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Agency theory, beginning with Ross (1973), Mirrlees (1999), and Holmström (1979),
focuses upon how asymmetric information can explain observed contracting
arrangements. Holmström and Milgrom (1991) show that in a multitasking context when
signals concerning one task are not available, then the optimal contract may ignore
information regarding performance on other tasks.
While contract incompleteness and asymmetric information are central themes in this
literature, the role of human cognition is not. One reason, as observed by Oliver Hart
(1990), is that both agency theory and the property-rights literature assume that agents
select their actions immediately after the contract is signed. The contract is designed to
provide the appropriate incentives for performance at this stage, and hence if ex post
unanticipated events occur these cannot affect actions that are sunk, and therefore
cannot affect the structure of the optimal contract. Agents may anticipate events that
cannot be described ex ante, but this is a different problem, and one which Maskin and
Tirole (1999b) demonstrate that under the appropriate conditions does not affect the
ability of individuals to optimally regulate their relationship, leading Tirole (1999) to
conclude that there does not exist a satisfactory foundation for the theory of incomplete
contracts (ICT).
How then do we reconcile these results in contract theory demonstrating the irrelevance
of human cognition for contract formation with Williamson's (1985) view that bounded
[3]
rationality is central to the theory of transaction costs? My first point is that we can
usefully categorize different contracting problems as a function of when information is
revealed. In section 2 the sequence of moves for the agency model, the hold-up model,
and Simon's authority model are reviewed. While these are important classes of
problems that correspond to many interesting contracting situations, they are not
exhaustive. In many principal-agent situations the agent is called upon to respond to
unexpected events in a way that is personally costly, but for which there is not sufficient
time to renegotiate the outstanding contract with the principal. I call this contracting
hazard ex post hold-up, and show in section 3 that the nature of human cognition may
play an important role in the optimal regulation of the relationship.
Many employment relationships have exactly this characteristic. For example, a fireman
may have to respond quickly to events while a building is burning, and cannot
renegotiate the contract with the city in mid-blaze. Emergency room doctors must deal
with a variety of unexpected events, some of which are dangerous to the physician,
especially when the patient has a communicable disease. In these situations hold-up can
take one of two forms. First the agent after taking an action may not receive the
compensation that he or she feels is appropriate. Secondly, the principal may worry that
the agent may not have the correct incentives to take the appropriate action ex post.
Section 3 continues with a discussion of why contracting in these situations is difficult. If
each event that an agent faces could be described beforehand, along with the
appropriate response, then ex post hold-up would be solved with a complete state-
contingent contract. However when the services to be provided entail multitasking with
random benefits and costs, the number of contract contingencies grows exponentially
with the number of tasks. This implies that even with a moderate number of tasks,
complete state-contingent contracting is impossible. It is worth emphasizing that contract
incompleteness in this case is not exclusively due to the bounded cognitive abilities of
the contracting parties: when complexity grows exponentially with a variable of interest,
the problem quickly becomes intractable for any finite computation device for even
modest values of this variable.[4] This is an empirically useful result because it suggests
that the number of tasks in a relationship is a measure of transaction costs that is
independent of individual characteristics.
Anderlini and Felli (1994) take a complementary approach to contract incompleteness.
They use the notion of a computable contract, namely any complete contract must have
the property that it is possible to determine the terms and conditions using a finite
number of computations. They give examples of contracts that are not computable, and
hence are incomplete. Though this condition is necessary, it is not sufficient to ensure
the existence of a complete contract. All the state-contingent contracts considered in this
chapter satisfy Anderlini and Felli's necessary condition, however, like many problems in
computer science, being solvable in finite time does not imply practical solution since the
time needed to write a complete contract is an astronomically long period.[5] This
approach is extended in Anderlini and Felli (1999) where they derive the optimal
incomplete contract as a function of complexity costs.
In this chapter a somewhat diffierent approach is explored. Even if contingent contracting
is impossible, the contract may still provide a mechanism to determine what constitutes
appropriate performance ex post, and ensure that the agent is rewarded for taking the
appropriate action. This issue is addressed in section 4, where it is shown that the
problem of performance evaluation is formally a problem in pattern recognition where the
goal is to characterize event-action pairs into the sets acceptable or not acceptable. In
cognitive science it is widely recognized that while humans are quite poor at thinking
logically, they have very powerful pattern recognition abilities.[6] For example, the reason
that humans are good at chess is not because of their ability to reason about the game,
a skill for which computers are far more skilled, but rather their ability to recognize board
patterns that represent strong positions.[7] This ability is so difficult to program that only
recently have computers been consistently better than humans at chess, and only with
programs that are highly specialized. This implies that human judgment of performance
is in many situations superior to any mechanical measuring system, and hence optimal
contracts should be designed to incorporate this ability.
Incentives can be provided in these cases by observing that both the principal and agent
have subjective evaluations of an agent's performance. As long as these evaluations are
sufficiently correlated, then it is possible to construct a mechanism that ensures efficient
performance. The optimal contract in this case takes the form of a bonus payment by the
principal to the agent when the principal has judged performance to be acceptable.
Given that third parties, such as the courts, are at a disadvantage in determining if
performance is acceptable, the optimal contract must depend upon the agent's self-
assessment of performance. Should the principal not reward the agent when the agent
believes he or she is deserving then the optimal contract requires the principal to pay a
penalty to a third party. The difficulty with such payments is that they are subject to the
hazard of renegotiation. In the event of a disagreement, the principal and agent have a
strong incentive to renegotiate to avoid paying the third party. Two well-known solutions
to this problem are discussed in section 5: enforcement with repeated interaction
combined with the threat of termination and the use of rank-order tournaments. This is a
useful exercise because it answers an open question in the legal theory of relational
contract raised by Goetz and Scott (1981). They observe that the right to unilateral
termination, while part of many bilateral relational contracts, is not a usual condition for
collective agreements, and hence they question the efficacy of such termination rights.
The results here show that unilateral termination clauses may be a necessary condition
for efficiency when bargaining is restricted to two individuals, and can be modified only
when there are three or more individuals in a relationship.

[1]
A. Denning, The Discipline of Law (1979, p. 56). As quoted in Farnsworth (1990, p. 543).

[2]
In particular the discussion in section 2.1 of Williamson (1975).

[3]
See chapter 1.

[4]
A point that is well appreciated in the computer science literature. See for example Garey
and Johnson (1979). Williamson (1975, p. 23) makes a similar point in reference to the game
of chess.

[5]
For example, decoding an encrypted message is a computable problem that it can be
achieved in finite time. However, such messages are believed to be secure because the time
required is sufficiently long as to be impracticable.

[6]
See Churchland and Sejnowski (1993) for an excellent introduction to these issues.

[7]
This was shown in a wonderful paper by Newell, Shaw and Simon (1963).
2 Contracting scenarios
Consider the following generic exchange problem between an agent (he) who produces
a good or service for a principal (her) in exchange for compensation:
1. The agent is expected to choose an action y from a set of possible
actions Y (in general multidimensional) at a cost C (y, ), where is a
random parameter chosen by Nature.
2. The benefit to the principal from this action is qB (y, ), where is
random parameter chosen by Nature, and q is the quantity of trade,
which is normalized to represent trade (1) or no-trade (0), or the
probability of trade if q (0, 1).
3. The principal and agent write a binding contract at the beginning of the
relationship conditional upon their expectations and information available.
I assume that the principal has all the bargaining power at each stage.[8]
The payoffs to the principal and agent are respectively given by:


The principal is assumed to offer a contract that maximizes her payoff subject to the
agent receiving his reserve payoff from the relationship. The term "contract" is used in
the economist's sense rather than in the more restrictive legal sense. That is, the
contract specifies a mechanism or game between the principal and agent, including
expected actions and beliefs, even when these cannot be verified in court. In contrast the
legal notion of contract refers to promises enforced by the threat of court-awarded
damages in the case of default. In particular for the economist these damage awards are
an explicit part of the agreement between the two parties, as are actions taken after
events that only the contracting parties can observe. An important element of this
broader notion of contract is the potential for one party (the principal) to reallocate
bargaining power to the other party (the agent). This reallocation of bargaining power is
central to the property-rights literature beginning with Grossman and Hart (1986). The
purpose of this section is to illustrate how the form of the optimal contract and the nature
of property rights are sensitive to the timing of information revelation. I briefly outline the
three important classes of contracting problems that have been considered in the
literature, agency theory and the hold-up problem of Williamson (1975) and Grossman
and Hart (1986), and Simon's (1951) authority model, and discuss the relevance of
theories of bounded rationality for each of these contracting problems. I then introduce
the hazard of ex post hold-up, that is more appropriate for addressing the role of human
cognition in contract formation.

2.1 Agency theory
Agency theory, beginning with Ross (1973) and Holmström (1979), is the starting point
for the modern theory of contract. It is always possible to view the economic theory of
contract as an application of agency theory: namely observed contracts are the result of
negotiations between a principal and an agent, who choose optimal contracts as a
function of the available information. However, in this chapter I follow Hart and
Holmström (1987), and adopt a narrower definition of agency theory corresponding to
the class of models that focuses upon how to structure contracts as a function of
mutually observed (and enforceable) signals of performance. In the context of our simple
model let us fix , and set q = 1. The timing of decisions are as illustrated in figure 13.1.
At date 0 the contract is signed, then the agent chooses y, which is assumed to be a real
number representing effort or some personally costly action: #C/#y > 0. The choice of
effort affects the underlying distribution of in such a way that more effort is beneficial to
the principal: #E(B(y, ))/#y > 0 for all . The principal then pays the agent a wage that
is a function of the observed benefit, or W = f (B).




Figure 13.1: Time line for agency relationship
In agency theory it is typically assumed that the agent is risk averse, and hence he would
prefer a wage W that is independent of the random shock . In this case the agent has
no incentive to work and would select y to minimize the personal cost of effort. A major
insight of this literature, as discussed in Hart and Holmström (1987), is in order to avoid
this moral-hazard problem the optimal contract should be a function of any signal that
adds information regarding worker effort.

There is a great deal of evidence to suggest that the basic hypothesis of agency theory
is correct, namely individuals do respond to incentives. Hence, if workers are paid a
wage that is independent of income one expects to observe some shirking. Despite this
fact, explicit pay-for-performance systems, while common, are far from being ubiquitous,
leading many experts such as Gibbons (1997) and Prendergast (1999), to conclude that
agency theory alone cannot explain all the variation observed in the data.
One solution, provided by Holmström and Milgrom (1991), begins with the observation
that while effort is often multidimensional, performance measures may not be sufficiently
rich to capture this variation. For example suppose that a home owner is contracting for
the services of a contractor who must allocate effort between speedy completion of the
project and quality, whose actions are represented by vector y ={ys, yq}, where ys
represents speed and yq represents quality. In the absence of explicit contract terms, the
cost-minimizing effort is strictly positive:

It is also reasonable to suppose that quality and speed are substitutes, and hence Csq >
0.
In this simple example the benefit to the home owner is assumed to have no uncertainty
and is given by B(y). Given that the payoff represents the subjective preferences of the
home owner, then one cannot write a contract conditional upon an explicit measure of B
or for that matter quality yq, also a subjective variable. Rather, the only contractible
variable is ys, speed. In this case, assuming that the problem is convex, it follows that
under the optimal contract {y*s, y*q} solves:




The first term is the consequence of the contractor minimizing costs in the quality
dimension, while the second term is the first-order condition for speed. Since speed and
[9]
quality are substitutes (Csq > 0) then it follows that y*s is less than the first best. Under
Holmström and Milgrom's (1991) assumption, if the substitution effect is sufficiently
strong, or Cqq sufficiently small, then y*s < yos. In other words the optimal contract may
entail providing either no incentive or negative incentive for speed.

Hence incomplete contracts in agency theory arise from a paucity of information
regarding performance. Notice that the hypothesis of rational expectations is central to
the theory. The principal structures the incentive contract as a function of her
expectations regarding future performance by the agent. The introduction of bounded
rationality regarding the formation of expectations would imply that we may sometimes
observe incentive contracts with unintended consequences (a possibility that is often
observed in practice, as the examples in Kerr's, 1975 seminal article demonstrate).
However, aside from the potential for error, agency theory provides little guidance
regarding the implications of bounded rationality for observed contract form.
Also, Holmström and Milgrom's (1991) explanation for the lack of high-power incentives
for quality performance ignores the potential for incentives based upon non-contractible
signals. In the case of the contractor, their model suggests that in a one-period
relationship the contractor would simply choose his most preferred quality. Yet, disputes
over quality are quite common during construction. In many cases contracts are
structured so that in areas that the quality is lacking, the builder may ask the contractor
to take corrective actions, even though some aspects of quality were not explicitly
contracted upon ex ante. This type of ex post renegotiation over non-contractibles is
central to the hold-up model considered next.

2.2 Hold-up
Suppose now that the contractor is building a custom-designed house. Given that time of
completion is contractible, we focus only upon the provision of non-contractible quality.
The main difference with respect to the agency model is the existence of a physical
asset whose ownership rights can be transferred. Uncertainty plays a role in that ex post,
it may be more efficient to allocate the good to another buyer in the market. Suppose
that the value of the house to the principal and the market are, respectively, given by
B(yq, ") and Bo(yq, "), where it is assumed that B(yq, ") Bo(yq, ") = k("), and k(") is
an uncertain amount of relationship-specific rent that depends upon the state of nature ".
When this is negative, it is efficient to breach the contract, while performance is efficient
when k(") > 0. Let the expected value of the relationship given that there is efficient
breach, be positive and given by k = E(max {0, k(")}) > 0. The time line for the contract
is illustrated in figure 13.2.




Figure 13.2: Time line for hold-up problem
The insight of the property-rights literature, beginning with Williamson (1975) and
Grossman and Hart (1986), is that the ex post distribution of bargaining power is an
important determinant of the efficiency of the relationship, and that this bargaining power
can be reallocated via ownership rights. Consider first the case in which the principal
owns the house. Given that the principal has all the ex post bargaining power we obtain
exactly the same solution as in the agency model above: the contractor selects his
o o
preferred quality, y q, and agrees to a fixed-price contract p = C(y q. In this case if ex
post efficiency requires that the building be owned by another person, then the principal
would simply sell the building to that person. Though this contract ensures ex post
allocative efficiency, the lack of performance incentives implies that the contractor does
not supply an efficient level of quality.
An alternative contract is for the principal to sell her right to the project to the contractor
at price p = maxyqE{Bo (yq, ")} C(yq), with the provision that she must be given the
chance to match any offer that the contractor might receive from the market. This is a
contract that provides the principal with the right of first refusal, a contract that was
[10]
common in Hollywood for some actors and producers. Under this contract whenever
Bo(yq, ") > B(yq, ") the principal is unwilling to match the market price and the
o
contractor receives B (yq, "). Whenever B(yq, ") > Bo(yq, "), the principal simply
o
matches the market offer, and again the contractor obtains B (yq, "). It is assumed that
the marginal return from quality is the same in the market and for the principal, and
hence this contract provides first-best incentives for quality, while ensuring efficient
matching. More formally the payoff of the contractor is:



This case is an example of general investment combined with turnover costs that are
independent of investment. As in MacLeod and Malcomson (1993), it is also possible to
obtain the first best in this case with appropriately chosen liquidation damages
(proposition 5).
There is a literature that explores how the complexity of the ex post environment makes
it impossible to write an efficient contract (Segal 1999, Hart and Moore 1999a). In these
papers it is assumed that ex post there are a large number of potential goods that may
be traded, but it is optimal to trade only one of these. When the nature of these goods
cannot be specified ex ante, as the number of possible goods approaches infinity the
optimal contract is a fixed price contract, which in turn implies that the level of investment
in the relationship is inefficient. This result demonstrates how environmental complexity
can cause individuals to optimally choose an incomplete contract, though this result is
not an implication of bounded rationality and cognition per se. Both papers assume that
contracting parties anticipate correctly the consequences of any mechanism they choose,
hence do not explore the implications of unforeseen contingencies, and are rather
concerned with "indescribable contingencies" (see Maskin and Tirole 1999b for a further
discussion of these points).
Hart (1990) further argues that hold-up models provide an inadequate foundation for the
study of the implications of human cognition for organization and contract design. For
example, suppose there is an unforeseen event " for which it is efficient that the asset
be sold to the market. Ex post renegotiation ensures that this indeed will be the outcome.
However, given that specific investments have been sunk at the time individuals learn
about " , the occurrence of this event plays no role in setting ex ante incentives.
Structuring relationships to efficiently deal with unforeseen contingencies is one of the
motivations for Simon's (1951) original model of the employment relationship.

2.3 Authority
Simon's (1951) model of employment is concerned with the role played by authority. His
idea is that in a complex world, rather than planning for all future events, one might gain
by delaying decision-making until after an event occurs. The formal timing for his model
is illustrated in figure 13.3. After the contract is signed the principal is able to observe the
state of nature, denoted by " ={ , } $, where $ is the set of possible states, and can
direct the agent to perform a task y as a function of this information (without loss of
generality we set q = 1). In Simon's model giving the principal authority imposes costs on
the agent ex post since he may be asked to carry out tasks with large private costs, C(y,
). Simon supposes that the authority relationship is characterized by a wage, W, and a
o
set of tasks Y Y from which the principal may choose. Giving the principal more
authority corresponds to choosing a larger set of tasks, Yo, that the employee may be
asked to carry out in exchange for a higher wage. Notice that since control is specified in
o
terms of Y , and not states, then the model incorporates a well-defined protocol to be
followed when an unforeseen event occurs.




Figure 13.3: Time line for authority relationship
If this set is a single action, i.e. Yo ={y}, then Simon calls this a sales contract and the
concept of authority has no relevance. Simon shows that the optimal contract gives the
principal some authority over the agent when the benefits of flexibility outweigh the costs.
Notice that the potential for renegotiation changes this result. Suppose that the agent
accepts any sales contract {
W *, y *} satisfying W * E{C(y *, )}= 0, then it will follow that the expected utility of the
agent is at least zero. After the event " ={ , } occurs, under the sales contract the
agent receives U *A ( ) = W * C(y*, ) ex post. Suppose that the principal has all the
bargaining power. In this case, she can offer a new efficient contract that would be
accepted by the employee as long as the utility is at least U *A ( ). Hence we have the
following result:
Proposition 1



If renegotiation before the agent chooses his action is possible, then the sales contract
results in the first best.




For this contracting problem the allocation of bargaining power is not important, rather
the key ingredient is the hypothesis that renegotiation can occur between the time the
state is observed and the agent selects her action. In contrast to the hold-up problem,
the addition of renegotiation in this case increases, rather than decreases, efficiency.
However, there are a number of situations for which the hypothesis of renegotiation is
not reasonable. For example firefighters must make second-by-second decisions on how
to respond to a burning building, teachers need to be able to deal with new and
unexpected questions and events in the class, surgeons must be able to deal with
unexpected events during an operation. While not stated explicitly, it is likely that Simon
had in mind situations such as these for which renegotiation to an efficient action in real
time is not possible. Certainly, this is a case that is clearly not considered to be part of
the standard hold-up model where renegotiation is assumed to be possible.
However, when renegotiation is not possible, the exercise of authority may also be
imperfect. Alchian and Demsetz (1972) make this point when they argue that in
employment relationships there is typically no real authority. The agent follows the
principal's directives because he believes that he will be rewarded in the future. If the
agent is dissatisfied then he is free to leave for another employment relationship. Alchian
and Demsetz argue that the key point is the ability to monitor the agent's actions in order
to be able to choose the appropriate level of compensation. Yet when performance is
non-contractible, and the agent is unable to renegotiate her contract, she faces the
prospect of taking a personally costly action, without any assurance that she will be
rewarded because the principal can always claim that existing compensation is sufficient.
This leads to a contracting hazard that I call ex post hold-up.

2.3 Ex post hold-up

In the contracting problems we have considered thus far, either the principal can observe
the state of nature before the agent takes an action (authority) or the state of nature is
revealed after the agent selects her action (agency and hold-up). A case that has not
been considered, but is ubiquitous in many employment relationships, is one where the
agent is expected to respond to uncertainty before the principal has knowledge of the
event or can guide the agent in selecting the appropriate action. I have already
mentioned the case of fire fighters and surgeons, but this case also includes many
employment situations where the employee is expected to internalize the objectives of
the principal, and make decisions on the principal's behalf.
The hazard of ex post hold-up arises from the need to have an agent respond
appropriately to events as they occur in the absence of an explicit and enforceable
contract. The time line for this contracting problem is illustrated in figure 13.4. A defining
feature of employment relations facing ex post hold-up is the need for the agent to
allocate activity among a number of different tasks in response to the costs and benefits
of the different tasks. More formally, suppose that the agent is facing a multitasking
problem parameterized as follows:
1. There are k tasks: y Y ={{y1, y2, , yk} y1 + y2 + + yk T}, where
T is the agent's total time available to allocate between tasks.
k i i i i
2. The cost function takes the form: C(y, ) = % i=1 c(y , ), where c(y , )
is the cost of allocating effort to task i. If yi is zero, then this cost is zero,
i
y2i + f. The cost parameter i
otherwise it is is a random variable that
can take on one of m discrete values {d1, , dm}.
T
3. The benefit function is assumed to take the form: B(y, )= y, where
T 1 1 2 2 k k
y= y+ y+ + y is the benefit to the firm from the
i i
agent's effort. The marginal benefit of task y is , a random variable
that can take at most n values: {a1, , an}.




Figure 13.4: Time line for ex post hold-up
In this parameterization, the state space is given by the possible benefit and cost
k
parameters: $ ={{a1, , an} — {d1, , dm}} . For each " $, the optimal response is
defined by:
An important assumption I make for the rest of the chapter is that both the benefit and
cost measures are themselves non-contractible. In the case of the benefits, consider for
example a secretary in a large firm. His or her keyboarding output is important to the firm,
but there is no way to attach relative values to say keyboarding versus filing. Similarly,
the dollar value of a research paper written by a professor, or an hour devoted to seeing
students, is not known in practice. If the benefits were contractible, then the provision of
an incentive contract would be straightforward. Similarly costs represent dis-utility to the
agent, and hence are also difficult/impossible to verify accurately in practice.

2.5 State-contingent contracts and complexity
Though a single measure of performance may not be available, it may be reasonable to
suppose that the principal can observe, or put into place a system that evaluates an
agent's response to a specified state in a verifiable way. One way to avoid the potential
for opportunistic behavior when an agent is simply told vaguely to do a good job is to
outline explicitly what is expected for certain contingencies. For example, one may
require a secretary to explicitly stop what he or she is doing if a client comes in and
needs attention. Such an explicit condition may be necessary when an employee faces
conflicting goals, for example if the secretary must decide between completing a
keyboarding task immediately or addressing the needs of a client. For each possible
state " suppose there is an appropriate response, denoted y*("). Given that the agent
is risk neutral, one may use a forcing contract that rewards the agent if and only if she
achieves a satisfactory performance. This can be formally represented by the judgment
function:

where J(", y) is 1 if the choice of y given " is satisfactory, otherwise it is zero. In the
case of an optimal complete contract, the principal defines the judgment function by J
*(", y) = 1 if y y*("), and zero otherwise, and then offers a contract {w, bJ*(",
y*("))}, where w is a fixed payment and bJ (", y*(")) is the bonus payment. This forms
an optimal contract if it satisfies the individual rationality constraints and the incentive
compatibility constraints:



With no restrictions on the sign of w, as long as costs are bounded then there always
exists a contract satisfying these conditions.
Notice that in order to implement this contract one is required for every event " to
specify ex ante the expectations for the agent, and to reward the agent if these
expectations are met. However, when the number of tasks is moderately large this is
simply impossible. In this model the number of tasks is k, and the number of productivity
and cost levels are, respectively, m and n. The complexity of the contract is a measure of
the costs of designing, writing and implementing the contract as a function of the data
describing the relationship. Suppose that the cost of agreeing upon a contingency " is ,
kk
then since the number of possible events is n m , the cost of a complete contingent
contract is nkmk . Since these costs are exponential in the number of tasks, they quickly
rise to an astronomical level. For example, suppose that = 1 ¢, and that the number of
cost and performance levels is the same (n = m), then table 13.1 presents the cost of a
complete contract as a function of the number of tasks and effort levels.


Table 13.1: Cost of a complete state-contingent contract
Number of tasks


Number of cost 2($) 5($) 10($) 15($)
and performance
levels
2 0.16 10 10,000 10
million
3 0.81 600 35 2
million trillion
4 2.56 10,000 11 11,000
billion trillion
5 6.25 100,000 1,000 10
billion million
trillion
Cost of considering 1¢
a contingency:

As one can see from table 13.1, when there are several tasks, even with just two
performance levels, the cost of even thinking about a complete state-contingent contract
would be astronomical. Observe that it is the multitasking that increases the complexity
costs, and not the number of cost and performance levels (the discreteness of the state
space). In other words if the benefits and costs vary in a number of dimensions, then it is
simply impossible to create a contingency plan for every possibility. This example
illustrates the point made by Williamson (1975), and earlier still by Savage (1972), that in
any realistic environment the number of possible contingencies is so large that complete
state-contingent planning is impossible.[11] In particular, it is worth emphasizing that
thinking in terms of human bounds on rationality is not helpful in these cases, rather one
faces fundamental limits that make it impossible to construct complete contingent plans
and contracts. To deal with this complexity, humans have developed algorithms and
techniques for decision-making in complex environments that can be used for the design
of more efficient contracts.[12]

[8]
For simplicity, I follow Hart and Moore (1999a) and Maskin and Tirole (1999a) and assume
that the principal has all the bargaining power in any ex post negotiation. This assumption can
be dropped, but at the cost of unnecessarily complicating the argument.

[9]
A similar equation is derived by Baker (1992) who works out the optimal contract when the
contractible variable is not perfectly aligned with benefits.

[10]
In personal correspondence relating his discussions with Ben Klein and Earl Thompson,
Alchian (1998) observes that many Hollywood contracts for shows were exactly of this form.
An actor or producer on a long-term contract could entertain outside offers. However, if the
studio matched the offer, the individual had an obligation to stay with his or her studio. Alchian
argues informally that the right of first refusal serves the purpose of providing incentives for
efficient specific investment.

[11]
See Dekel, Lipman and Rustichini (2001) for an interesting axiomatic approach to modeling
decision-making in complex environments.

[12]
See Churchland and Sejnowski (1993) for a good review of computational neuroscience
exploring the algorithmic foundations of human decisionmaking.
3 The sales contract revisited: ex ante governance
Even though the contracting parties cannot consider every possibility, they can still write
a complete contingent contract, of which Simon's (1951) sales contract is an extreme
case. The sales contract is a form of ex ante governance requiring the agent to perform
y, regardless of the state of nature, and represents the polar opposite contract, in terms
of complexity, to a complete state-contingent contract. Dye (1985) proposes that one
endogenizes the complexity of the contract by specifying actions for a limited set of
events. For example the event might be that there is a need to have a paper keyboarded,
which is then associated with the action ˜keyboard the paper today'. This event and
response may not be efficient because demanding the paper be keyboarded immediately
may lead to mistakes, or there may be more pressing tasks. The optimal contract trades
off the quality of the contract against the cost of increased complexity. More formally, let
N ={E1, E2, , EN} be a partition of the state space $, and let YN ={y1, y2, , yN} be the
associated actions. This defines a contract of complexity N, under which the agent in
exchange for a wage W agrees to carry out the following actions:

Though this contract is complete in the sense that it defines an action for every state, it is
not efficient. This is because all states in a single event Ei are associated with the same
action, which many not necessarily be efficient.
For purposes of this example suppose that for each N the principal and agent agree
upon a particular partition N. Further suppose that if N > N, then for every E ,
N

there is an E such that E E. That is, if we agree upon a more complex contract,
N

it refines the events of less complex contracts. Let c*N (") denote the optimal contract
relative to defined by:
N




where E" N is the unique event such that " E". Under these assumptions we have
the following proposition, whose proof is straightforward.
Proposition 2


The ex ante surplus generated by c*N ("),

is an increasing function of N.




Notice that this expression is strictly increasing when going from N to N + 1 if and only if
the additional partition causes the optimal action to change for some events. This reflects
that well-known fact that information is valuable only when it causes a change in one's
decision. For the multitasking problem of the previous section this is true for a generic
choice of parameters and . The surplus net of transaction costs from the optimal
contract of complexity N is S*N N, where is the cost of adding a contract
contingency. As illustrated in table 13.1, even if is very small, transaction costs for a
complete state-contingent contract may be very large, and hence we are unlikely to
observe such a contract. Suppose that the agents choose the complexity of the contract
to solve


then we have the following result:
Proposition 3


Suppose that — #$ > S * where #$ is the number of states and S * is the maximum
surplus under a complete contingent contract then:
1. The optimal contract complexity is decreasing with contracting costs .
2. Keeping the transaction cost fixed, then a proportional increase in
the value of trade: SN, > 1, increases the optimal complexity of the
contract.




This result highlights the fact that increasing transaction costs lowers the complexity of a
state-contingent contract. Secondly, as the value of trade rises, then so does the
complexity of the contract, a result that is consistent with Macauley's (1963) observations
regarding the commercial contracts. The benefit of ex ante governance is that the agent
knows and understands exactly what is expected for every event Ei. However, it is
precisely because of the fact that the contract is well defined and binding that the
principal faces the hazard of opportunism. Consider the following example from the
Lincoln Electric case in which the firm attempted to expand its system of piece rates to
secretarial staff. Let " denote the correspondence to be keyed in a particular day, and
suppose that task i is the number of times that one strikes a particular letter. To improve
productivity the company decided to reward individuals as a function of the number of
keystrokes hit or %yi. Clearly the intent is that the secretary keys a particular text at a
higher speed, but what occurred is in one case a secretary repeatedly hit the same key
[13]
during her lunch break to improve her earnings!

This is a rather stark example of Williamson's (1975) concept of opportunism. If the
terms of employment simply specify the payment as a function of the number of
keystrokes without mention of the quality of output, then even if the output is useless, the
explicit terms call for payment to the secretary. The firm would argue (probably
successfully) that the intent in this case is that the secretary produce useful documents,
however the secretary could argue that this sophisticated firm had written an explicit
contract and should be held responsible for its decisions. Unfortunately, organizations
often make this kind of mistake, as highlighted in the famous article by Kerr (1975) who
outlines several examples of workers responding to incentives in undesirable ways. As
Kerr points out, many organizations are "rewarding A while hoping for B."
Yet, propositions 2 and 3 suggest that in principle a sufficiently contingent contract would
be close to the first best, a view point that has led many economists to promote the
increased use of pay for performance contracts (see for example Milkovich and Wigdor
1991). Moreover, as table 13.1 illustrates, the complexity of jobs involving multitasking is
such that even very sophisticated firms may not be able to anticipate all the
consequences of a contract. As Kerr observes, an explicit contract creates an incentive
for the agent to discover ways to improve measured performance rather than a firm's
performance, a behavior that is reinforced by the legal presumption that explicit contracts
[14]
are legally binding. (This point is illustrated in the case of Wakefield v. Telecom .) In
this case a salesperson, Wakefield, was employed on an explicitly at-will basis, but was
also paid commissions for sales in his office. After several years of employment, he was
dismissed just before he was to receive a commission payment from a significant sale.
Northern Telecom did not pay this commission, arguing that the at-will nature of
employment relieved it of this obligation. However, the court ruled that employment at
will did not absolve the firm from its explicit obligation to pay a commission, and
established the protection of explicit performance pay, highlighting the risk that a firm
faces when using a poorly constructed contract.
In principle increasing the complexity of a contingent contract should enhance
performance. However, not only does the complexity of the environment imply that a
complete contract is impossible, it may also be the case that the contract provides
incentive for an individual to discover unanticipated actions that are Pareto-inefficient but,
under the terms of the explicit contract, are in the interests of the employee to implement.
Section 4 discusses how subjective evaluations may be used to address this issue.

[13]
See Irrgang (1972, p. 13).
[14]
Wakefield v. Telecom, 769 F. 2d 109 (20 Cir.), 1985.
4 Judgment and subjective performance evaluation
An important insight of Simon's (1951) model is the idea that actions should be decided
upon after the state of nature is revealed. Even when the determination of the
appropriate action, given ", is of low cost, the large number of potential states make
such contingent planning impossible, a complexity that is dramatically reduced by
delaying decision-making until after the state is revealed. The difficulty is that now we
face the problem of the agent being held up. If he takes an appropriate, but costly, action
how can he be sure that the principal will reward him appropriately?
Secondly, given that our maintained hypothesis is that there is no univariate measure of
performance, in the absence of an ex ante agreement, how is the agent going to know
what is appropriate performance, and how is the principal going to judge such
performance? As Prendergast (1999) observes, in many cases both the principal and
agent engage in subjective evaluations based upon human capabilities that cannot be
replicated by any mechanical system. For example, the owner of a restaurant judges the
performance of a chef by tasting the food. At the moment there is no known device that
can automate such a process. When deciding upon whether to accept a paper for
publication in a journal, once the referee has decided that the results are correct, the
final decision turns upon the notoriously vague criteria of "importance" or "contribution to
the literature."
In these examples, evaluation depends upon the superior performance of human versus
mechanical evaluations of performance. From the cognitive science literature we know
that humans have remarkable pattern recognition abilities that we are only just beginning
to understand and model. The formal link of incentives to pattern recognition can be
modeled with the introduction of a judgment function J(", y). Formally this function is a
classifier that divides the set $ — Y into two sub-sets:


where A denotes "acceptable performance" and U denotes "unacceptable performance."
When there is multitasking, then the state space $ is very large, making a complete
state-contingent contract impossible. Given that the classification problem simply
involves dividing a space into two sets, then this seems an easier problem than writing a
state-contingent contract. This is in fact not the case. Notice that any contract can be
written as specifying whether or not performance has occurred in a state, and hence the
complexity of a classifier is the same as the original contracting problem. Moreover, the
seminal work of Minsky and Papert (1988) has proven that the identification of a
classifier is a "hard" problem, a point that Anderlini and Felli (1994) have made explicitly
in the context of contract formation.
While classification is a hard problem that challenges even the most sophisticated
computing machines, research in cognitive science has found that the brain is
specifically designed to be very good at pattern recognition (see for example Churchland
and Sejnowski 1993). Though human classification is not perfect, it is the case that
individuals can learn to be good at categorizing inputs. For the purposes of this chapter,
the aspect of categorization I wish to emphasize is the ability to judge whether
performance is acceptable or not (as opposed to providing a numerical measure of its
quality). In the next sub-section it is shown that as long as the employer and employee
have judgments that are correlated, then it is possible to construct contracts that are not
explicitly state-contingent, yet nevertheless result in high performance.

4.1 Subjective contracting
Consider a situation for which a principal and an agent agree to a contract that requires
the agent to formulate a response to a large number of events. When an event occurs,
the agent is assumed to choose effort that determines the probability of good
performance for that event. We do not explicitly model either the underlying state space,
nor the set of possible actions. Rather, motivated by the previous discussion, it is
assumed that both the principal and agent evaluate the response to the event, and
decide whether or not performance is acceptable. Given that these evaluations are both
non-contractible and that ex post, it is not possible to write a screening contract, this
greatly constrains the set of possible performance contracts. In particular, it is shown that
if judgment is not perfect, then the optimal contract necessarily entails the potential for
conflict between the principal and agent.
More formally, suppose that the cost of effort [0, 1] to the agent is c( ), where c(0) =
0 (cost of no effort is zero), c , c > 0 (more effort costs increase at an increasing rate)
and c ( ) &' as & 1 (perfection is impossible). When success occurs, then a reward
B * is produced, otherwise there is no return. Hence the expected net surplus of the
relationship for this reduced-form model is given by:

fb fb
with the first-best level of effort, , satisfying B* = c ( ).
Let us assume that these parameters are commonly known, and that if success does not
occur, then this is commonly known by both parties (this assumption can be relaxed at
the cost of greatly complicating the analysis). Subjective evaluation is modeled by
supposing that when success does occur, then the principal and agent may or may not
agree upon this. In the event of objective success, let ij, i, j {A, U }, be the probability
that the principal believes quality is i and the agent believes quality is j, where A and U
denote "acceptable" and "unacceptable," respectively. Thus if the good outcome occurs,
then is the probability that both principal and agent agree on this. It is assumed that
AA

the signals are positively correlated, that is > 0. If the beliefs of the
AA UU UA AU

principal and the agent are perfectly correlated then = = 0.
AU UA


Owing to the complexity of the relationship it is not possible to write a contract
conditional upon the objective characteristics of output, nor can it be made binding upon
the beliefs of the individuals. However the agents can agree to a contract that makes
payments conditional upon messages sent by the principal and agent. Formally the
contract between the principal and agent is given by:

where (ij, wij are the payments to the principal and agent under the contract as a
function of the message i, j {A, U }, satisfying the constraint (ij + wij 0.[15] This
constraint allows the total payments to be less than zero, a possibility that will prove to
be crucial. The ex post hold-up problem has the following sequence of moves:
1. The principal makes a take-it-or-leave-it contract offer to the agent,
who accepts or rejects.
2. An event " $ occurs.
3. The agent selects [0, 1], which is his level of effort, in response to
this event, to produce an observed response y.
4. The principal and agent observe {", y} and form subjective judgments
regarding the success of the agent's action and simultaneously send
messages from the set {A, U } to the third party enforcing the contract.
5. The payoffs are determined.
I assume that the principal is able to select the most efficient incentive-compatible
contract. The payments under the contract to the principal and agent when they report k,
but their true state is l are, respectively:



The principal's problem is to maximize expected payoff subject to the agent's individual
rationality and incentive compatibility constraints:


subject to
where ((c) = %i,j {A,U } (ij ij and w(c) = %i,j {A,U} wij ij are the expected transfers to the
principal and agent, respectively, when the good outcome occurs. Constraint (21)
requires the agent to earn at least his outside payoff, constraint (22) is the requirement
that the agent select effort to maximize his payoff at stage 2. Constraints (23) and (24)
are the stage 3 incentive compatibility constraints ensuring that the principal and agent
truthfully report their subjective judgments to the third party enforcing the contract. The
final constraint is the budget-balancing constraint for the contract.
Notice that if the contract is budget balancing, (ij + wij = 0 for all i, j {A, U}, then the
contract defines a constant-sum game at the message stage between the principal and
agent. Such games have a unique value, and hence the payoff cannot depend upon
subjective information. Thus in order that a subjective evaluation system induce positive
effort on the part of the agent it is necessary that in some states there be a net loss to
[16]
the relationship. The next result provides a complete characterization of the optimal
contract when we relax the budget breaking requirement.
Proposition 4


Suppose that AA UU AU UA > 0 then optimal contract with subjective performance
evaluation has the form in table 13.2 where

The optimal effort * solves ,
where A* = AA + AU is the probability that the principal believes
performance is acceptable.
The bonus satisfies: b* = c ( *)/ A*.
The fixed wage satisfies: w = Uo + c( *) *c ( *).
The penalty satisfies P = c ( *)/ A.




Table 13.2: Contract payoffs




The proof of this proposition is in MacLeod (2002). The optimal contract has the property
that the agent's payment is independent of his report, and hence he has no incentive to
misrepresent his self-evaluation. The principal provides the agent with effort incentives
by paying him a bonus whenever she believes that he has provided acceptable
performance. Given that we expect subjective evaluation to be used when explicit
contracts are more expensive, then this implies that the incidence of bonus pay should
be greater in jobs of greater complexity, an implication that has some empirical support,
as shown by Brown (1990) and MacLeod and Parent (1999).
If the principal reports unacceptable performance when the agent reports acceptable,
then she must pay a penalty P. It is the prospect of paying a penalty when the reports
from the agent and principal differ that provides the appropriate incentives for truthful
revelation by the principal. When correlation is imperfect and UA > 0, there is a positive
probability that the principal will pay the penalty. Given that the size of the penalty
depends upon the size of the bonus promised, the lack of correlation increases the
marginal cost of providing incentives. This is reflected in the term
the amount by which the marginal benefit from effort is reduced in the optimal contract.
Thus if the probability of the principal having an unacceptable evaluation while the agent
has an acceptable self-evaluation is zero we obtain the first best. This result shows that
the optimal contract is structured so that the principal's evaluation determines whether or
not the agent receives a bonus, while the role of the agent's evaluation is to provide the
necessary incentives for the principal to be truthful.

MacLeod (2002) extends this result to the case of risk averse agents and multiple signals
of performance. In that case, the optimal contract with subjective evaluation entails a
compression of the rewards to performance, relative to the optimal contract with
objective measures of performance. The pooling is more extreme as the correlative
between the principal's and agent's evaluations decreases. In the extreme case of no
correlation in beliefs, Levin (1998) in the case of a risk neutral agent, and MacLeod
(2002) in the case of risk aversion, have shown that the optimal contract pools all
evaluations into two levels, acceptable or not.

4.2 Relational contracts
Goetz and Scott (1981) define a relational contract as one for which "parties are
incapable of reducing important terms of the arrangement to well-defined obligations," a
case that includes the problem of contracting with subjective evaluation studied here.
They argue informally, as I do formally above, that such contracts arise when the number
of contingencies is so large that it is not possible to write a complete contingent contract,
creating problems for the interpretation and enforcement of contract terms and
conditions.[17] This definition of a relational contract is not, however, universally accepted.
The term originates with Macneil (1974), for whom the term refers to the complex set of
behaviors and norms characteristic of individuals engaging in long term commercial
transactions.
Following Axelrod (1981), the prisoner's dilemma problem is often viewed as capturing
the essence of relational contracts. In this game two individuals simultaneously decide
whether to cooperate or not each period. The model can capture the essence of the
contracting with subjective evaluation when beliefs are perfectly correlated. In that case,
the strategy cooperate can correspond to truthfully reporting one's evaluation. In these
models it is typically assumed that budget balancing is imposed, and hence directly
imposing a cost P is not possible. Since the principal has an incentive to report low
performance if a bonus payment is required, then the only equilibrium in the one-shot
game is to not pay the bonus, and hence the agent would choose low effort.
Equilibria with high levels of effort are constructed using a self-enforcing contract,
modeled formally as a repeated game (see Bull 1987 and MacLeod and Malcomson
1989). The agent agrees to work hard, and in return the principal agrees to paying a
bonus if the agent works hard. The relationship is terminated should either person
renege. MacLeod and Malcomson (1989) provide necessary and sufficient conditions for
the existence of a high-effort equilibrium in such a contract: it must be the case that the
value of the relationship is strictly greater than the value of their next best alternatives by
an amount exactly corresponding to the value of the penalty P derived above.
This result, in common with much of the literature on repeated games, takes the game
[18]
form as given and then analyzes the set of possible equilibria. These equilibria all
share a common feature, namely in any given period there are a number of possible
equilibria that can be played. Performance incentives are generated by a norm of
behavior (equilibrium play) in which agents agree to move to an equilibrium specifying a
lower payoff to any agent that cheats in the pervious period. The maximum punishment
that can be inflicted upon an individual will therefore depend upon the structure of the
constituent one-stage game. This approach creates a complex relationship between the
structure of the game and the set of possible equilibria. (See in particular Kandori and
Matsushima 1998 and Levin 1998.)
To better understand the role of cognition and contract incompleteness for the structure
of the optimal contract, I have instead assumed that contracting parties have unlimited
punishment ability. The result above illustrates a number of features of relational
contracts that appear to be consistent with observed practice. The first is that the
potential for conflict and disagreement that can generate a cost P, is a necessary
ingredient of any productive relationship when subject evaluations are used and beliefs
are not perfectly correlated. Given that organizational conflict is a ubiquitous
phenomenon, this result is in some sense heartening because it implies that observed
behavior is consistent with this theory! Moreover, as management consultants
emphasize, such conflicts can be reduced when individuals have shared values, and
there is general consensus that the system of evaluation is fair.[19]
Conflict is not the only mechanism that can generate such a cost. When disagreement
results in the termination of a relationship, costs can also arise due to unemployment
(Shapiro and Stiglitz 1984) or the loss of relationship-specific investments (Becker 1975
and Williamson, Wachter and Harris 1975). Other market mechanisms include reputation
effects (Kreps et al. 1982 and Bull 1987), tournaments (Carmichael 1983 and
Malcomson 1984), wages attached to jobs (MacLeod and Malcomson 1988), social
networks (Kandori 1992 and Kranton 1996) and gifts (Carmichael and MacLeod 1997).
In addition, the value of a relationship can be affected by the use of explicit pay for
performance contracts, that can affect the set of self-enforcing agreements, as explored
in Baker, Gibbons and Murphy (1994) and Pearce and Stacchetti (1998).
The common feature of these labor market institutions is that they can be seen as
market responses to the problem of contract incompleteness arising from the use of
subjective evaluation, which in turn is used to induce high performance in the case of ex
post hold-up. This is a distinctively different problem from the standard hold-up model,
whose implications for the theory of the firm have been explored in the work of Baker,
Gibbons and Murphy (1997) and Bolton and Rajan (2000). One suspects that ultimately
a complete theory of the firm will entail an integration of the problems of ex ante and ex
post hold-up.

[15]
From the Revelation Principle (e.g. Myerson 1979) we know that without loss of generality
we can identify the message space with the information that is private to each individual.

[16]
This is a recurrent theme in the theory of incentives. See Green and Laffort (1979) for a
discussion of the early Literature and Moore (1992) regarding the implecations of
implementation theory for contract formation.

[17]
See Schwartz (1992b) and Scott (2000) for discussions of relational contracts that argue
against too much court intervention.

[18]
See Abreu's (1988) seminal contribution characterizing the set of equilibria in a repeated
game, and the survey of cooperation and repeated game theory by Pearce (1992).

[19]
See Milkovich and Newman (1996, chapter 10).
5 Discussion
Contract incompleteness is a ubiquitous phenomenon, yet the welfare theorems of
economics require complete markets and contracts to ensure the existence of an
[20]
efficient equilibrium. Hence, a complete understanding of the efficiency of observed
economic institutions depends upon understanding both why contracts are incomplete,
and the extent to which such incompleteness generates inefficiencies. The traditional
answer to this question follows from the research of Herbert Simon and Oliver
Williamson, who argue that complexity and bounded rationality are the central
ingredients of a complete theory. Yet, as Hart (1990) has argued, complexity
considerations do not play an important role in the determination of the optimal contract
for the hold-up model, a situation that corresponds to non-contractible investment
decisions being made before resolution of uncertainty.
Moreover, there is a growing literature that demonstrates that in many situations
contracting parties choose to write incomplete contracts. When there are costs for
including contract terms, Shavell (1984) argues that in the case of low-probability events
it is cheaper to let courts fill in the gaps. While Dye (1985) explicitly derives the optimal
risk-sharing contact in this case, work that has been extended to dynamic contract
formation by Battigalli and Maggi (2000). The example in section 3 illustrates that costly
contingent contracting is a reasonable hypothesis when performance is multidimensional.
In contrast, Ayres and Gertner (1989) and Bebchuk and Shavell (1991) show that the
presence of asymmetric information may lead individuals to choose incomplete contracts,
even when transaction costs for including additional terms are zero. Bernheim and
Whinston (1998) demonstrate that strategic ambiguity can result in a similar effect.
In contrast, in the case of the hold-up model, renegotiation can introduce inefficiency, as
emphasized by Hart and Moore (1999a). For example, Che and Hausch (1999) show
that renegotiation in a hold-up model with cooperative investments may result in an
optimal contract that is incomplete, but not first best. Segal (1999) shows that one
obtains a similar result when the good being traded is complex in the sense that one
cannot describe the good ex ante, while Schweizer (2000) derives necessary and
sufficient conditions for efficient allocation to be implementable in a hold-up model with
renegotiation. When renegotiation is not possible, Maskin and Tirole (1999a) have
shown that one can achieve an efficient allocation even when the good is not describable
ex ante.[21]
These conflicting results suggest not that incomplete contracts are unimportant, but that
the term itself is possibly too encompassing of the different problems that arise from
contract design. Rather, the main point of the chapter is to suggest that the extent to
which complexity affects the form and efficiency of a contract is very sensitive to the
timing of uncertainty and decision making in a relationship. The problem of ex post hold-
up follows naturally from Simon's model of the employment relationship, and refers to
situations for which it is not possible for an agent to renegotiate her contract between the
time she learns the parameters of her decision problem and the time at which an action
must be taken. The complexity of the environment makes a complete contingent contract
impossible, and hence performance incentives depend upon ex post evaluation and
reward by the principal.
My second point is that the focus upon human cognitive limitations is misplaced. In the
case of ex post hold-up I have argued that the contracting problem is complex in an
absolute sense. That is, complete contracts are physically infeasible, and thus not
dependent upon constraints imposed by (very real) human cognitive limitations. In
contrast, I suggest that the use of subjective evaluation is a way to harness the superior
pattern recognition abilities that humans possess. The quality of the contract in this case
is an increasing function of the correlation between evaluations of the principal and agent.
Finally, I have suggested that the hazard of ex post hold-up, or what the legal scholars
refer to as the problem of relational contracting, can provide an economic explanation for
a number of observed features of the employment relationship. These include the
[22]
importance of corporate culture to ensure employees have a shared set of values, the
use of rankorder tournaments, bonus pay rather than explicit pay for performance, up-
front gifts during recruiting in the form of dinners etc. Though in the end when
appropriate incentives for employer performance do not exist, it may simply be optimal to
[23]
lose one's temper when the boss gives you an unfair evaluation!
[20]
See Magill and Quinzii (1996) for a comprehensive review of general equilibrium theory
with incomplete markets.

[21]
Though Maskin and Tirole (1999a) also show that one can relax the renegotiation
constraint with risk averse agents and the introduction of lotteries ex post.

[22]
See Hermalin (1999) for a review of this literature.

[23]
On the role of emotions and contracts see Hirshleifer (1987), Frank (1988), and Posner
(1997).
Notes
Chapter 13 was originally published as "Complexity and Contract," in Revue d'Economie
Industrielle (92, 2000).

I very much appreciate the comments of the referees, Tom Lyon, Eric Rasmusen,
Sherwin Rosen, Eric Tally, and Oliver Williamson on this work, as well as seminar
participants at the University of California Davis, Stockholm School of Economics,
University of Oslo, University of Bergen, and the Yale Law School. I am also grateful to
Mehdi Farsi for able research assistance. The financial support of National Science
Foundation grant SBR-9709333 is gratefully acknowledged.
1. A. Denning, The Discipline of Law (1979, p. 56). As quoted in Farnsworth
(1990, p. 543).
2. In particular the discussion in section 2.1 of Williamson (1975).
3. See chapter 1.
4. A point that is well appreciated in the computer science literature. See for
example Garey and Johnson (1979). Williamson (1975, p. 23) makes a
similar point in reference to the game of chess.
5. For example, decoding an encrypted message is a computable problem
that it can be achieved in finite time. However, such messages are
believed to be secure because the time required is sufficiently long as to
be impracticable.
6. See Churchland and Sejnowski (1993) for an excellent introduction to
these issues.
7. This was shown in a wonderful paper by Newell, Shaw and Simon (1963).
8. For simplicity, I follow Hart and Moore (1999a) and Maskin and Tirole
(1999a) and assume that the principal has all the bargaining power in
any ex post negotiation. This assumption can be dropped, but at the cost
of unnecessarily complicating the argument.
9. A similar equation is derived by Baker (1992) who works out the optimal
contract when the contractible variable is not perfectly aligned with
benefits.
10. In personal correspondence relating his discussions with Ben Klein and
Earl Thompson, Alchian (1998) observes that many Hollywood contracts
for shows were exactly of this form. An actor or producer on a long-term
contract could entertain outside offers. However, if the studio matched
the offer, the individual had an obligation to stay with his or her studio.
Alchian argues informally that the right of first refusal serves the purpose
of providing incentives for efficient specific investment.
11. See Dekel, Lipman and Rustichini (2001) for an interesting axiomatic
approach to modeling decision-making in complex environments.
12. See Churchland and Sejnowski (1993) for a good review of
computational neuroscience exploring the algorithmic foundations of
human decision-making.
13. See Irrgang (1972, p. 13).
14. Wakefield v. Telecom, 769 F. 2d 109 (20 Cir.), 1985.
15. From the Revelation Principle (e.g. Myerson 1979) we know that without
loss of generality we can identify the message space with the information
that is private to each individual.
16. This is a recurrent theme in the theory of incentives. See Green and
Laffort (1979) for a discussion of the early Literature and Moore (1992)
regarding the implecations of implementation theory for contract
formation.
17. See Schwartz (1992b) and Scott (2000) for discussions of relational
contracts that argue against too much court intervention.
18. See Abreu's (1988) seminal contribution characterizing the set of
equilibria in a repeated game, and the survey of cooperation and
repeated game theory by Pearce (1992).
19. See Milkovich and Newman (1996, chapter 10).
20. See Magill and Quinzii (1996) for a comprehensive review of general
equilibrium theory with incomplete markets.
21. Though Maskin and Tirole (1999a) also show that one can relax the
renegotiation constraint with risk averse agents and the introduction of
lotteries ex post.
22. See Hermalin (1999) for a review of this literature.
23. On the role of emotions and contracts see Hirshleifer (1987), Frank
(1988), and Posner (1997).
Authority, as Flexibility, is at the Core
Chapter 14:

of Labor Contracts
Olivier Favereau, Bernard Walliser
1 Introduction
From an external point of view, the treatment of labor contracts by modern
microeconomic theory reveals an exceptional uneasiness. Either they are entirely
unspecific, similar to sales contracts for a commodity (except that the commodity
consists now of a service, rather than a good stricto sensu): this is the road followed by
general equilibrium theory (see Debreu 1959, §2.4; for more subtle details, see Arrow
and Hahn 1971, pp. 75“6); or they show some specific features, which makes them
instances of more general types of contracts: insurance contracts (see Rosen 1985) or
principal“agent relationships (see Salani© 1994). Indeed lawyers from any country in the
industrial world (see Supiot 1994, part II) could only be surprised by the apparent
reluctance of economic theory to deal straightforwardly with the essential property of
labor contracts: the compliance of the salaried worker with his employer's authority (i.e.
the acknowledged right of giving orders), in exchange for a predetermined wage,
independent for the main part of the final proceeds.

Now the surprise is reinforced, not alleviated, by the fact that there is one “ exactly one “
such model of labor contract, in the economic literature: the one built by Simon (1951).
Of course, some economists were aware that an authority relationship should lie at the
heart of the contractual link between employer and employee (for an early mention, see
Coase 1937). But it was not until 1951 that the first mathematical model of authority
relationship was devised by Simon, drawing on the work of Barnard (1938), an expert in
management and not an academic. What is even more surprising is that this
pathbreaking paper had, to the best of our knowledge, no offspring at all: although
quoted from time to time (Arrow 1974; Williamson 1975; Kreps 1990, 1996; Marsden
1999), it never gave rise to a new strand of literature, in spite of its appeal to realism. So
there is a kind of a puzzle, also from an internal point of view: economic theory is most of
the time silent about the defining feature of labor contracts and when at last a model
appears to deal with that feature, it makes no use of it. It rather follows the opposite path,
by stressing the autonomous behavior of the agent, with respect to the principal!

This chapter tries to offer a partial and tentative answer to the simple question: why is it
so? Our thesis is that the true analytical structure of Simon's labor contract model has
not yet been brought to light. We establish that, in order to prove the efficiency of
employment contracts relative to sales contracts, Simon implicitly used the very
framework Henry was going to use explicitly in 1974 (almost a quarter of a century later!)
in order to measure the "option value," which ought to be integrated to the benefits of
flexible decisions versus irreversible ones. Such an unexpected connection makes it
clear, for the first time, that authority is at the heart of employment relationship because
flexibility is at the heart of authority. We think this could give stronger foundations for a
new way of devising models of labor contracts, more in touch with direct observations.
In section 2, we recall the results of decision theory in the context of irreversible actions
and improving information, by means of a pedagogical model. In section 3, we show,
through the same kind of model, that Simon's comparison between sales and
employment contracts is simultaneously a prefiguration and an extension of these results;
in the concluding section 4, we suggest some possible lines of research, beyond Simon's
model.
2 Decision, irreversibility, and information
A two-period individual decision model combining considerations of flexibility of
investment and acquisition of information was introduced by several authors (Arrow and
Fisher 1974; Henry 1974) and later on nicely formalized (Jones and Ostroy 1984). In the
first period, an available action is more or less flexible (or reversible) with regard to the
actions it permits for the second period; more precisely, a given action is more flexible
than another if the set of actions it allows for the future contains the set permitted by the
other. Between the two periods, the uncertainty on the actions' results is reduced by
additional information, either exogenous or conditioned by the first-period action; more
precisely, a given message is more informative than another if the belief structure it
induces on the states of nature is less dispersed. Since a flexible action is more able to
take into account that information than an irreversible one, it can be shown that the
former is preferable to some extent; a more informative message makes a more flexible
action better under various sets of sufficient conditions.
For instance, a highway may be constructed in a reversible way (option a1), i.e. first
constructed with 2 — 2 lanes and further on widened to 2 — 3 lanes (action b1) or not
(action b2) according to the traffic observed, heavy (state z1) or light (state z2), after
partial realization. It may also be constructed in an irreversible way (option a2), i.e.
immediately and definitely either with 2 — 3 lanes (action b1) or with 2 — 2 lanes (action
b2), traffic being observed afterwards (states z1 and z2 of probabilities p1 and p2) (figure
14.1).




Figure 14.1: Highway construction

The utility of the decision-maker, aggregating the consumer surplus (related only to
traffic) and the investment cost (related to option and action), obeys the following
properties:
1. Constructing 2 — 2 lanes always induces the same costs:


2. Constructing 2 — 3 lanes immediately is less costly than widening from 2
— 2 lanes:
3. For the reversible option, 2 — 3 lanes is better than 2 — 2 lanes with
heavy traffic and reciprocally with light traffic:


4. For the irreversible option, 2 — 3 lanes is better in expectation (only for
convenience):




By using "rightly" (to be explained below) the backward induction procedure (leading to
the double-lined chosen actions on the tree in figure 14.1), the expected utility of each
option can be computed:



The difference between both options can be written as:


The rational decision-maker, maximizing his intertemporal utility, will choose the flexible
(irreversible) option if is positive (negative). Nevertheless, that is not the end of the
story for the economist, even if it is for the (rational) homo oeconomicus. The recourse to
backward induction has a deep analytical meaning, which was not correctly perceived
before Henry as well as Arrow and Fisher (independently) in 1974 revisited the confusing
notion of "option value" introduced ten years earlier by Weisbrod (see Favereau 1989).
Backward induction allows to put to the fore a property of flexible decisions, hidden
under a straightforward translation of expected utility criterion to intertemporal choices,
as in the ususal definition of Net Present Value (see Hirshleifer 1970; Hey 1983; Kreps
1988; Dixit and Pindyck 1994). That property is the ability of flexible decisions to fully
exploit forthcoming information: for instance, in the decision tree associated to our model
(figure 14.1), the decision maker does not know today whether the traffic will be z1 or z2,
but he knows today that he will know it tomorrow. So if he selects the flexible option
today, he is sure to select the best action tomorrow: then backward induction enables
him, at the last choice node, to compute the expected value of a "max," rather than the
"max" of an expected value. That makes a difference, which Henry as well as Arrow and
Fisher showed to be positive, under very general conditions, and which has an
undisputable right to be called an "option value," since it is a supplementary benefit of
flexibility.
Let us compute the "option value" in our model. Using the straightforward expected utility
criterion is equivalent to reverse state ()) and actions (*) for the first option on the tree.
The expected utilities of three plans of action have to be calculated, in order to choose
between the two options:




The difference between both options (usually called "option price") according to the
straightforward criterion of expected utility, can be written as:




The "option value" v is then defined by the difference between the two preceding
comparative results:
The important (and highly intuitive) result is that v is always positive (but of course that is
not true of either or which may be positive or negative): keeping the opportunity of a
flexible action is appreciated in the first period when further information is expected
before the second; in fact, it could be shown that v corresponds to the "value of
information" relative to the (certain) message received as a by-product of the
implementation of the reversible action (Ponssard 1975; Freixas and Laffont 1984;
Conrad, 1980). Last but not least, the reader should take notice of the formal (or
paradoxical) nature of that concept of "option value" (see Favereau 1989): the decision-
maker has not really to compute the option value; he is interested only in the difference
(which is the sum of the option price and the option value).
3 Contract, irreversibility, and information
We suggested, in the introduction to the chapter, that "a situation in which it may be
advantageous to postpone a decision in order to gain from information obtained
subsequently" was examined by Simon (1951) in a context of choice between two forms
of contracts, relating a worker and a businessman. In an "employment contract," the
worker gets a given wage from the employer, but accepts his authority to choose a task
later on from a predetermined set, according to further information the boss will obtain
exogenously about the uncertain result of the task. In a "sales contract," the worker's
task is defined in advance and cannot be changed after it is accepted, but his wage
depends on the specific task and is probably lower on average than before.
Simon's model is very similar to the general framework defined above (the first contract
being reversible and the second irreversible), except that the results of the decision-
making process are evaluated by two players instead of one. For instance, the
employment contract (option a1) and the sales contract (option a2) may be compared for
two tasks (actions b1 and b2) and two states of nature (states z1 and z2). The outcomes
are evaluated by two utility functions, for the employer and worker, respectively, where
each combines linearly the wage (depending on the contract and eventually the task)
and the value attached to the realized task (depending on the task and the state, but not
the contract) (figure 14.2).




Figure 14.2: Simon's model
Contrary to his later and definitive opposition to utility maximization, Simon concludes
that the agents select the best actions by a (backward induction) maximizing procedure;
in fact, he argued later (1978) that utility maximization is not necessary to support his
conclusions, but less restrictive assumptions on agents' behavior are only suggested and
not justified. More precisely, Simon states that in the second period of the employment
contract, a task is chosen according to the employer's point of view while, in the first
period, both types of contracts are compared from a collective point of view summarized
by a collective utility function: U = k2F1(b, z) k1 F2(b, z). It can be shown (more easily
than he does) that all Pareto-outcomes may be generated with the task b maximizing the
collective function. The wage w (assumed here not to depend on b) is variable (just
constrained to give a positive utility to both players) and plays the role of a lateral
transfer determining the distribution of individual utilities:




The further assumptions made by Simon on both utility functions are very similar to the
assumptions made for the highway problem on the unique utility function:
1. holds for each component F1 and F2, hence by combination for the
collective function, but not for each individual one (if w2 + w1)
2. holds with = 0 for each component F1 and F2, hence for the collective
function, but not for each individual one (if w 2 + w1)
3. is stated only for component F1, hence for the employer's utility function
(since the wage is the same)
4. is stated for the collective utility function U.
If the first- and second-period actions were both considered from the employer's point of
view as far as utility is concerned, the employment contract would always be better. In
that case, = p2 2 is always positive because when z1 happens, both options are
equivalent and when z2 happens, option a1 is better than a2. However, since Simon
combines the employer's and the collective points of view, the sales contract may be
collectively better if the worker has a strong enough preference for the first task. In that
case, one computes:



In the first expression of , the first difference is always positive and the second is of any
sign. It expresses the fact that the employment and the sales contract lead to the action
b1 if z1 happens, but to actions b2 and b1 respectively if z2 happens, hence, a1 is better
than a2 if for z2, b2 is collectively better than b1. Moreover, if one puts p2 = 0 in the first
expression and p1 = 0 in the second, the sales contract turns out to be better than the
employment contract under certainty. Finally, the difference (which is the only one
calculated by Simon) is equal to the option value v since the option price is zero
(according to assumption (ii) and (iv), = 0). Hence, Simon implicitly used an option
value, and moreover, in a non-formal way, since the option value had to be effectively
computed in order to choose between the two contracts.

In that framework, Simon demonstrated two important theorems about the theory of
contracts: a qualitative one and a quantitative one. First, should there be no uncertainty
at all, the sales contract would always be optimal; in a world of certainty, there is no
room left for a labor contract as an authority relationship. Second, considering a
continuum of states of nature like Jones and Ostroy, the greater the degree of
uncertainty (appropriately formalized through what is known as a mean-preserving
spread; see Rothschild and Stiglitz 1970), the greater the advantage of the (reversible)
employment contract over the (irreversible) sales contract.
The second result can be illustrated in our example, by considering in our model the
following case for F1 (F2 being unchanged “ and even a constant function for Simon):




with / = p1 / p2
When is fixed (i.e. we arbitrarily choose the task b1 as the benchmark) and and are
increasing, we have a mean-preserving spread since the expected value of F1(b2,.) is
constant, and its variance growing, while F1(b1,.) is unchanged. The first difference in the
first expression of the option value can be directly computed (the second being
unchanged): = p2k2 . Hence, when increases, the option value increases too,
1

which enhances the possibility for being positive, i.e. for the case where the
employment contract becomes optimal. The reader will note the asymmetry in the
increasing risk: the growth of meaning a downward move in the expectation of the
businessman (with respect to the consequences of an inappropriate selection of the task
b1, via a sales contract), our version of Simon's model replicates the "bad news principle"
of Bernanke (1983; see also Dixit and Pindyck 1994, pp. 40“1).
4 Conclusion
When compared to the papers of Henry (1974), Arrow and Fisher (1974), and others, on
irreversibility and uncertainty, which adopt the point of view of a single decision-maker
and put irreversibility (and flexibility, as a consequence) as some material properties of
an investment choice, Simon's contribution derives its originality from the deep collective
meaning of his problem concerning the available actions as well as the pursued
objectives. In the papers by Henry, Arrow and Fisher or later on Bernanke (1983), and
Dixit and Pindyck (1994), the option value originates in technical/environmental features
of a decision an individual has to take: for instance the adaptability of a piece of
equipment (see Stigler 1939, for an early analysis of that kind of flexibility) or, more
plainly, the opportunity of delaying the decision (as emphasized by the analysis of "real
options": see Amran and Kulatilaka (1999)). Moreover, the option value is evaluated only
by that single agent. In Simon's work, it originates in a social construction shaped by two
agents, which enlarges the scope of individual sets of options (actually only the
employer's set of options, but that could be easily generalized by taking into account the
renewal of the employment contract), and is evaluated through a collective utility function.

Simon's contribution is also original by suggesting another argument in the long standing
debate around the relative merits of markets and organizations, considered as
combinations of different forms of contracts. Most current models relate the advantages
of organizations to a few factors: negotiation and transaction costs, information costs and
asymmetry of information, externalities and non-convexities, bounded rationality. Simon
suggests a new argument by considering that organizations, in contexts of uncertainty,
are a means for keeping a large set of possibilities open, and in that sense, appear as
more flexible than the market!

More precisely, the employment contract, i.e. the admission into an internal labor market
with its authority relationship and its binding rules, reveals much more flexibility than the
so-called sales contract, with its typical "take-it-or-leave-it" structure. At first glance, it
may seem surprising that Simon makes the institutional efficiency of organizations
(rather than markets) rest on "flexibility," since markets are usually praised as a symbol
of flexibility, in our deregulating times. There should be no surprise for an economist
paying attention to micro-foundations: flexibility ought to be defined with respect to
actions, not to prices. The ultimate strength of Simon's approach to coordination may be
to give economic meaning to the classical distinction, in social philosophy, between
"constitutive rules" which create new forms of behavior (e.g. the rules of chess) and
"regulative rules" which regulate antecedently given forms of behavior (e.g. the Highway
Code) (Rawls 1955; Searle, 1969, 1999); whereas the "regulative" approach to flexibility
means simply alleviating constraints on existing opportunity sets, the "constitutive"
approach “ exemplified by Simon “ means creating intertemporal devices for enlarging
opportunity sets.
It was objected to Simon's work (Williamson 1975) that the terms of the truce were not
fair, one kind of contract being flexible and the other quite rigid ex definitione. The
objection is correct but it should be appropriately understood, when translated into a new
program of research, beyond the great leap forward prompted by Simon as early as
1951. One obviously needs a truly dynamic framework, in which the two-period situation
of his model would be repeated several times (on an undeterminate horizon) as well as a
richer menu of contracts. But true dynamics should not be investigated where it could not
be found. Without any doubt, it would be extremely fruitful to reconsider the growing
stock of contract models with renegotiation, through the spectacles of "option values"
(see Chaserant 2000, for a promising view of renegotiation along these lines).
Nevertheless, the important point made by Simon would not be affected: flexibility of the
employment contract does not come from any renegotiation of the contract, it comes
from its very application.
Indeed the strongest piece of criticism of Simon's model has a paradoxical flavour: if it
probably overstates rigidity of spot contracts, it also underscores flexibility of employment
contracts. Real-world labor contracts are mostly incomplete, whereas contracts studied
here rely on an exhaustive description of the tasks (for the worker) and the market risks
(for the employer). If anything, the incompleteness of employment contracts will increase
its potential for flexibility, by making it possible for both agents to develop individual and
collective learning. So the main weakness of Simon's model of labor contract is the
absence of learning and this is probably due to the absence of bounded rationality
Note
Chapter 14 was originally published as "La subordination, en tant qu'elle est source de
flexibilit©, est l'essence du contrat de travail," in Revue d'Economie Industrielle (92,
2000).

We thank X. Freixas and C. Henry for their comments on a preliminary version of the
chapter. We are also grateful for the critical remarks of three anonymous referees. Of
course, we claim full responsibility for any remaining errors.
Positive Agency Theory-Place and
Chapter 15:

Contributions
G©rard Charreaux
1 Introduction
One of the most-quoted articles of economic literature, by specialists in organizational
economics or in management sciences - in particular, researchers in finance - is that of
Jensen and Meckling (1976). This article provided the foundations of the positive agency
theory (hereafter PAT), the influence of which extended considerably beyond finance.
From the beginning, it was a part of an ambitious project (Jensen and Meckling 1998)
initiated at the University of Rochester, at the beginning of the 1970s: to build a theory of
organizational behavior based on the actors' rationality assumption, in particular of

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