The principal in this game faces the following credibility problem with respect to her verification strategy. Suppose that the monetary incentive scheme and a pre-announced verification strategy induce the agent to act in her interests. As verification is costly, the principal can save costs if she does not stick to her announcement to verify. This, of course, will be foreseen by the agent and the principal’s pre-announced verification strategy will not be credible ex-post. As a consequence, the optimal contracting under commitment is not optimal under non commitment. The principal’s inability to commit to her verification strategy then introduces an additional moral hazard problem on the part of the principal. I capture this issue by requiring sequential rationality by the principal with respect to her verification strategy. (1) The principal chooses her verification effort to minimize her expected costs, given the agent’s mixed strategy. (2) The agent decides on his mixed strategy, given the principal chooses her verification effort by (1).
5.1 Auditing under non commitment
Consider first the case in which the principal chooses an auditing strategy to implement high effort,
e = 1. Then at stage 4 of the game, given an outcome
xi is realized, her belief about the agent’s behavior is
μi = 1, and she chooses an effort level
vi to minimize expected costs
$$ p\left( v_{i}\right) s_{iH}+(1-p\left( v_{i}\right) )s_{iL}+cv_{i}, $$
with
vi ≥ 0. Optimally, the principal then chooses
\(v_{i}^{\ast }\) such that
$$ p^{\prime }\left( v_{i}\right) \left( s_{iH}-s_{iL}\right) +c\leq 0. $$
This condition describes the principal’s incentive constraint for auditing in outcome
xi. An immediate consequence from this condition is that, if auditing takes place, the agent’s payment in case the signal indicates a normal level of effort has to be higher than for a high effort level; that is,
siL >
siH. That is, she pays the agent more, if the audit contracts her initial belief. The interpretation of this condition is that the principal rewards the agent for his bad luck: although he implemented effort
e = 1, verification showed a normal effort level. But this can only be possible because of the imprecision of the signal and the corresponding error in judgement. It is for this reason that the principal has to reward the agent, even if auditing indicates that he chose
e = 0, given she wants the agent to choose high effort.
As a consequence, the principal cannot incentivize the agent to choose the high level of effort with certainty if auditing is not binding.
14 Besides the possibility to offer the optimal contract without auditing (see Proposition 1), the principal then has to give up her desire to implement
e = 1 with certainty. In this case, she incentivizes the agent to choose some mixed strategy over choosing high or normal effort, such that her overall profit is higher under auditing than in the case without verification. To analyze this possibility, let
\(\alpha \in \left (0,1\right )\) be the probability that the agent chooses
e = 1. At stage 4 of the game, the principal forms a belief
μi about the agent’s behavior after observing an outcome
xi and then chooses an auditing effort
vi ≥ 0 to minimize expected costs. Updating her a priori probability
α according to Bayes’ rule implies that the probability that the agent chooses high effort is given by
$$ \mu_{i}=\frac{\alpha \pi_{i}(1)}{\alpha \pi_{i}(1)+\left( 1-\alpha \right) \pi_{i}(0)}=\frac{\alpha }{\alpha +\left( 1-\alpha \right) \delta_{i}}. $$
The principal’s expected costs then are given by
$$ \begin{array}{@{}rcl@{}} &&\mu_{i}\left( p\left( v_{i}\right) s_{iH}+(1-p\left( v_{i}\right) )s_{iL}\right) +\left( 1-\mu_{i}\right) \left( p\left( v_{i}\right) s_{iL}+(1-p\left( v_{i}\right) )s_{iH}\right) +cv_{i} \\ &&\qquad =\mu_{i}s_{iL}+\left( 1-\mu_{i}\right) s_{iH}+p\left( v_{i}\right) \left( 2\mu_{i}-1\right) \left( s_{iH}-s_{iL}\right) +cv_{i}. \end{array} $$
Optimally, the principal chooses
\(v_{i}^{\ast \ast }\) such that the derivative of her expected costs is non-positive,
$$ p^{\prime }\left( v_{i}\right) \left( s_{iH}-s_{iL}\right) \left( 2\mu_{i}-1\right) +c\leq 0. $$
Suppose that auditing takes place,
vi > 0. Then
$$ p^{\prime }\left( v_{i}\right) =\frac{c}{2\left( s_{iH}-s_{iL}\right) \left( \frac{1}{2}-\mu_{i}\right) }. $$
Hence, if
\(\mu _{i}>\frac {1}{2}\) and it is more likely that the agent chose the high level of effort, the principal has to offer a higher reward if the signal indicates
e = 0 than if the signal indicates
e = 1,
siL >
siH.
15 If
\(\mu _{i}<\frac {1}{ 2},\) it is more likely that he did not choose the high level of effort, and she offers a higher reward if the signal indicates high instead of normal effort,
siH >
siL. In both cases, the agent’s reward then is higher if the audit contradicts her belief about his behavior. Note also that, by choosing his probability
α, the agent influences the principal’s optimal auditing effort
vi via her updated belief
μi. In particular,
μi \(\gtrless \frac {1}{2}\) is identical to
$$ \alpha \gtrless \frac{\delta_{i}}{\left( 1+\delta_{i}\right) }=\frac{\pi_{i}(0)}{\pi_{i}(1)+\pi_{i}(0)}; $$
that is, the principal only believes that the agent chooses the high level of effort if his actual probability of choosing
e = 1 is lower than the conditional probability for this event, and vice versa.
Given the optimal auditing strategy
\(\left (v_{1}^{\ast \ast },...,v_{n}^{\ast \ast }\right )\) at Stage 2, the agent chooses a probability
\(\alpha \in \left (0,1\right )\) to maximize his expected utility. Indifference requires that his expected utility is identical when he chooses the high or the normal level of effort:
$$ \begin{array}{@{}rcl@{}} &{{\sum}_{i=1}^{n}}\pi_{i}(1)\left( p\left( v_{i}^{\ast \ast }\right) s_{iH}+(1-p\left( v_{i}^{\ast \ast }\right) )s_{iL}\right) -c_{H} \\ &={{\sum}_{i=1}^{n}}\pi_{i}(0)\left( p\left( v_{i}^{\ast \ast }\right) s_{iL}+(1-p\left( v_{i}^{\ast \ast }\right) )s_{iH}\right) \end{array} $$
Since the principal’s optimal auditing strategy in Stage 4 depends on his behavior, he then chooses
α such that
$$ {\sum\limits_{i=1}^{n}}\pi_{i}(1)\left( p^{\prime }\left( v_{i}^{\ast \ast }\right) \frac{\partial v_{i}^{\ast \ast }}{\partial \alpha }\left( s_{iH}-s_{iL}\right) \left( \alpha -\left( 1-\alpha \right) {\delta }_{i}\right) \right) =0. $$
At Stage 1, the principal then offers a monetary incentive scheme to maximize her expected net profits, given the agent’s indifference and her sequential rationality constraint with respect to her auditing efforts. The optimal solution
\(\left (s_{1L}^{\ast \ast },s_{1H}^{\ast \ast },....,s_{nL}^{\ast \ast },s_{nH}^{\ast \ast }\right )\) then maximizes the following problem (
P4):
$$ \begin{array}{@{}rcl@{}} &&\alpha \left( {\sum\limits_{i=1}^{n}}\pi_{i}(1)\left( x_{i}-p\left( v_{i}^{\ast \ast }\right) s_{iH}-(1-p\left( v_{i}^{\ast \ast }\right) )s_{iL}-cv_{i}^{\ast \ast }\right) \right) {\kern67.5pt}(\text{P4}) \\ &&+\left( 1-\alpha \right) \left( {\sum\limits_{i=1}^{n}}\pi_{i}(0)\left( x_{i}-p\left( v_{i}^{\ast \ast }\right) s_{iL}-(1-p\left( v_{i}^{\ast \ast }\right) )s_{iH}-cv_{i}^{\ast \ast }\right) \right) \text{ such that} \\ &&{\sum\limits_{i=1}^{n}}\pi_{i}(1)p\left( v_{i}^{\ast \ast }\right) \left( \left( \left( 1-\delta_{i}\frac{1-p\left( v_{i}^{\ast \ast }\right) }{ p\left( v_{i}^{\ast \ast }\right) }\right) s_{iH}\right) \right. \\ &&\left. +\left( \frac{1-p\left( v_{i}^{\ast \ast }\right) }{ p\left( v_{i}^{\ast \ast }\right) }-\delta_{i}\right) s_{iL}\right) =c_{H} {\kern156.5pt}(\text{ICA4a})\\ &&{\sum\limits_{i=1}^{n}}\pi_{i}(1)\left( p^{\prime }\left( v_{i}^{\ast \ast }\right) \frac{\partial v_{i}^{\ast \ast }}{\partial \alpha }\left( s_{iH}-s_{iL}\right) \right) \left( \alpha -\left( 1-\alpha \right) {\delta } _{i}\right) =0 {\kern55.5pt}(\text{ICA4b}) \\ &&p^{\prime }\left( v_{i}^{\ast \ast }\right) \left( s_{iH}-s_{iL}\right) \left( \frac{\alpha -\left( 1-\alpha \right) \delta_{i} }{\alpha +\left( 1-\alpha \right) \delta_{i}}\right) +c\leq 0. {\kern109pt}(\text{ICP4}) \end{array} $$
Several remarks are worth making. First, it is the agent who indirectly bears the cost of verification in both outcomes. In fact, if no verification would take place in outcome
xi,
i =
k − 1,
k, the agent can expect a reward equal to
$$ \frac{1}{2}\pi_{i}(1)\left( s_{iH}^{\ast \ast }+s_{iL}^{\ast \ast }\right) \left( \alpha^{\ast \ast }+\left( 1-\alpha^{\ast \ast }\right) \delta_{i}\right) . $$
But if auditing occurs,
\(v_{i}^{\ast \ast }>0,\) his expected reward is
$$ \begin{array}{@{}rcl@{}} &&\alpha^{\ast \ast }\pi_{i}(1)\left( p\left( v_{i}^{\ast \ast }\right) s_{iH}^{\ast \ast }+(1-p\left( v_{i}^{\ast \ast }\right) )s_{iL}^{\ast \ast }\right) \\ &&\quad +\left( 1-\alpha^{\ast \ast }\right) \pi_{i}(0)\left( p\left( v_{i}^{\ast \ast }\right) s_{iL}^{\ast \ast }+(1-p\left( v_{i}^{\ast \ast }\right) )s_{iH}^{\ast \ast }\right) \\ &=&\frac{1}{2}\pi_{i}(1)\left( s_{iH}^{\ast \ast }+s_{iL}^{\ast \ast }\right) \left( \alpha^{\ast \ast }+\left( 1-\alpha^{\ast \ast }\right) \delta_{i}\right) \\ &&\quad +\pi_{i}(1)\left( \alpha^{\ast \ast }-\left( 1-\alpha^{\ast \ast }\right) \delta_{i}\right) \left( \left( p\left( v_{i}^{\ast \ast }\right) - \frac{1}{2}\right) \left( s_{iH}^{\ast \ast }-s_{iL}^{\ast \ast }\right) \right) . \end{array} $$
For \(s_{k-1L}^{\ast \ast }>s_{k-1H}^{\ast \ast }=0\) in case \(\mu _{i}>\frac {1 }{2}\), the second term is negative as \(\left (\alpha ^{\ast \ast }-\left (1-\alpha ^{\ast \ast }\right ) \delta _{k-1}\right ) >0\). And for \( s_{kH}^{\ast \ast }>s_{kL}^{\ast \ast }=0\) in case \(\mu _{i}<\frac {1}{2},\) this second term is also negative as \(\left (\alpha ^{\ast \ast }-\left (1-\alpha ^{\ast \ast }\right ) \delta _{k}\right ) <0\). Hence, by getting a lower reward in case of auditing, the agent indirectly pays for the verification of his behavior.
Second, it is necessary for the principal to set incentives such that she verifies the agent’s behavior in two outcomes and not only in one. To see this, note that
$$ \frac{\partial v_{i}^{\ast \ast }}{\partial \mu_{i}}=\frac{p^{\prime }\left( v_{i}^{\ast \ast }\right) }{p^{\prime \prime }\left( v_{i}^{\ast \ast }\right) \left( \frac{1}{2}-\mu_{i}\right) }. $$
Hence the principal’s auditing effort decreases in
α if she believes he did not choose the high level of effort, and vice versa. That is,
16$$ \frac{\partial v_{i}^{\ast \ast }}{\partial \alpha }<0\text{ for }\mu_{i}< \frac{1}{2}\text{ and }\frac{\partial v_{i}^{\ast \ast }}{\partial \alpha }>0 \text{ for }\mu_{i}>\frac{1}{2}. $$
In particular, for
\(\mu _{i}=\frac {1}{2}\), the principal’s expected costs in outcome
xi are
\(\frac {1}{2}\left (s_{iH}^{\ast \ast }+s_{iL}^{\ast \ast }+2cv_{i}^{\ast \ast }\right )\), and she would decide not to audit. Now suppose the principal would set positive rewards in only one outcome
xi. Then the agent would set his optimal effort choice such that
\(\alpha ^{\ast \ast }=\delta _{i}/\left (1+\delta _{i}\right )\), implying no verification and hence a higher expected wage; see our first remark above. But this cannot be optimal for the principal since the optimal contract without verification pays for the highest outcome level and implements
e = 1 with certainty. To avoid this behavior of the agent, the principal therefore has to offer monetary incentives for two outcomes such that her auditing efforts are credible in both. In fact, if there exist two outcomes in which the principal has an incentive to audit, the agent never chooses a probability
α such that no auditing will take place in one of these outcomes. This is because the principal’s auditing behavior in the other outcome then leads to the highest loss in expected payment. To see this formally, note that the agent chooses his optimal
α∗∗ such that his marginal utility is zero:
$$ \begin{array}{@{}rcl@{}} &&\pi_{k-1}(1)p^{\prime }\left( v_{k-1}^{\ast \ast }\right) \frac{\partial v_{k-1}^{\ast \ast }}{\partial \alpha }\left( \alpha -\left( 1-\alpha \right) {\delta }_{k-1}\right) s_{k-1H}^{\ast \ast } \\ &&\qquad =\pi_{k}(1)p^{\prime }\left( v_{k}^{\ast \ast }\right) \frac{ \partial v_{k}^{\ast \ast }}{\partial \alpha }\left( \alpha -\left( 1-\alpha \right) {\delta }_{k}\right) s_{kL}^{\ast \ast }. \end{array} $$
Since
\(\partial v_{k-1}^{\ast \ast }/\partial \alpha <0\) and
\(\partial v_{k}^{\ast \ast }/\partial \alpha >0\) it follows that
$$ \frac{\delta_{k}}{\left( 1+\delta_{k}\right) }<\alpha^{\ast \ast }<\frac{ \delta_{k-1}}{\left( 1+\delta_{k-1}\right) }. $$
Third, under auditing, the principal’s auditing efforts and the monetary payments are now complements in both outcomes:
$$ \frac{\partial s_{k-1H}^{\ast \ast }}{\partial v_{k-1}^{\ast \ast }}>0\text{ and }\frac{\partial s_{kL}^{\ast \ast }}{\partial v_{k}^{\ast \ast }}>0, $$
since
\(p^{\prime \prime }\left (v\right ) <0\). That is, if the principal wants to increase her auditing effort, she necessarily has to pay the agent a higher wage in the lower and in the higher outcome. This observation results directly from the principal’s incentive constraint (
ICP$) for the outcome levels
xk− 1 and
xk. The intuition is as follows. According to our first remark, the agent has to bear the principal’s verification costs to make auditing credible. But this implies that the principal has to compensate the agent with a higher payment if she increases her auditing effort. According to our second remark, she rewards the agent in a high outcome level where she believes the agent only chooses normal effort, and in a low outcome level where she believes he chooses high effort and the audit contradicts her belief. But this implies the agent’s payment and her auditing effort in both outcome levels are complements. Note that this property differs from our finding in the case of commitment. There an increase in the principal’s auditing effort implied a lower payment to the agent, so that both variables were substitutes under commitment. Of course, auditing under non commitment is still beneficial for the principal because the agent’s expected reward is lower whenever auditing occurs.
17
And fourth, when contrasting Proposition 4 to Proposition 1, the agent’s optimal monetary incentive payment scheme is now less extreme. In the non-verification setting, the agent only receives a bonus if the maximal outcome level occurs. In the non commitment setting the agent now gets paid in two subsequent outcome levels in which auditing takes place. But this necessarily implies that these payments are less extreme than the bonus in the non-verification setting, similar to the case of a risk-averse agent (e.g., Baiman and Demski
1980 or Dye
1986).
5.2 Monitoring under non commitment
Consider now the case in which the principal uses monitoring as a verification procedure to verify the agent’s behavior. At Stage 2 of the model, the principal then chooses her monitoring effort simultaneously with the agent’s choice of an effort level. Given
\(\alpha \in \left [ 0,1\right ] ,\) effort
v then minimizes her expected costs
$$ \begin{array}{@{}rcl@{}} &&\alpha \left( \sum\limits_{i=1}^{n}\pi_{i}\left( 1\right) \left( p\left( v\right) s_{iH}+(1-p\left( v\right) )s_{iL}\right) \right) \\ &&+\left( 1-\alpha \right) \left( \sum\limits_{i=1}^{n}\pi_{i}\left( 0\right) \left( p\left( v\right) s_{iL}+(1-p\left( v\right) )s_{iH}\right) \right) +cv, \end{array} $$
with
v ≥ 0. Optimally, the principal then chooses
v∗∗ such that
$$ p^{\prime }\left( v\right) \sum\limits_{i=1}^{n}\pi_{i}\left( 1\right) \left( s_{iH}-s_{iL}\right) \left( \alpha -\left( 1-\alpha \right) \delta_{i}\right) +c\leq 0. $$
Simultaneously, given
v ≥ 0, the agent chooses the probability
\(\alpha \in \left [ 0,1\right ] \) to maximize his expected utility. Indifference requires that his expected utility is identical when he chooses the high or the normal level of effort,
$$ {\sum\limits_{i=1}^{n}}\pi_{i}(1)\left( p\left( v\right) s_{iH}+(1 - p\left( v\right) )s_{iL}\right) -c_{H} = {\sum\limits_{i=1}^{n}}\pi_{i}(0)\left( p\left( v\right) s_{iL}+(1 - p\left( v\right) )s_{iH}\right) . $$
At Stage 1, the principal then offers a monetary incentive scheme to maximize her expected net profits, taking the optimal decisions
\(\left (v^{\ast \ast },\alpha ^{\ast \ast }\right ) \ \)as given. The optimal solution
\(\left (s_{1L}^{\ast \ast },s_{1H}^{\ast \ast },....,s_{nL}^{\ast \ast },s_{nH}^{\ast \ast }\right )\) then maximizes the following problem (
P5):
$$ \begin{array}{@{}rcl@{}} &&\alpha^{\ast \ast }\left( {\sum\limits_{i=1}^{n}}\pi_{i}(1)\left( x_{i}-p\left( v^{\ast \ast }\right) s_{iH}-(1-p\left( v^{\ast \ast }\right) )s_{iL}\right) \right) {\kern90pt}(\text{P5}) \\ &&+\left( 1-\alpha^{\ast \ast }\right) \left( {\sum\limits_{i=1}^{n}}\pi_{i}(0)\left( x_{i}-p\left( v^{\ast \ast }\right) s_{iL}-(1-p\left( v^{\ast \ast }\right) )s_{iH}\right) \right) -cv^{\ast \ast }\text{ such that} \\ &&{\sum\limits_{i=1}^{n}}\pi_{i}(1)\left( s_{iL}^{\ast \ast }-\delta_{i}s_{iH}^{\ast \ast }\right) +p\left( v^{\ast \ast }\right) {\sum\limits_{i=1}^{n} }\pi_{i}(1)\left( s_{iH}^{\ast \ast }-s_{iL}^{\ast \ast }\right) \left( 1+\delta_{i}\right) =c_{H} {\kern21pt}(\text{ICA5}) \\ && p^{\prime }\left( v^{\ast \ast }\right) \sum\limits_{i=1}^{n}\pi_{i}\left( 1\right) \left( s_{iH}^{\ast \ast }-s_{iL}^{\ast \ast }\right) \left( \alpha^{\ast \ast }-\left( 1-\alpha^{\ast \ast }\right) \delta_{i}\right) +c\leq 0. {\kern57.2pt}(\text{ICP5}) \end{array} $$
If I compare this result with the one under auditing, several remarks are worth making. First, and similar to the case of auditing under non commitment, monitoring implies that the principal rewards the agent in two different outcome levels – in one outcome for choosing normal effort and in another outcome for choosing high effort. But the reason is different. Whereas under auditing the agent could adjust his behavior to influence the principal’s auditing efforts via her updating of his effort choice, such a reaction is not possible when the agent decides simultaneously with the principal. Under monitoring, the principal takes the agent’s effort choice as given and reacts accordingly, without any further information about the realized outcome and updating of her beliefs. It is this difference that renders payments for two outcomes optimal. Whereas under auditing, paying only in one outcome was not optimal because the agent could then adjust his behavior to avoid any verification, paying in only one outcome under monitoring is not optimal because it requires that the principal expects the agent not to have chosen the high level of effort with a certain probability. To maximize his expected payments, the agent, however, would then choose e = 1 with certainty. But then the principal’s expectations are not consistent. Hence the principal also has to reward the agent for a normal level of effort.
Second, and also different from the case of auditing, the optimal incentive scheme under monitoring does not reward the agent in subsequent outcome levels. Instead, under monitoring he is paid for a high level of effort in the highest outcome if the signal indicates high effort, and he is rewarded for a normal level of effort in the lowest outcome if the signal indicates
e = 0. This difference stems from the fact that to make her monitoring credible, the principal now has greater flexibility when designing her monetary incentive scheme: she can adjust her payments across all outcome levels, whereas this was not possible under auditing where she had to offer appropriate payments for those outcomes where auditing was optimal. To see how the principal optimally uses this flexibility, consider her incentive constraint (
ICP5) for making monitoring credible, with positive rewards only in outcome
xk and
xj when the signal indicates a normal or a high level of effort,
skL > 0 and
sjH > 0,
$$ p^{\prime }\left( v\right) \left( \pi_{k}\left( 1\right) \left( \alpha -\left( 1-\alpha \right) \delta_{k}\right) s_{kL}-\pi_{j}\left( 1\right) \left( \alpha -\left( 1-\alpha \right) \delta_{j}\right) s_{jH}\right) =c. $$
If monitoring signals high effort, the payment
sjH should then be granted for the highest possible outcome
xn. This is beneficial for the principal for two reasons. First, the agent’s incentives for choosing high effort are highest in this case because the MLRC implies that choosing a high instead of a normal level of effort increases the relative likelihood of a better outcome. And second, since she uses the reward in the highest outcome to motivate the agent to choose high effort, her monitoring effort
v and the payment
snH are now substitutes. Hence, by paying the agent in outcome
xn, the principal can reduce monitoring effort and therefore verification costs. To make verification credible, the principal then rewards the agent for normal effort in the lowest outcome; that is,
s1L > 0. To see this, consider the payment
skL in which monitoring signals normal effort. Then this payment should be given for the lowest realized outcome
x1 for the same two reasons. First, it increases the agent’s incentives to choose high effort. This is because the principal’s incentive constraint requires that
α is sufficiently high,
\(\alpha >\delta _{k}/\left (1+\delta _{k}\right )\), so the probability that the agent chooses high effort is highest for the lowest outcome level
x1. And second, since the agent bears the principal’s verification cost, the monitoring effort
v and the payment
skL remain complements for this outcome level, so that paying the agent in an outcome that is as low as possible again reduces her verification costs.
Note that agent’s probability of choosing the high level of effort is higher as in the case of auditing. This follows directly from the fact that the principal can use the reward in the highest outcome for motivating the agent to choose high effort. In particular, this is beneficial for the principal when the productive gains from high effort are sufficiently high. In this case, she prefers monitoring to auditing.
This corollary now comes without surprise. If I compare auditing and monitoring, the latter procedure has two relative advantages: on the one hand, it gives the principal greater flexibility for making her verification effort credible and, on the other, monitoring avoids that the agent influences her expectations about his effort choice as he does under auditing. The corollary then follows from the fact that these differences result in a higher probability for choosing high effort; see Propositions 4 and 5.
Note that Corollary 2 is in direct contrast with Proposition 5 of Strausz (
2005). In his “extremely stylized” model, Strausz has three key assumptions. First, if the agent chooses high effort, the outcome of the project run by the agent is always a success, whereas with low effort the outcome is a failure with some positive probability. Second, the outcome of the project is not verifiable. And third, the principal’s verification effort is binary – she either costly verifies actively and then reveals the agent’s effort perfectly, or she does not verify. Given these assumptions, a feasible contract in Strausz requires that the principal pays the agent a certain bonus for choosing high effort unless verification reveals low effort. Hence she audits failed projects to avoid paying the bonus. More importantly, auditing of failed projects does not take place in equilibrium, since the principal uses auditing only as “a threat to withhold the agent from shirking”; see Strausz (
2005, p. 97). To induce him to take high effort, she then pays a sufficiently high bonus so that auditing of successful projects is not necessary. And finally, since a failure occurs only if the agent chooses low effort, she can incentivize the agent to choose high effort with certainty. His Proposition 5 then follows since under monitoring the agent is induced to choose high effort only with a certain probability in equilibrium. This reasoning does not hold in the present paper. First, since outcome is contractible, paying a bonus that is independent of the level of outcome is never optimal. Second, the principal will always make the agent’s payments outcome-contingent so that auditing to avoid paying a bonus is not a reason for verification. Third, auditing by the principal is not a threat but actually takes place in equilibrium. Hence, different from Strausz where the principal’s incentive to audit is strict, she truly faces a double moral hazard problem in my model. And fourth, whereas in Strausz (
2005, p. 97) “the principal’s inability to commit does not constrain the equilibrium” , non commitment in my model implies that the agent never chooses high effort with certainty. This last result also implies why in my model monitoring is optimal when the productive gains from high effort are sufficiently high: whereas in Strausz (
2005) the agent’s effort is higher under auditing than under monitoring, the reverse is true in my model.