing e
M
while ℛ = ℛ̃ , creates a rent for M.
However, to induce B to depart from his optimum ℛ as follows from proposition 4.2,
M will need to bribe B an amount 𝑇 > 𝑇̂ . As long as 𝑤
𝑀
−
1
2 𝑒 2
𝑀
> 𝑇̂ this will leave M with a rent. B cannot extract this rent since M retains all bargaining power in the sidecontracting stage 
Now that I showed that M has an incentive to bribe B, I can establish the conditions under which M is able to bribe B. Under the optimal contracts B does not incur reputation damage as it always reports the truth. For B, choosing ℛ ≠ Φ comes at a cost of potentially incurring reputation damage and thus M needs to offer
26

compensation to B to offset this cost. I call M’s bribe effective if it is large enough to offset the potential reputation damage for B.
Lemma 5.2
When B anticipates that M will offer an effective bribe:
𝑇̂ = 𝐸[𝜋𝜂|ℛ − Φ|] if optimally 𝑒
𝐵
= 1
𝑇̂ = 𝐸[𝜋𝜂|ℛ − Φ|] − 𝑐 if optimally 𝑒
𝐵
= 0
Proof: The optimal level of T depends on what the optimal level of 𝑒
𝐵
is for B in the stage where it chooses effort. B will anticipate whether M is able to pay the bribe and knows that M will bribe if possible. If B chooses 𝑒
𝐵
= 1 , even if it anticipates a bribe, paying 𝑇 > 𝐸[𝜋𝜂|ℛ − Φ|] is required to overcome the expected reputation loss of reporting ℛ ≠ Φ . If B chooses 𝑒
𝐵
= 0 , 𝑇 > 𝐸[𝜋𝜂|ℛ − Φ|] − 𝑐 is sufficient to bribe
B. This is because B’s utility under the optimal contract 𝑈
𝐵
(ℛ = Φ, 𝑒
𝐵
= 1,∙ ) = 𝛼
𝐵
+ 𝛽
𝐵
− 𝑐 and when anticipating the bribe 𝑈
𝐵
(ℛ ≠ Φ, 𝑒
𝐵
= 0,∙ ) = 𝛼
𝐵
+ 𝛽
𝐵
+ 𝑇 − 𝜋𝜂|ℛ − Φ| . The minimum required bribe thus decreases because B does not have to incur monitoring cost 

Lemma 5.2 shows that 𝑇̂ increases in the expected reputation damage of B under collusion. However, the required bribe may decrease once B does not have an incentive to monitor anymore. This is because monitoring represents a cost for B and when this cost is not incurred under collusion, this lowers the bribe that M needs to pay to B. The potential reputation damage B incurs will also depend on the value of 𝑒
𝑀
that M will choose as this directly influences Φ . Next, I define 𝜃 as the smallest amount of payment M can make to T, meaning 𝜃 = lim 𝑥→0 𝑥 .
27

Lemma 5.3
Given an equilibrium where B and M collude under the optimal contract as defined in proposition 4.2:
 𝑒 ∗
𝑀
 𝑒 ∗
𝑀
= 𝜋𝜂 if and only if 𝑒
𝐵
= 1 and 𝜋𝜂 < 1
= 1 if and only if 𝑒
𝐵
= 1 and 𝜋𝜂 ≥ 1
 𝑒 ∗
𝑀
= 0 if 𝑒
𝐵
= 0
Proof: Under the possibility of collusion (𝑈
𝑀
|𝑒
𝐵
= 1, ℛ = Φ ∗ ) = 𝛼
𝑀
+ 𝛽
𝑀
− 𝑇 −
1
2 𝑒 2
𝑀
. Where 𝑇 > 𝐸[𝜋𝜂|ℛ − Φ|] . This means that 𝑇 = 𝐸[𝜋𝜂|ℛ − Φ|] + 𝜃 is sufficient to effectively bribe B. If B monitors then 𝐸[|ℛ̅ − Φ||𝑒
𝐵
= 1] = |ℛ̅ − 𝛿 ℎ
− 𝑒
𝑀
| . Since
B monitors it can make sure to only attract the high ability type M, which is in its best interest as this reduces the expected reputation damage at no cost. Then M chooses 𝑒
𝑀 to maximise 𝛼
𝑀
+ 𝛽
𝑀
−
1
2 𝑒 2
𝑀
− 𝜋𝜂|ℛ̅ − 𝛿 ℎ
− 𝑒
𝑀
| − 𝜃 . This means that 𝑒 ∗
𝑀
= 𝜋𝜂 , which is optimal only as long as 𝜋𝜂 ≤ 1 . Since the optimal contract pays the bonus for 𝑒
𝑀
= 1 , it cannot be profitable for M to exert 𝑒
𝑀
> 1 . If 𝜋𝜂 > 1 exerting 𝑒
𝑀
= 𝜋𝜂 > 1 is not optimal because this will lead to negative utility for M independent of the required bribe it needs to pay. Then it is optimal for M to exert 𝑒
𝑀
= 1 if 𝜋𝜂 > 1 , because MC( 𝑒
𝑀
) = 𝑒
𝑀
and MB( 𝑒
𝑀
) = 𝜋𝜂 > 1 . The other extreme where 𝑒
𝑀
= 0 is not optimal, because it requires a bribe of 𝜋𝜂|1 − 𝑒
𝑀
| > 1 and the maximum bribe is given by 𝑤
𝑀
−
1
2 𝑒 2
𝑀
(lemma 5.1) with 𝑤
𝑀
=
1
2
under the optimal contract. M then cannot bribe B, which means B will adhere to the optimal contract and thus it is also in M’s best interest to do so. From lemma 4.1 it follows that if 𝑒
𝐵
= 0 then 𝑒 ∗
𝑀
= 0 .
Also under collusion if 𝑒
𝐵
= 0 it is impossible for M to make a credible promise on any other amount of effort than 𝑒
𝑀
= 0 

Lemma 5.3 shows that M’s optimal effort level changes when B and M collude.
However, it is not necessarily the case that M exerts no effort. If 𝑒
𝐵
= 1 then it is always optimal to exert effort for M since this decreases the expected reputation damage and thus decreases the required bribe M needs to pay. The above also shows if 𝜋𝜂 ≥ 1 and 𝑒
𝐵
= 1 , M will exert optimal effort also under the threat of collusion.
This means that if the expected reputation effect is large enough this makes it unprofitable for M to bribe B.
28

5.2
Monitoring decision of the board under collusion
B has to offer a contract Κ to M such that S does not veto it. The veto is a way for S to deter collusion if profitable. I will return to this issue in proposition 5.2, because I first need to find the conditions under which M and B will collude. Given these conditions I can show which contracts S will veto. I will proceed given the optimal Κ as given in lemma 4.8. Having established this, I focus on the decision of B to monitor first.
Lemma 5.4
Consider an equilibrium, then B will always choose 𝑒
𝐵
= 1 under the optimal contract as defined in proposition 4.2
Proof: First, note that B prefers to be bribed if possible, because it makes him just better off by 𝜃 . However, if B is indifferent between 𝑒
𝐵
= 0 and 𝑒
𝐵
= 1 it will choose 𝑒
𝐵
= 1 by assumption. Given the optimal contract in proposition 4.2, B anticipates whether M is able to bribe. If M can effectively bribe B, as shown in lemma 5.3, it can still be optimal for B to monitor as this leads to 𝑒
𝑀
= 𝜋𝜂 or 𝑒
𝑀
= 1 instead of 𝑒
𝑀
= 0 if 𝑒
𝐵
= 0 . From lemma 5.3 it follows that if 𝜋𝜂 < 1 , M will exert 𝑒
𝑀
= 𝜋𝜂 if 𝑒
𝐵
= 1 . If B then chooses to monitor it can either stick to the contract with S or otherwise M will offer a side-contract that makes B better off by 𝜃 . If M does not offer a side-contract that makes B better off then B will not accept it. By monitoring B can thus never by worse off. Then if 𝜋𝜂 < 1 B chooses 𝑒
𝐵
= 1 .
If 𝜋𝜂 ≥ 1 it follows from lemma 5.3 that M is not able to bribe B and will choose 𝑒
𝑀
= 0 if 𝑒
𝐵
= 1 and 𝑒
𝑀
= 1 if 𝑒
𝐵
= 1 . This means it is strictly better for B to choose 𝑒
𝐵
= 1 , because 𝑒
𝐵
= 0 would lead to positive expected reputation damage 

Lemma 5.4 thus shows that B will always monitor under the optimal contract, even under the threat of collusion. This is because if the potential reputation damage is low
( 𝜋𝜂 < 1) , then B may find it profitable to collude with M but is indifferent between monitoring or not. By assumption B will then monitor and M will optimally exert 𝑒 ∗
𝑀
= 𝜋𝜂 . If the potential reputation damage is high (𝜋𝜂 ≥ 1) the required bribe is too high for M and he is better off adhering to the optimal contract.
Proposition 5.1
29

M and B will collude given Κ {𝛼 𝑙
𝑀
< 0 & 𝛼 ℎ
𝑀
= 0,
1
2
, δ h
+ 1} if and only if 𝜋𝜂 < 1
Proof: Lemma 5.4 shows that under the optimal contract B will always monitor. From lemma 5.3 we know that if 𝜋𝜂 ≥ 1 then 𝑒 ∗
𝑀
= 1 . This means that both M and B adhere to the optimal contracts and do not collude. If 𝜋𝜂 < 1 then lemma 5.4 shows that 𝑒
𝐵
= 1 and lemma 5.3 shows that then 𝑒 ∗
𝑀
= 𝜋𝜂 . M will then bribe B if
1
2
+
1
2
(𝜋𝜂) 2 − 𝜋𝜂 > 0 , which always holds for 0 < 𝜋𝜂 < 1 . This means that if 𝜋𝜂 < 1 B and M will collude if Κ {𝛼 𝑙
𝑀
< 0 & 𝛼 ℎ
𝑀
= 0,
1
2
, δ h
+ 1} 
5.3
Collusion proof optimal contracts
Now that I have established the situations in which B and M find it profitable to collude under the optimal contract I can check how S can prevent collusion. Fraure-
Grimaud, et al. (2003) define the collusion-proofness principle which states that there is no loss of generality in restricting the analysis to collusion-proof contracts in which the optimal side-contract entails no manipulation of reports and zero side-transfers.
Therefore, I can restrict the analysis to solving the collusion as defined in proposition
5.1.
Proposition 5.2
To efficiently deter collusion and realise 𝐸[𝑈
𝑆
∗ |𝜒, 𝜋𝜂 < 1} it is sufficient for S to vote against any
Κ ≠ Κ {𝛼 𝑙
𝑀
< 0 & 𝛼 ℎ
𝑀
= 0,
1
2
(𝜋𝜂) 2 , δ h
+ 𝜋𝜂}
Proof: It follows directly from proposition 5.1 that the optimal contract does not need adaptation if 𝜋𝜂 ≥ 1 as there will be no collusion in this case. If 𝜋𝜂 < 1 there will be collusion since M’s wage is high enough to offset B’s potential reputation damage and M can then pay an effective bribe. To deter collusion S must then lower M’s wage to a level where he cannot pay an effective bribe. Taking into account that B chooses 𝑒
𝐵
= 1 and then 𝑒 ∗
𝑀
= 𝜋𝜂 this leads to 𝑤
𝑀
−
1
2 𝑒 2
𝑀
= 0 if the required level of 𝑒
𝑀
= 𝜋𝜂 . This is because for M to exert effort it must be that 𝛽
𝑀
≥
1
2 𝑒 2
𝑀
. With 𝑒 ∗
𝑀
= 𝜋𝜂 this means 𝛽
𝑀
≥
1
2
(𝜋𝜂) 2 . Then the optimal bonus 𝛽
𝑀
=
1
2
(𝜋𝜂) 2 . A higher level
30

will not increase effort and a lower level means 𝑒
𝑀
= 0 , which is not optimal for S since now MB( 𝑒
𝑀
) = 𝜋𝜂 and MC( 𝑒
𝑀
) = 𝜋𝜂 . This means that S needs to veto any any
Κ ≠ Κ {𝛼 𝑙
𝑀
< 0 & 𝛼 ℎ
𝑀
= 0,
1
2
, δ h
+ 𝜋𝜂} to realise 𝐸[𝑈
𝑆
∗ |𝜒, 𝜋𝜂 < 1} 

Proposition 5.2 shows that S can always deter collusion by lowering the required firm value contribution of M. Since this departs from the optimal firm value, it leads to a lower level of utility for S. I thus show here that collusion happens if the potential reputation damage of B is low resulting in a decrease of realised firm value.
Proposition 5.3
The equilibrium outcome of the game under the threat of collusion is:
 If 𝜋𝜂 ≥ 1 or 𝑐 >
1
2 𝜋𝜂δ h
+ 𝜋𝜂(1 − 𝜆) o Given by proposition 4.2
 If 𝜋𝜂 < 1 o And if : 𝑐 ≤
1
2 𝜋𝜂δ h
:
 𝜒 {𝑐, 0,0}, Κ {𝛼 𝑙
𝑀
< 0, 𝛼 ℎ
𝑀
= 0,
1
2
(𝜋𝜂) 2 , δ h
+ 𝜋𝜂}
 𝐸[𝑈
𝑆
] = 𝛿 ℎ
+ 𝜋𝜂 −
1
2
(𝜋𝜂) 2 − 𝑐 o And if:
1
2 𝜋𝜂δ h
< 𝑐 ≤
1
2 𝜋𝜂δ h
+ 𝜋𝜂(1 − 𝜆)
 𝜒 {
1
2 𝜋𝜂δ h
, 𝑐 −
1
2 𝜋𝜂δ h
, δ h
+ 𝜋𝜂 − 𝜆 },
Κ {𝛼 𝑙
𝑀
< 0, 𝛼 ℎ
𝑀
= 0,
1
2
(𝜋𝜂) 2 , δ h
+ 𝜋𝜂}
 𝐸[𝑈
𝑆
] = 𝛿 ℎ
+ 𝜋𝜂 −
1
2
(𝜋𝜂) 2 − 𝑐
Proof: As proposition 5.2 shows there is no collusion if 𝜋𝜂 ≥ 1 or 𝑐 >
1
2 𝜋𝜂δ h
+ 𝜋𝜂𝜆 .
Therefore, under these conditions the optimal contracts in proposition 4.2 do not change. If 𝜋𝜂 < 1 , it follows from proposition 5.2 that S vetoes any inefficient contract and from lemma 4.8 we know that B will set the contract of M accordingly.
B will monitor as shown in lemma 5.4 and can thus deter the low ability M. This means that M’s contract will be given by Κ {𝛼 𝑙
𝑀
< 0, 𝛼 ℎ
𝑀
= 0,
1
2
(𝜋𝜂) 2 , δ h
+ 𝜋𝜂} both if: 𝑐 ≤
1
2 𝜋𝜂δ h
and if :
1
2 𝜋𝜂δ h
< 𝑐 ≤
1
2 𝜋𝜂δ h
+ 𝜋𝜂𝜆 . Then 𝐸[𝑈
𝑆
] = 𝛿 ℎ
+ 𝜋𝜂 −
31

1
2
(𝜋𝜂) 2 − 𝑐 in both cases. Since 𝜋𝜂 < 1 it follows that 𝜋𝜂 >
1
2
(𝜋𝜂) 2 and it is thus always better for S to induce effort.
The contract 𝜒 needs to change only if
1
2 𝜋𝜂δ h
< 𝑐 ≤
1
2 𝜋𝜂δ h
+ 𝜋𝜂(1 − 𝜆) , since from lemma 4.3 and 4.9 it follow that if 𝛽
𝐵
> 0 it must be that ℛ̅ < ℛ̃ . It follows that ℛ̅ = δ h
+ 𝜋𝜂 − 𝜆 is optimal 
As I show in proposition 5.3, the optimal contracts under the threat of collusion are similar to the optimal contracts without collusion. The main difference is that the utility of S decreases under the threat of collusion if the reputation effect is low. How much 𝐸[𝑈
𝑆
] decreases depends on how big 1 𝜋𝜂 is. For both M and B there is no change in final utility levels as S is still able to extract all the rents. The latter is a result of the assumption that S has full bargaining power in contracting with B.
It is also clear from the propositions above that whether collusion will occur does not depend on the compensation of B. Whether B receives a bonus or not does not influence the probability that B and M will collude. Whether we might observe collusion does depend on the expected impact of reputation damage. In equilibrium however collusion will never occur because S deters collusion by lowering M’s required contribution to firm value by using her veto power on Κ .
6.
Discussion of results and limitations
Here I will discuss the main findings of the analysis in section 4 and section 5 and relate them to the different findings in the organisational economics and corporate finance literature. I will also discuss a couple of limitations to the results that provide interesting ground for further development of the model. I will provide a discussion of the results first and second a discussion of the limitations.
6.1
Discussion of the results
In this thesis I analyse whether and how busy boards with reputation concern are effective monitors. I focus specifically on the optimal contract to induce effective monitoring. My model provides evidence in line with the optimal contracting approach. The results show that director bonus pay is optimal if the monitoring cost is too high for fixed pay to be effective, but low enough to induce effective monitoring with a bonus. My results also show that fixed pay can be optimal given low monitoring cost and given that paying a bonus to the director increases the cost of
32

contracting for the shareholders. The latter makes it optimal for the shareholders to choose fixed pay if indifferent between fixed and bonus pay. The results also show that efficient monitoring is impossible if the monitoring cost is too high. In general, my results thus provide evidence that the busier directors (the higher cost of monitoring) the weaker corporate governance, in line with Fich and Shivdasani
(2006). My model also provides a potential explanation for the differences found between countries by Hahn and Lasfer (2010). If levels of monitoring cost and reputation damage are different between countries this may result in different optimal contracts between continents, countries or even firms.
The main debate in the corporate finance literature is on whether bonus pay is necessary to make sure directors spent sufficient time and effort (e.g. Shen (2005)) on monitoring or that bonus pay leads to collusion. My results do not provide evidence that collusion is more likely with bonus pay. The results do show that if the expected reputation damage is low, the possibility of collusion leads to lower CEO effort and thus lower than optimal firm value. Similar to Thiele (2013), I find that lowering manager incentives can deter collusion, but this comes at the cost of lower firm value compared to the situation without collusion. My results also show similarity with
Giebe and Gürtler (2012) in that I also show that under certain conditions (in my model low monitoring cost) it is optimal to pay the board of directors a fixed wage independent of the agent’s effort.
The optimal value of CEO contribution to firm value can be realised both under fixed and variable pay. This shows that we cannot evaluate efficiency based on the form of director compensation only. Important factors in determining monitoring efficiency are the monitoring costs versus the expected reputation damage. It is thus questionable whether board members as independent as possible are the most effective monitors. Following the results of my model, board members are more likely to monitor if they incur a negative utility when their report differs from actual
CEO contribution to firm value. The impact of the reputation effect consists of both the severity of damage of false reporting (𝜂) and the probability ( 𝜋) that the true value of manager contribution to firm value (Φ) is observed. If either of the two increases, this also increases the probability that the board will monitor. The last factor of influence is the difference in ability of managers ( 𝛿 ℎ
) . If this difference increases, the benefit of monitoring increases. This is because the potential reputation
33

damage is dependent on the difference between the report and the true value of CEO contribution to firm value. If the board does not monitor, it does not observe the ability of the manager and cannot screen out low ability managers. Once the difference between high and low ability managers becomes larger, this also has a larger influence on the potential reputation damage. This shows that directors may thus actually be more effective monitors, if their utility is dependent on realised CEO contribution to firm value. However, it is possible to derive an argument from the model to favour independent boards. I show that if a bonus is awarded to the director and the required level of manager contribution to receive this bonus is higher than the required level for the CEO to receive his bonus, then the director bonus is ineffective in incentivising the board to monitor. This effect is created by the fact that the CEO can reduce his effort while making sure that the board is just better off reporting its required amount irrespective of the true CEO contribution. As the board’s required amount is at least as high as the CEO’s, this is also enough for the CEO to receive his bonus. Although in my model this is an out of equilibrium situation, if observed in reality it could be support for the managerial power approach. If the CEO’s influence is so high that he can basically set his own required contribution to firm value, this could lead to a situation where he does just enough to ensure a positive board report.
That would mean he exerts less than optimal effort.
Bertrand and Mullaiathan (2001) and Bebchuk et al. (2010) find that CEO and director compensation are related to luck more than providing incentives to overcome the agency problem. My results show this could be the situation where the monitoring cost is too high to induce effective monitoring. In this case the board receives a positive wage independent of firm performance while the manager adds no value through productive effort. The model also provides evidence that the board can still be an effective monitor if chosen by the CEO. When monitoring costs are low enough compared to the potential reputation damage of false reporting, the board will prefer monitoring and possibly truthful reporting. This could then also provide evidence for the hypothesis that even board members chosen by management could still be effective monitors, as argued by Hermalin and Weisbach (1998).
Another issue, that is especially part of a hot debate in public, is whether the level of director pay is too high or not, irrespective of the form of compensation. The level of director wages is largely dependent on the cost of monitoring that needs to be overcome by the wage payment. High wages may thus be considered as efficient if
34

the cost of monitoring for board members is high. There seems to be ground to assume high monitoring cost since members of the board of directors usually have multiple different positions. This raises their opportunity cost of monitoring at the firm concerned, requiring higher wage payments. On the other hand, the model also suggests that there is a natural cap on director wages provided by this same cost of effort. Once the cost of monitoring is too high, inducing monitoring becomes impossible and the wage payment decreases.
Part of the research on boards in the corporate finance literature is about the size of boards as an important factor in determining effective monitoring. My result that the cost of monitoring is crucial in determining effective monitoring may affect the optimal size of boards. The optimal size of boards would then depend on how the monitoring decision is made in practice. If the board member with the lowest monitoring cost determines the monitoring decision, this could be ground for having a large board. That is because in a large board the probability of having at least one board member with low enough monitoring cost is higher. The issue with this reasoning is that the free-rider problem may cause board members to rely on other board members to exert monitoring effort. Then it could also be that average cost of monitoring of the board determines the monitoring decision, which would not provide grounds for a certain board size a-priori.
Following from my results on collusion as well as efficient monitoring, there seems to be a more effective opportunity than the form of contracts and manager compensation to deter collusion and increase the chances of efficient monitoring from a regulatory perspective. This opportunity concerns the reputation damage incurred by a director when engaging in favourable reporting. The reputation damage consists of the severity of damage and the probability that the true value of effort and ability is discovered publicly. From an institutional point of view there may be opportunity to increase the severity of damage and/or increase the probability of the information becoming public. Increasing punishment on director collusion and false reporting could increase reputation damage, if incurred. Oftentimes the monitoring bodies
(boards of directors) of firms are not legally held accountable for mismanagement or bad monitoring of corporations. Increasing the accountability and more severe punishment of wrongdoings may increase the reputation damage and decrease the likeliness of collusion. The other option is increasing the probability that information on the true efforts of directors becomes public. An example here might be increasing
35

the transparency of reporting by (the boards of) firms to include more on the contribution of the CEO to firm value in a way to justify their payment. Increasing the transparency of management contributions in any way could contribute to decreasing opportunities for collusion.
6.2
Discussion of the limitations
An additional important reason for observing bonuses in reality may be that they provide a way to link the current effort to future performance. A lot of the work of directors will not just impact the current period, but also future periods. Bonuses tied to future firm results may be a way to incentivise the board to monitor effectively.
This effect is not taken into account in the model. Extending the model to include multiple periods and incorporating this effect may provide further interesting insight in the use of bonuses. This would be in line with Barton and Wiseman (2015)’s conclusion that we need to tie director compensation more to long-term firm results to induce effective monitoring.
Considering the assumptions of the model, a point of interest is the verifiability of the report made by the board. The result that the shareholders cannot provide better incentives to the board to induce honest reporting under high cost of monitoring depends on the assumption that the report is cheap talk and cannot be verified in any way before wage payments are made. One interesting expansion would be to look at the situation where the shareholder can make the report more verifiable. This could provide rationale for paying a bonus to the board. Another interesting expansion would be the situation where the wage of the director could be made contingent on the signal. In practice this could resemble long-term options or bonus payments contingent on firm results a couple of periods ahead as discussed above.
The results also depend largely on the cost of monitoring. I make the assumption that the shareholders know this cost. In reality the shareholders may be less well informed and only know the distribution of the monitoring cost. It could be interesting to incorporate this in the model. Intuitively however, this should not matter too much for the results. The shareholder will choose to offer the optimal contract if the expected value of monitoring cost is low enough. My results should thus be quite robust to unknown cost of monitoring. The more important assumption may be that the shareholder knows the cost of effort of the manager. This effectively means that the shareholder knows what the efficient contract for the CEO is and leaves the board no
36

opportunity but offering the optimal contract, because the shareholders veto any other contract offered to M. If instead the effort cost of the manager is unknown, the shareholder would not know the optimal contract and this could provide more room for collusion between the board and the manager as the power of the veto decreases.
Another element of importance is the reputation concern of the board. In my model the potential reputation damage is dependent on the difference between the report and the true value of manager ability and effort, the probability that the true value is observed and the incurred damage if it is observed. Another element that may influence the reputation damage could be the director’s wage. A higher wage might result in higher expectations of director abilities and monitoring effort. The reputation damage incurred if reporting favourably might then be greater if the wage of the board is higher. In the equilibrium of the model this should not have an effect as the board reports truthfully in equilibrium. However, under the threat of collusion higher wages for the board may decrease the probability of collusion. This is because by increasing the wage the potential reputation damage would increase making collusion less profitable. In this scenario higher director wages could be a way to deter collusion between the board and the CEO.
Finally, in the model there is no link between the monitoring cost and the severity of reputation damage of the board. In reality it might be that busyness of a director is related to severity of reputation damage. A director with more board positions will have a higher cost of monitoring. However, once a director has more monitoring jobs the severity of reputation damage may be higher since there is more at stake for this director. In this way a higher cost of monitoring might be sustainable, because directors with a higher cost of monitoring also have higher reputation damage.
7.
Conclusion and recommendations
I find evidence in line with the optimal contracting approach that bonus pay is optimal for certain values of monitoring cost. I also show that the cost of monitoring as well as the reputation concern of the board of directors are important elements in providing explanations and recommendations on the effectiveness of the board of directors and cannot be ignored when determining optimal contracts and evaluating board effectiveness.
37

I find that monitoring by the board is more likely once cost of monitoring is low relative to the impact of reputation damage. In equilibrium the shareholder can deter collusion, but this comes at the cost of lower than optimal firm value if the expected board reputation damage is low. This is because with low expected reputation damage the shareholder needs to lower CEO incentives, necessarily leading to lower than optimal firm value. However, if the expected reputation damage is high enough, the optimal contracts without collusion are still effective. Furthermore, if monitoring costs are too high the board will never monitor which is costly for the shareholder.
Too high cost of monitoring for a certain firm or country may thus destroy firm value.
The model used in this thesis provides several interesting insights supporting the ongoing discussion in public and the literature on the compensation of the board of directors. Further development of the model may aid the discussion especially in providing theoretical foundations for the sometimes seemingly contradictory findings in the literature. Different findings on the effectiveness of directors (compensation) might be influenced by the cost of monitoring relative to the potential reputation damage for different boards, continents or countries. Further research should take these differences into account to come up with a more coherent model on board of director monitoring and compensation. Several interesting expansions of the model could be made in future research. First, one could look at the effect of making reputation effects dependent on the wages of the board and the busyness of the director. Second, it could be interesting to make the cost of monitoring and effort cost of the CEO unknown to the shareholder and analyse the effect on contracts and collusion. Finally, it would be interesting to expand the model with long term payments to the board, made dependent on the true values of manager effort and ability if these are observed over a longer time horizon.
38

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