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See Moe (1984), among many others.
5 Conclusion
This chapter has given a definition of transaction costs which proves to be operational to
adapt standard incentive theory and make it a better tool to describe real-world
institutions and organizations. These transaction costs should be taken as primitives of
the model. These transaction costs create contractual incompletenesses and not the
reverse as often appears in the transaction-cost economic literature. These
incompletenesses of the grand contract leaves scope for further contractings and as a
result various contractual externalities emerge. These externalities, in turn, perturb the
rent-efficiency trade-off of the standard incentive literature. Reduced-form formulae to
analyze these perturbations were given. These forms should be viewed as guidelines for
the modeler facing more complex and probably intractable settings than those described
in this chapter. In those settings possibly multiple contractual incompletenesses may
interact and a reasonable starting point of the economic analysis should be to see how
the various contractual externalities add up and how far away the resulting organization
is from the optimal rent-efficiency trade-off.
The approach followed in this chapter acknowledges some limitations: we did not talk
about the hold-up problem, specific investments, and more generally the derived
property-rights literature àla Grossman and Hart (1986). In our view, the profession as a
whole has somewhat over-emphasized this hold-up problem in the definition of
contractual incompleteness it has tried to come up with over the last fifteen years.
Basically, it has become quite natural in the folklore of the profession to think of this type
of incompleteness as the only possible explanation of organizational forms and authority
structures. This approach may have been relatively successful in explaining firm
boundaries, but we feel less convinced by its insights when it comes to understanding
the internal structure of the firm itself or the design of political constitutions where, clearly,
other contractual incompletenesses which have nothing to do with the hold-up problem
are at work.
The point of this chapter is that some other types of contractual incompletenesses can
still be analyzed with almost standard tools and this kind of analysis is clearly worth
being made in a first step. In a second step, more ambitious work should be devoted to
explaining and endogenizing what we have taken as the primitives of our approach: the
various transaction costs which are the impediments to the use of the Revelation
Principle. This seems an exciting challenge for further research.
Notes
Chapter 10 was originally published as "Transaction Costs in Incentive Theory," in
Revue d'Economie Industrielle (92, 2000). We thank the editor Eric Brousseau for the
opportunity he gave us to participate to this issue. We also thank two referees for their
remarks.
1. See Green and Laffont (1977); Dasgupta, Hammond and Maskin (1979);
Harris and Raviv (1979); and Myerson (1979).
2. See Hart and Holmström (1987b) for survey of these two fields.
3. See Laffont and Tirole (1993).
4. See Laffont and Maskin (1982).
5. See Mirrlees (1971) for his seminal and pathbreaking paper.
6. See Brainard and Martimort (1997), for instance.
7. See Fudenberg and Tirole(1991, chapter 7). Moreover, Myerson and
Satterthwaite (1983) have shown that the Pareto-efficient bargaining
procedures under informational constraints require some allocative
inefficiency.
8. See Cramton, Gibbons and Klemperer (1987), on this point.
9. Here, we have omitted the incentive compatibility constraint of the
inefficient firm and the participation constraint of the inefficient one which
both turn out to be strictly satisfied at the optimum.
10. In the property-rights literature, the debate between Maskin and Tirole
(1999b) and Tirole (1999) and Grossman and Hart (1986) and Hart and
Moore (1999a) also shows that the perfect ability to describe
contingencies and the corresponding payoffs and to perform backward
induction, in other words, unlimited rationality, is enough to recover
efficiency even when no ex ante contract can be written as long as
renegotiation of the revelation games used to implement this outcome is
not an issue.
11. See nevertheless Green and Laffont (1986).
12. See Dalton (1959), Gouldner (1961), and Crozier (1963), among others.
13. See Moe (1984), for instance.
14. See Williamson (1985, chapter 11) for a clear overview of these bilateral
deals and the corresponding contractual externalities.
15. See Wilson (1989), Martimort (1996b), and Dixit (1996), who all argue or
formalize that the difference between public and private bureaucracies
comes from the fact that bureaucrats are controlled by multiple principals
in the former case.
16. See Green and Laffont (1977), and various contributions therein.
17. See Epstein and Peters (1996) for a definition of the set of relevant types
to which the Revelation Principle should apply. This set includes both
physical types and market-like information (the contracts of other
principals).
18. Moreover, the French Code des Contrats, for instance, allows contractual
partners to write a new contract if they wish so.
19. See Dewatripont (1988, 1989), Hart and Tirole (1988), and Laffont and
Tirole (1993, chapter 9).
20. See Beaudry and Poitevin (1993).
21. In both examples above, the loss of control is particularly acute since
there is a multiplicity of "principals of the principal" (voters and
shareholders) who may fail to coordinate in exerting perfect control of the
latter.
22. Note that the assumption of integration is important here, indeed under
non-integration the buyer may not have such a monitoring technology at
his disposal (see Williamson 1985, chapter 4) or even if he has this
monitoring technology, he may not have the auditing rights to use it.
23. See Tirole (1986) for a discussion of this kind of informative signals
which can be concealed but not manipulated by the supervisor.
24. See Williamson (1985, chapter 6).
25. These authors interpret this division of tasks as a separation of powers in
their application of this idea to a regulatory framework.
26. Martimort (1997) applies the same idea and techniques to an instance of
horizontal collusion between workers. This model also endogenizes the
observation made in Laffont and Meleu (1997) that reciprocal deals are
easier to enforce.
27. On this last issue, see Martimort and Rochet (1999).
28. I.e. contracting with the intermediate principal once he has learned some
information on the seller.
29. These latter two authors explicitly model the possibility that the top
principal and the intermediate one may have conflicting preferences on
the sub-set of agents who must definitively produce. This adds a "no-
shut-down" constraint which creates new agency costs.
30. See Spengler (1950).
31. The case of Type 1 externality (see Laffont and Martimort 1997 for a
typology of these externalities in a common agency framework) where Si
(q1, q2) depends on both outputs is fully analyzed by Martimort and Stole
(1999b).
32. Martimort (1998) shows that there exist multiple equilibria in a two-type
model with perfect complementarity as above. We select thereafter the
Paretodominant one. In the case where is a continuous variable,
Martimort (1992, 1996a) and Stole (1990) show also that there exist
multiple ranked symmetric equilibria for imperfect complementarity.
33. In the case of imperfect substitutes, there exists no pure strategy
equilibrium in the two-type model as shown in Martimort and Stole
(1999b). Martimort (1992, 1996a) and Stole (1990) show also that there
exists a unique symmetric equilibrium in the case of substitutes (perfect
and imperfect) with being distributed continuously over an interval. In
the case of a continuous variable, we have ( ) [0, 1] with ( )=0
and defined over the whole interval [ , ] and where is replaced by
the hazard rate of the distribution with F( ) the cumulative distribution
of and F = f.
34. This is the expression coined by Laffont and Tirole (1993, chapter 10).
35. Of course, in such a setting, the objective function of the buyer can be
written as S(q, qe) where qe is the output put on the final market by his
competitor.
36. See Moe (1984), among many others.
Norms and The Theory of the Firm
Chapter 11:
Oliver Hart
1 Introduction
Most standard models of incentives and/or organizations assume that economic agents
are self-interested and must rely on formal contracts enforced by the courts to uphold
their relationships. In reality, of course, many economic transactions are sustained by
self-enforcing ("implicit") contracts, or norms of behavior, such as honesty or trust. An
interesting question to ask is: does ignoring norms/self-enforcing contracts lead to
misleading conclusions? That is, would a theory of incentives or organizations that
incorporated norms look very different from the standard theory?

In this chapter, I will consider this question, focusing particularly on some of the attempts
economists have made in the last ten years or so to integrate norms into the theory of
the firm. I will argue that (a) although norms are undoubtedly very important both inside
and between firms, incorporating them into the theory has been very difficult and is likely
to continue to be so in the near future; (b) so far norms have not added a great deal to
our understanding of such issues as the determinants of firm boundaries (the "make-or-
buy" decision) “ that is, at this point a norm-free theory of the firm and a norm-rich theory
of the firm don't seem to have very different predictions.
3 Modeling difficulties
As I have already noted, theoretical progress on analyzing norms and organizations has
been slow. The main reason is that economists do not have a very good way to formalize
trust. Three main approaches have been tried, and each has significant drawbacks. In
this section I will briefly describe them.
The most commonly used approach is based on the framework of infinitely repeated
games. Although this will be familiar to many, it is probably worth illustrating since I will
use it later on. Suppose that a buyer B and a seller S want to trade a widget each period.
S can deliver a high-quality widget or a low-quality widget; the former has value that
exceeds its cost, while the latter has zero cost and zero value. The quality of the widget
is observable (to B and S), but not verifiable (in a court of law). In a one-shot version of
this game, trade will not occur if the parties are purely self-interested (and hence are not
trustworthy). The reason is that if B promises to pay S as long as S supplies a high-
quality widget, then it is always in B's interest to claim that the widget's quality was low,
whether or not this is true, and, anticipating this, S has no incentive to supply high quality.
(This example is isomorphic to the employer“employee example mentioned earlier.)
If this game is repeated infinitely often, however, trade at the high-quality level can be
sustained. The way this works is (roughly) as follows. B promises to pay S a price P per
period, where P lies between B's value and S's cost, as long as the widget quality is high
in that period (recall that B observes widget quality). In return, S promises to supply a
high-quality widget each period unless in some previous period B has broken her
promise to pay, in which case S supplies low quality forever more.
It is easy to see that these promises are mutually self-enforcing, as long as the parties
do not discount the future too much. The reason is that, while B can gain something
each period by pretending that S's quality is low and withholding payment, this short-
term gain is dwarfed by B 's loss from never receiving a high-quality widget again.
Unfortunately, as is well known, this approach to explaining cooperation or trust runs into
[3]
several difficulties. First, it relies crucially on the assumption that there is no upper
bound to the number of times the game is played. Suppose in contrast that it is known
that the game will not be played more than times. Then, however large is, the parties
will realize that in the last period B will break her promise to pay S (as in the one-shot
game, there is no future to discourage her); anticipating this, S will supply a low-quality
widget in the last period; hence B will have no incentive to pay in the previous period
(she recognizes that this will have no effect on what happens in the last period), etc. In
other words, the self-enforcing contract unravels. The conclusion is that, as in the one-
period model, no trade will take place in any period, however big is.

Unfortunately, the assumption that there is no upper bound to the number of times the
game will be played is hard to square with the fact that people have finite lives.
A second problem with the infinitely repeated game approach concerns the issue of
renegotiation. Suppose B breaks her promise in some period. According to the
equilibrium, S is meant to "punish" B by supplying a low-quality widget forever more (in
effect, no trade occurs). However, by punishing B, S is also punishing himself since he
won't get any payment. The question then is, why don't the parties let bygones be
bygones and reinstate the cooperative outcome? After all, it is not as if S has learned
anything adverse about B. B 's characteristics are known, and the fact that B has broken
her promise today tells S nothing about whether she will do so again.
The trouble is that, if B anticipates that cooperation will be restored after she breaks her
promise, then this increases B 's incentive to break her promise, and cooperation may
not be sustainable. In other words, if the parties are rational enough to realize that they
will renegotiate after a breach, then this may prevent cooperation occurring in the first
place, i.e. the outcome may be as in the one-shot game.[4]
Partly because of these difficulties with the infinitely repeated game approach, another
strand of the literature has instead supposed that the game is played finitely many times
“ t, say “ but that the parties are not perfectly informed about each other: there is
asymmetric information.[5] Suppose, for example, that there is a small probability that B is
someone who always keeps her promises no matter what. (She is "irrational.") B knows
whether she is the rational type or the irrational type, but S does not. Then in the early
stages of the game, B has an incentive to pretend to be the irrational type even if she
isn't, in order to encourage S to trade with her. In fact, it can be shown that, if t is large
enough, then in every equilibrium of the t-period game, cooperation will be sustained
almost all of the time.
The asymmetric information approach has the advantage over the infinitely repeated
game approach in that it does not require an infinite horizon and can deal with the
problem of renegotiation. However, it faces another difficulty. It turns out that the
approach is very sensitive to the precise characteristics of the irrational type, about
which we as modelers know very little. One way to see this is the following. Suppose that
in addition to the irrational honest type there is another "irrational type," who is totally
dishonest but, with some probability, has an irresistible urge to propose an agreement to
trade in any period. Then there is an equilibrium of the following form. The parties do not
trade in any period. The irrational buyer who has an irresistible urge proposes to S that
they should trade: S turns her down because he rationally sees that this type of buyer
will never pay him. The other buyer types propose nothing because there is no point:
they would be confused with the irresistible urge type and thought to be dishonest and
not worth trading with. This way the no-trade equilibrium is sustained however large t is.

The conclusion is that the asymmetric information approach does not provide a very
solid foundation for the idea that cooperation will necessarily occur when play is
repeated many times.
A third approach is to move away from thinking about the trustworthy type as a fringe,
irrational agent and instead to recognize that all agents are trustworthy to some extent.
One way to do this is to suppose that each agent incurs a psychic cost $C if she breaks
a promise, where C is distributed in the population according to a known probability
distribution and a person's C, although known to her, may or may not be known to others.
This approach, like the asymmetric information approach, can explain cooperation in a
[6]
finite horizon model. However, not surprisingly, as with the asymmetric information
approach, its conclusions are very sensitive to assumptions made about the distribution
of C in the population and also about the nature of C “ matters that again the modeler
knows little about. For example, suppose B pays S slightly less than what she promised.
Does she incur the whole psychic cost C or just part of it? Or suppose B promises n
different sellers that she will pay them if they perform well (they are workers, say) and
then simultaneously breaks her promise to them all. Does B incur a total psychic cost of
$C or $nC? The nature of the optimal self-enforcing contract is likely to be very
dependent on these features of the model.
Not only are the asymmetric information and psychic cost approaches quite sensitive to
the precise modeling assumptions made, but also it turns out that these approaches are
not that easy to work with in a contractual or organizational setting. For these reasons,
most researchers have used the infinitely repeated game approach, in spite of its
shortcomings. In what follows, I will do the same. In the next section, I use the approach
to illustrate the effects of self-enforcing contracts on the determinants of firm boundaries.

[3]
For a discussion, see Fudenberg and Tirole (1991, chapter 5).

[4]
To be a bit more precise, suppose that the gains from renegotiation are split in a fixed
(exogenous) way. Then if B gets most of the gains she has a large incentive not to pay S in
any period; while if S gets most of the gains he has an incentive to renounce the self-
enforcing agreement at the beginning of a period (i.e. refuse to supply) and negotiate a better
deal.

[5]
See Kreps et al. (1982).

[6]
See, e.g., Hart and Holmström (1987).
4 Norms and firm boundaries
A good application of norms in the organizational context is to the issue of the
determinants of firm boundaries (the "make-or-buy" decision). Trust helps to sustain
agreements both inside the firm and between firms. An interesting question to ask is:
does trust favor one type of transaction relative to the other?

In the last fifteen years or so a formal literature “ the property-rights approach “ has
developed that tries to explain firm boundaries in terms of the optimal allocation of asset
ownership (see Grossman and Hart 1986 and Hart and Moore 1990).[7] This literature
shares with the earlier transaction cost literature of Williamson (1975, 1985) and Klein,
Crawford and Alchian (1978) the view that firms are important when contracts are
incomplete. It departs from the transaction-cost literature in being more explicit about the
role of decision rights and the link between decision rights and asset ownership.
According to the property-rights view, the owner of a non-human asset has residual
rights of control over the asset, i.e. the right to make all decisions concerning that asset
that have not been specified in a contract or that are not inconsistent with some law.
(When there are multiple owners of an asset or firm, they will typically delegate some of
the residual control rights to a board of directors.) Residual control or decision rights are
like any other good: there will be an optimal allocation of them. For example, suppose
that individuals 1 and 2 are involved in an economic relationship. If it is important to
encourage 1 to make an assetor relationship-specific investment, it may be efficient to
allocate ownership of some key non-human assets to 1. This way individual 1 is
protected to some extent against "hold-up" by 2 since, if the economic relationship with 2
doesn't work out, 1 always has the option to take her assets away and trade with
someone else. However, while allocating assets to 1 protects 1 from hold-up by 2, it has
the opposite effect on 2: since 2 has fewer assets to take elsewhere, 2 is now more
vulnerable to hold-up and so will be less willing to make an assetor relationship-specific
investment himself. Typically it will be optimal to divide the assets between the parties so
that each party has some. If we view each set of assets with a common owner as a firm,
this yields a theory of firm boundaries.

The property-rights theory has in the main been applied to static or one-shot situations
where parties are self-interested and not trustworthy. However, it is natural to ask how
the optimal allocation of assets or firm boundaries changes when norms and trust
operate. Some papers that study this issue include Baker, Gibbons and Murphy (2002)
and Halonen (2000). In what follows I will discuss some of the ideas behind these papers,
using as a vehicle the paper on trucking by Baker and Hubbard (2000) (the Baker“
Hubbard paper is not itself about norms or trust).
Consider a shipper S who at date 0 wants goods shipped from A to B. The shipper hires
a trucker T to do this. The trucker may come with his own truck, in which case he is an
independent contractor, or the shipper may provide the truck, in which case the trucker is
an employee. We will assume that the shipper and trucker can contract on the shipment
from A to B (known as the front-haul), but that they cannot contract on several other
things. First, the shipper may sometimes want the trucker to engage in a back-haul, i.e.
transport a second shipment of goods from B to another destination C. However,
whether there will be a back-haul and its nature “ how valuable the second shipment is,
whether it is easy to transport, and the identity of the destination C “ are variables that
are hard to forecast and become known only when the trucker arrives at B, at date 1, say.
[8]
So contracting about the back-haul must wait until then. Second, the parties cannot
contract on maintenance: how well the trucker drives the truck. The trucker may have an
incentive to drive fast, take time off to visit a friend, and then speed again to reach B; this
may be pleasant for the driver, but is bad for the truck. To make things simple, we will
assume “ at some cost of realism “ that maintenance is observable to the trucker and
shipper but is not verifiable.
Third, the trucker can spend time searching for alternative customers as he drives from A
to B. (He has a mobile phone/access to the internet, etc.) For those searches to pay off
the trucker must be able to drive the truck away at date 1. Some such searches are
productive “ they pay off in the absence of a profitable back-haul from B to C “ but
others are carried out to improve the bargaining power of the trucker when he negotiates
over the terms of the back-haul at date 1. To simplify we will follow Baker“Hubbard in
assuming that all search activities are on average unproductive, i.e. their return is less
than their (effort) cost.
Finally, we will assume that the owner of the truck bears all the increases or decreases
in the value of the truck; he is the residual income claimant. This may seem like a rather
traditional view of ownership, and it is extreme (it rules out value-sharing agreements
between the shipper and the trucker), but it is consistent with the residual control rights
approach in the following sense: the owner has the (residual) right to decide to whom to
sell the truck, when, and at what price. To the extent that the owner can always sell the
truck for 1 (the verifiable price) and at the same time agree to supply another service to
the buyer for an exorbitant price, he can ensure that he never has to share the sales
revenue with anyone else.

The key question is: who should own the truck? In the static or one-shot version of the
model, the trade-off is the following. If the trucker owns the truck he will maintain it (he
bears the value consequences), but he will engage in search or rent-seeking activities
(as owner of the truck, he can exploit these activities since he has the right to drive away
the truck at date 1). On the other hand, if the shipper owns the truck, the trucker will not
maintain it at all (he does not bear the value consequences), but neither will he engage
in rent-seeking activities (these do not pay off given that the trucker does not have the
right to drive the truck away).
To simplify matters, I will assume that in the one-shot model encouraging maintenance is
more important than discouraging rent-seeking and so it is best for T to own the truck, i.e.
T should be an independent contractor rather than an employee. To the extent that S
owns other assets than the truck and T doesn't, I will refer to this arrangement as "non-
integration," and to the arrangement where S owns the truck (and therefore has all the
assets) as "integration."

So far we have analyzed asset ownership or firm boundaries in a trustless environment. I
now want to ask the following question: how does trust affect the boundaries of the firm?
To the extent that there is a conventional wisdom on this matter, I suspect that it is that
an increase in trust will make it more likely that the parties will "use the market," i.e.,
choose to be independent (non-integration) “ and to be linked by a relational contract “
rather than to become one firm (integration). This conventional wisdom can probably be
traced to the fact that transaction-cost economics (TCE) tends to see the market as the
first choice if it is feasible, and in a high-trust environment it is likely to be feasible.
To analyze this choice more formally, let us proceed as in section 3 and suppose that the
relationship between S and T is repeated infinitely often and that both parties discount
the future at the common discount factor , where 0 < < 1. We are led to consider the
following self-enforcing contract: T promises to maintain the truck well and to engage in
minimal rent-seeking activity (search). In return, S promises a fixed payment P per
period. The self-enforcing contract is sustained as follows: if either party breaches, we
revert to the equilibrium of the one-shot game described above forever more. (In contrast
to section 3, this equilibrium involves some trade rather than no trade.) We will also
suppose (following Baker, Gibbons and Murphy 2002, but in contrast to Halonen 2000)
that ownership of the truck can be transferred at this point, i.e. if S owns the truck T will
buy it. (Recall that, given our assumptions, it is efficient for T to own the truck in the one-
shot game.)
Note that = 0 corresponds to the one-shot game, since, if the future does not matter at
all, no cooperation can be sustained. At the other extreme = 1 corresponds to the case
where trust can easily be sustained since the future overwhelms the present in
importance. Thus an increase in can be interpreted as a move to a higher-trust
environment.
Thus the question: how does trust affect asset ownership or firm boundaries? can be
rephrased as: how does an increase in affect asset ownership or firm boundaries?
The answer is that it all depends: an increase in does not have a clear-cut effect on
the choice between integration and non-integration (see Baker, Gibbons and Murphy
2002). To see why, note that an increase in improves all organizational forms. If is
close to 1, the first-best “ where T maintains the truck well and does not engage in rent-
seeking “ can be sustained under a self-enforcing contract whether S owns the truck or
T does. The reason is that no one wants to breach a self-enforcing contract since the
future gains from cooperation are so large relative to the short-run gain from breaching.
On the other hand, if is close to zero, then non-integration is best (given our
assumptions). This suggests that there is no simple monotonic relation between optimal
organizational form and the discount factor .
Specifically, it is easy to construct cases where integration is superior to non-integration
when is fairly close to 1, even though non-integration is superior to integration when
is close to zero. (Such cases turn the conventional wisdom on its head “ a higher-trust
environment favors large firms.) To see why, suppose that the cost of maintenance is
very low but the value is very high. In the static model (one-shot game), there will be no
maintenance under integration, which is highly inefficient. But in the dynamic model it is
easy to get maintenance by offering T a small bonus if he looks after the truck. Since the
bonus covers his (small) cost, T will maintain the truck as long as he expects to receive
the bonus; and S will pay the bonus since, given that it is small, there is little gain from
not doing so. Finally, there is no incentive for T to engage in rent-seeking under
integration since he can't drive away with the truck. So in this case the first-best can be
achieved under integration in the repeated game even for moderate discount factors .
In contrast, under non-integration, while T will maintain the truck (as in the static model),
he may need quite a large bonus from S to be deterred from engaging in rent-seeking
behavior; but the promise of a large bonus gives S a strong incentive to breach. Hence it
may be impossible to sustain the first-best under a self-enforcing contract for moderate
levels of when T owns the truck.
Note that, in spite of what I earlier called the conventional wisdom, there is some
evidence that trust does indeed favor large firms rather than small ones; on this, see La
Porta et al. (1997) and Kumar, Rajan and Zingales (1999).
It should be emphasized that, while in this example non-integration is optimal when is
small and integration is optimal when is large, it is easy to construct another example
based on the same model that yields the opposite conclusion.
I think that the correct conclusion to draw from this discussion is the following. The
boundaries of the firm will be drawn to elicit appropriate actions from the parties “ in this
case, truck maintenance and (absence of) rent-seeking. In broad terms the choice
between the two organizational forms will depend on the importance of these goals and
the ease with which they can be achieved. It is easier to encourage maintenance if T
owns the truck and to discourage rent-seeking if S does. This is true both in the static
model and the repeated game. Thus in qualitative terms trust does not change things
that much.[9]

[7]
For a summary of this literature, see Hart (1995).

[8]
For a formal justification of the idea that, when the future is uncertain, many aspects of a
contract will be negotiated ex post rather than ex ante, see Hart and Moore (1999a).

[9]
A possible qualification should be noted. In the static models of Grossman and Hart (1986)
and Hart and Moore (1990), joint ownership of an asset is never optimal. In contrast, the
repeated game model described in this section can explain joint ownership of an asset if it is
supposed that ownership of the asset cannot be transferred after the breach of a self-
enforcing contract (see Halonen 2000). The reason is that, since joint ownership is sub-
optimal in the static model, the threat of it can support cooperative behavior in the dynamic
model. Note, however, that joint ownership can be optimal in more complicated versions of
the static model, where it is important to discourage rent-seeking behavior of both parties (see,
e.g., Rajan and Zingales 1998). (If neither party can walk away with the asset, then each
party's incentive to search for alternative trading partners is reduced.) Thus in fact joint
ownership (or joint ventures) can be explained both in the static (no-trust) model and in the
dynamic (trust) model.
5 The role of formal contracts
So far I have discussed the role of norms in situations where the opportunities for writing
formal contracts have been quite limited. In section 3 formal contracts were impossible
and in section 4 the only formal contracts concerned the allocation of asset ownership
and spot (one-period) deals between S and T.
In this section I will make some brief remarks about the general impact of formal
contracts on the sustainability of self-enforcing contracts, and mention one implication for
judicial attitudes toward firms. Formal contracts have at least two effects on self-
enforcing contracts. First, the better formal contracts are, the smaller is the surplus
remaining for the parties to try to exploit via a self-enforcing contract. This reduces the
incentive of parties to breach a self-enforcing contract, since, given that there is less at
stake, the gains from opportunistic behavior are lower. Second, however, if a self-
enforcing contract is breached, the penalty is also lower since the parties can always rely
on formal contracts in the post-breach, no-trust environment; as a result, as argued by
Baker, Gibbons and Murphy (1994), the incentive to breach may rise.

Because these two effects are opposing, it is hard to draw clear-cut conclusions about
whether formal contracts will make it easier to sustain self-enforcing contracts (i.e. formal
and informal contracts are complements), or more difficult (i.e. formal and informal
contracts are substitutes). Which way it goes would seem to depend on the
circumstances.
In their interesting recent paper, Rock and Wachter (2001) take the position that one
would expect to see few formal contracts inside the firm given the concentration of
residual control rights in the hands of one party (the board of directors): rather the firm is
[10]
a place where informal agreements will flourish. My interpretation of (one part of) their
argument is that it is hard to imagine two divisions of a firm being bound by a formal
contract. The reason is that either party can be prevented from fulfilling the contract by
the board of directors, who can always ex post deny the members of the divisions
(including the division heads) access to key non-human assets or key decision-making
authority. Division members are unlikely to be prepared to enter into formal agreements
which require them to pay damages in the event of breach, given that they have so little
power to ensure that these agreements are implemented.
Not only do Rock and Wachter provide a persuasive argument as to why formal
contracts may be difficult to sustain inside the firm, but also the discussion of this section
suggests a reason why formal contracts may be undesirable even if they are feasible:
they may in some cases make it harder to sustain self-enforcing contracts (the case of
substitutes described above). This may provide some justification for the view that the
courts should be hesitant to intervene in the firm's informal business; that is, they should
take a hands-off attitude even in cases where they have the ability or expertise to
intervene.

[10]
A related, but distinct, idea is that firms will arise in situations where it is important to
suppress individual incentives and foster cooperative behavior. (See Holmström 1999.)
6 Summary and open questions
In this chapter, I have argued that it has been difficult to incorporate norms into the
theory of organizations; and also that, although there has been some interesting recent
work on this topic, this work has not to date greatly changed our views about the
determinants of organizational form.
I want to conclude by making a further qualification about the material discussed above.
The infinitely repeated game models of sections 3 and 4 are really models of individual
reputation or trustworthiness. That is, while it is tempting to think of the buyer and the
seller in section 3, and the shipper in section 4, as representing firms, an extra step is
really required for the argument to work. This step involves explaining why a particular
set of norms or reputation is associated with a firm or organization rather than with an
individual or set of individuals who work there.

To put it in stark terms: what ensures that, when the CEO of a company that is known for
high trust leaves, the high-trust reputation doesn't go with her? Somehow there has to be
some stickiness in the firm or system, so that a firm's reputation can be separated from
that of key personnel. To put it another way, a firm's reputation has to have some of the
characteristics of a non-human asset. However, exactly how this comes about is far from
obvious.

One attempt to explain how a reputation can be embodied in a firm rather than a set of
individuals is contained in a paper by Tadelis (1999).[11] Tadelis considers the
relationship between a firm and its consumers. Think of the way a firm treats its
customers, e.g. the way it services its product, as a norm. Tadelis assumes that every
consumer observes this norm, i.e. they know how past customers have been treated, but
that consumers do not know who owns (or manages) the firm. If ownership changes,
customers do not see this and so assume that the firm will continue to treat its customers
in the same way. As a result a firm that has treated its customers well in the past will
have a valuable reputation: moreover, outside buyers may be prepared to pay a lot for
this reputation since at least in the short run “ until and unless they show that they
cannot maintain the reputation “ they can charge more for their product than if they
started from scratch (without a reputation).

The Tadelis model provides a useful starting point in helping to understand why a firm's
intangible assets can be valuable. However, the idea that a firm's reputation matters only
when (a significant fraction of) consumers cannot observe a change in ownership is not
that plausible. It is to be hoped that in the future it will be possible to relax the
informational assumptions of the model. For the moment the creation of a theory of
norms attached to a firm or organization seems an even more challenging goal than the
development of such a theory for the case of an individual.

[11]
For earlier work, see Kreps (1990) and Tirole (1996).
Notes
I would like to thank Antoine Faure-Grimaud, Bengt Holmström, Matthew Rabin, and
Andrei Shleifer for helpful discussions and the National Science Foundation for financial
support.
1. For a discussion of the implications of transaction costs for contractual
relationships, see, for example, Williamson (1975).
2. But see Fehr and G¤chter (2000) for a discussion.
3. For a discussion, see Fudenberg and Tirole (1991, chapter 5).
4. To be a bit more precise, suppose that the gains from renegotiation are split in
a fixed (exogenous) way. Then if B gets most of the gains she has a large
incentive not to pay S in any period; while if S gets most of the gains he has
an incentive to renounce the self-enforcing agreement at the beginning of a
period (i.e. refuse to supply) and negotiate a better deal.
5. See Kreps et al. (1982).
6. See, e.g., Hart and Holmström (1987).
7. For a summary of this literature, see Hart (1995).
8. For a formal justification of the idea that, when the future is uncertain, many
aspects of a contract will be negotiated ex post rather than ex ante, see Hart
and Moore (1999a).
9. A possible qualification should be noted. In the static models of Grossman and
Hart (1986) and Hart and Moore (1990), joint ownership of an asset is never
optimal. In contrast, the repeated game model described in this section can
explain joint ownership of an asset if it is supposed that ownership of the
asset cannot be transferred after the breach of a self-enforcing contract (see
Halonen 2000). The reason is that, since joint ownership is sub-optimal in the
static model, the threat of it can support cooperative behavior in the dynamic
model. Note, however, that joint ownership can be optimal in more
complicated versions of the static model, where it is important to discourage
rent-seeking behavior of both parties (see, e.g., Rajan and Zingales 1998). (If
neither party can walk away with the asset, then each party's incentive to
search for alternative trading partners is reduced.) Thus in fact joint ownership
(or joint ventures) can be explained both in the static (no-trust) model and in
the dynamic (trust) model.
10. A related, but distinct, idea is that firms will arise in situations where it is
important to suppress individual incentives and foster cooperative behavior.
(See Holmström 1999.)
11. For earlier work, see Kreps (1990) and Tirole (1996).
Allocating Decision Rights Under
Chapter 12:

Liquidity Constraints
Philippe Aghion, Patrick Rey
1 Introduction
The debate on the foundations of incomplete contracts had focused essentially on the
Grossman-Hart (1986) framework, in which actions (in that case, trade versus no-trade)
are assumed to be ex ante non-describable but ex post verifiable. This class of
incomplete contracts models focuses on how ownership allocation affects ex ante
investments through its impact on the ex post bargaining between the contracting parties;
since actions are verifiable, this bargaining is always ex post efficient so that the main
source of inefficiency lies in the non-verifiability of ex ante investments. In this framework,
Maskin and Tirole (1999a) shows that message games played ex post can often be used
to circumvent the ex ante non-contractibility and even the non-describability of actions
and states. A main response to this criticism (see Segal 1999, Hart and Moore 1999a,
Maskin and Tirole 1999b) has been to add renegotiation and complexity considerations,
in order to generate optimal mechanisms that can be easily interpreted as ownership and
control allocations.
Another set of incomplete contracting models, starting with Aghion and Bolton (1992),
focuses instead on ex post inefficiencies resulting from the non-contractibility of actions,
combined with additional limitations on the ability to induce ex post efficient action choice
through adequate transfers to the controlling party. In Aghion and Bolton (1992)
(hereafter, AB), what limits the scope for ex post efficiency is the wealth constraint faced
by the entrepreneur whenever the outside investor is in control (which prevents the
entrepreneur from inducing the first-best action choice from the investor), together with
ex ante participation constraints which can make it non-feasible to allocate full control to
the entrepreneur (and then let the unconstrained investor make the ex post monetary
transfers to induce efficient action choice). In Aghion and Tirole (1997) and the
subsequent literature on authority, what prevents achieving ex post efficiency is the non-
responsiveness of the agent to monetary incentives.[1] Now, as Maskin and Tirole did for
the Grossman-Hart paradigm, one can also question the robustness of the control
allocations in AB or Aghion and Tirole (1997) to introducing message games and optimal
implementation mechanisms.
The main point of this chapter is to argue that there is no need to introduce complexity
considerations in order to provide suitable foundations to this second class of incomplete
contract models: that actions are ex post non-verifiable is sufficient. This non-verifiability
assumption, together with the restrictions already introduced on the set of ex post
feasible transfers, will often suffice to guarantee the optimality of control allocation
contracts even when revelation mechanisms are allowed. This issue had already been
discussed in the appendix to AB, but there the actions were implicitly assumed to be ex
post verifiable and only Nash-implementation was being considered. Here, we analyze
the extent to which ex post non-verifiability, combined with wealth constraints, limit the
power of message games.
We consider a contracting problem between two parties who must decide about a future
course of action which is ex post non-verifiable and generates non-verifiable payoffs to
both parties. After the initial contract has been signed, the two parties negotiate ex post
over the ultimate choice of action in a Nash-bargaining game in which one party can use
monetary transfers in order to influence the ultimate action taken by the controlling party.
While AB restricts attention to the case where only one party is liquidity constrained and
where that same party has all the bargaining power ex post, the present chapter
considers more general configurations of wealth and bargaining power distributions.
More specifically, we show that when actions are non-verifiable, the optimal contract
consists essentially of a control allocation, together with an initial monetary transfer from
one party to the other; in particular, revelation mechanisms have no bite, as there is
nothing to reveal before the negotiation stage, and once ex post bargaining has fixed the
choice of action, nothing "real" can be offered to reward information (monetary transfers
do not suffice to reward information in an incentive-compatible way). Our framework thus
provides simple foundations to control allocation contracts in a framework à la AB.
As in AB, the optimal allocation of control is indeterminate when agents are risk neutral
and have deep pockets, but it matters when at least one party faces wealth constraints;
who should get control ultimately depends upon how wealth constraints and relative
bargaining powers affect both ex ante participation and ex post efficiency in the choice of
action. We argue that ex post efficiency is easier to achieve when control is allocated to
the poorer party, whereas ex ante participation may require giving control to the
wealthier party. In addition, our discussion suggests that both ex post efficiency and ex
ante participation considerations dictate that control would be optimally allocated to the
party with the lower bargaining power.
The chapter is organized as follows. Section 2 outlines a simple contracting model with
ex post non-verifiable actions, and establishes that the optimal contract boils down to a
simple control allocation together with an initial monetary transfer from one party to the
other. Section 3 explores how wealth constraints and relative bargaining powers affect
the optimal allocation of control, emphasizing the interplay between ex post efficiency
and ex ante participation considerations. Finally, section 4 concludes by suggesting
avenues for future research.

[1]
Closely related to AB is the paper by Dewatripont and Tirole (1994), which includes an effort
variable before the non-contractible action is chosen and investigates the ability of the action
to provide effort incentives.
2 The basic framework
2.1 Preferences and actions
Two parties, 1 and 2, can together run a project which requires the choice of an action, a,
among a possible set of feasible actions . Each party i has an initial
wealth wi, a reservation level of utility Bi, and derives a private benefit bi (a) from the
chosen action. Party i has utility:

where mi denotes the net wealth of i. The potential conflict of interest between the two
parties is simply captured by the assumption:
A1: b1 and b2 are respectively decreasing and increasing in a.
That is, party i's preferred action is ai. In addition, we suppose that b1 and b2 are both
concave in a and that the Pareto-efficient action (assuming that transfers are feasible),
denoted by a* and defined by:

1 2
lies strictly between a and a . We also assume that the project is ex ante viable:


The following notation will be useful:
for i, j = 1, 2, bij bj (ai) and bi bi1 + bi2
for j = 1, 2, b*j bj (a*) and b* b*1 + b*2

Assumption A1 then implies that:


2.2 Contracting
If the action could be contracted upon and transfers were not limited by wealth
constraints, the two parties could run the project and contract on a = a*, together with an
initial transfer that would guarantee that both parties' participation constraints are
satisfied. In the remaining part of the chapter, we shall concentrate on the case where:
A3: The action and private benefits are ex post non-verifiable by any third party.

We shall however assume that the parties can contract on who will choose the action,[2]
as well as on monetary transfers.
Since a party's preferred action is inefficient, the parties have an incentive to renegotiate
and exploit the potential for residual Pareto-improvements. As the ultimate choice of
action is not verifiable by assumption A3, the extent to which the parties might be able to
reach a more efficient agreement will depend upon the economic environment
(frequency of interactions, reputation and credibility, information, lags between action
choices and payments, etc.). As in AB, we shall assume that, ex post, the two parties
can credibly trade a change in the action plan against a monetary transfer. We do not
wish to argue here that this assumption is always relevant but rather, explore its
implications for the design of the original contract. Aghion, Dewatripont and Rey (2000)
analyzes situations where instead the two parties cannot credibly alter the choice of
action through non-contractible bilateral negotiations.
Finally, we shall be interested in simple contracts that stipulate a transfer t0 between the
two parties, together with an allocation of decision rights on the choice of action; the next
sub-section establishes sufficient conditions under which such contracts are weakly
optimal. There are two possible allocations of control rights: to party 1 (" = 1") or to
party 2 (" = 2"). In particular, contracts cannot affect the bargaining powers in the
renegotiation game, but only the starting point of the renegotiation: this status quo is of
the form (a, t = t0), where a is the preferred action of the party who has the decision right;
i
thus, a = a if = i. In addition to setting the starting point of the negotiation, the initial
contract can also stipulate a mechanism (e.g. a revelation game) to be implemented
once the negotiation has taken place.

2.3 Renegotiation game
We assume that the outcome of the negotiation is given by the generalized Nash-
bargaining solution, with bargaining powers 1 and 2( i 0, 1 + 2 = 1) for the two
parties; that is, starting from a status quo , and assuming that the set of transfers is
, the outcome of the negotiation is given by[3]:
restricted to



2.4 Timing

The timing of events can be summarized as follows:
First, the two parties sign an initial "contract," which can specify (a lottery
over) control rights[4] and initial transfers, and decide whether or not to
run the project; if they have agreed to run the project, then
Second, they "negotiate" the eventual choice of action, together with
additional transfers;
Lastly, they implement any additional mechanism stipulated in the initial
contract.

[2]
In Aghion, Dewatripont and Rey (2000), we refer to this type of actions as actions with
contractable control, in contrast to non-verifiable actions over which the allocation of control is
not-verifiable, although control may can be credibly transfered from one party to the other.

As suggested by Bengt Holmström, one can interpret control allocation as giving the
"key" to access a room, and where only those who enter the room can observe the
action to be taken there. Control allocation (who gets the key) can then be verifiable,
even though the choice of action is not.

[3] 0
Note that t refers to the overall net transfer, not to the additional transfer t t negotiated on
0
top of the initial transfer t .

[4]
While allowing lotteries (e.g. random control allocations), we shall assume that the outcome
of such lotteries is realized before the negotiation starts.
3 The optimality of "decision-rights" contracts
3.1 Benchmark case: no wealth constraint
In the absence of wealth constraints (when both w1 and w2 are large), ex post negotiation
leads to the efficient action choice a* no matter what the initial allocation of decision
rights: if the initial contract ( , t0) is signed in the first stage, the outcome of renegotiation
is given by the solution to


and is thus characterized by a = a* and by a net transfer t*( , t0) such that:

The final levels of utility u1( , t0) and u2( , t0) are thus respectively equal to:



Ex ante participation by party i then requires:

Since the project is viable by assumption A2, for any {1, 2} there exists an initial
transfer t0( ) such that the two individual rationality constraints are simultaneously
satisfied. The allocation of decision rights thus does not play any prominent role in the
absence of wealth constraints.

3.2 Simple contracts under wealth constraints
We now reintroduce wealth constraints (wi small for at least one party i) and establish the
optimality of control allocation contracts. Since contracts cannot affect the "rules" of the
bargaining but only its starting point, there is little room for contracts more sophisticated
than a simple "decision-right" contract of the form ( , t0), that simply allocates the right to
choose the action and stipulates a monetary transfer. In particular, there is nothing to
"reveal" before ex post bargaining takes place; and once ex post bargaining has fixed
the choice of action, any subsequent revelation game would be a constant-sum game
and therefore could not implement anything but a mere transfer, independent of the
[5]
action chosen. The parties might however wish to alter the outcome of the
renegotiation game, and can do so by restricting the set of admissible transfers (beyond
the restrictions already implied by wealth constraints). However, this is not the case
when for example they wish (and are able to) reach ex post efficiency:
Proposition 1


a. There is no loss of generality in restricting attention to lotteries over
contracts ( , t0, T) that simply: (i) allocate the control right to one
party ( = 1 or 2); (ii) stipulate an initial transfer t0; and (iii) restrict
the set of final transfers to T ( t0).
b. Moreover, there is no loss of generality in restricting attention to
lotteries over "simple contracts" ( , t0) that only allocate the control
right to one party ( = 1 or 2) and stipulate an initial transfer t0, when
either of the following conditions holds:
i. benefits are twice continuously differentiable and the parties
focus on ex post efficiency,
ii. limiting the set of transfers at the ex post negotiation stage
can only hurt both parties.




Proof: (a) The optimal contract generates (possibly randomly) a starting point ( , t) for
the negotiation stage and a "game" to be played after the negotiation stage to determine
the final transfer. The rules of this game can depend explicitly upon the transfer
[6]
negotiated by the parties but not upon the negotiated action since it is non-verifiable
(the strategies may however depend both on the action and the transfer); we denote this
game by G (t). Since no information arrives before the negotiation stage, there is clearly
no loss of generality in directly setting ( , t) as the starting point of the negotiation and
making the parties play G (t) after the negotiation stage. We shall denote by
the equilibrium strategies of this game and by
the transfer that is finally implemented when the
outcome of the negotiation stage is (a, t).
The equilibrium transfer clearly cannot depend on a. To see this, first note that,
necessarily, for any a and a :



The first inequality stems from the fact that by definition party 2 prefers playing
rather than in the equilibrium that follows the negotiation outcome (a, t),
whereas the second equality stems from the fact that party 1 prefers to
in the equilibrium that follows the negotiation outcome (a , t). Similarly,

where the first inequality stems now from the fact that party 2 prefers to
in the equilibrium that follows (a , t), whereas the second equality stems from the fact
that party 1 prefers to in the equilibrium that follows (a, t). Combining
the two sets of conditions yields .
It follows that the equilibrium transfer depends only upon the negotiated transfer.
Denoting by this function, the negotiated outcome (a, t) is then determined as the
[7]
solution to the program :



which is equivalent to max


with and . Therefore, the same
equilibrium outcome could be achieved with the simple contract ( , t0, T ).
(b) Part i. Let denote the outcome of the renegotiation when it
1 2
starts from a status quo (a = a or a , t0) and transfers are restricted to t T, and Tw
[ w2, w1] denote the unrestricted set of transfers (apart from the wealth constraints). It
suffices to show that for any ( , t0, T) such that , then
.
Consider therefore a contract ( , t0, T) leading to . Note first that
is a solution to the first-order condition:[8]

Differentiating this condition with respect to a and t yields:



where both the coefficients of dt and da are strictly negative. Hence, an agreement will
be reached on a* only if the negotiated transfer is . Now, consider the
outcome of the negotiation without any restriction on the set of possible transfers (that is,
T = ); since in this case negotiation induces an efficient choice of action (a = a*), it
must therefore induce a negotiated transfer, equal to . That
is, solves:


But then, since: , we necessarily have: .
Part ii. It suffices to note that, for a given starting point ( , t0), restricting the set of
transfers T can lead only to a Pareto-inferior outcome. More precisely, denoting by
the solution to the program:


and by (a, t) the solution to the program:


it is necessarily the case that (a, t) Pareto-dominates if T [ w2, w1] since the
function that is maximized is increasing in both parties' payoffs, b1(a) t and b2(a) + t.
Therefore, without loss of generality we can restrict attention to lotteries over simple
options of the form ( , t0).
Proposition 1 asserts that there is no loss of generality restricting attention to simple
contracts when the parties focus on ex post efficiency (and private benefits are smooth),
or when restricting transfers hurts both parties. When private benefits are "smooth" (i.e.
twice continuously differentiable), starting from an initial contract ( , t0) the outcome of
the ex post negotiation is efficient (a = a*) if and only if t*( , t0), defined by (1), is feasible.
Any binding restriction thus involves a loss of efficiency. However, restricting transfers
may still enhance one party's bargaining strength; that is, the outcome of the restricted
negotiation is always less efficient but can be more favorable to one of the two parties. In
that case, restricting transfers sacrifices ex post efficiency but may help meeting one
party's participation constraint, as shown in the following example.[9]
Example 1


The two parties are respectively a wealthy buyer (wB > 0) and a poor seller (wS = 0) who
a2
must agree on a level of trade a [0, 1]. The buyer's valuation is v(a) = a /2, while the
a2
seller's cost is c(a) = /2. Their utilities are thus respectively equal to: B = v t and S = t
c; the two parties have equal bargaining weights ( = = 1/2) and reservation levels B >
1 2

0 and S = 0. First-best efficiency is achieved for a* = 1/2, while wealth constraints imply t
0.




To fix ideas, suppose that the status quo is = S (and thus a = 0) and t0 = 0; then the
outcome of the negotiation without transfer restriction, is:

Any larger transfer t0 > 0 to the seller can only lead to a lower equilibrium utility for the
buyer. If instead the transfers are restricted to t 7/54, the outcome is
. That is, restricting the transfers from the
buyer to the seller reduces trade efficiency but increases the utility that the buyer gets
out of the negotiation. Thus, the parties may find it mutually profitable ex ante to restrict
the set of feasible transfers if for example the buyer's reservation utility B lies between B
* and .
An alternative would be to allocate control to the buyer ( = B); together with an initial
transfer t0, it will lead to efficiency only if the outcome is the same as with no restriction
on transfers: a = a* and a net transfer t given by (1), that is here: t = t0 1/4. Therefore,
in order to reach efficiency, the initial transfer t0 must be sufficiently large, namely such
that t = t0 1/4 0, or t0 1/4. To be acceptable to the seller, the initial transfer t0 must
be even larger and satisfy t c* = t0 3/8 0, or t0 3/8. Conversely, in the absence
of contractual restrictions on transfers, any initial transfer t0 < 1/4 leads the seller to "buy-
back" as much reduction in a as possible (i.e. the net transfer is t = 0) and thus gives the
seller a negative utility ( c(a) < c* < 0).
Therefore, if (i) the buyer 's reservation B utility lies between B * and and (ii) the
buyer's wealth is too small (wB 3/8), then there is no contract without restrictions on
transfers that is acceptable by both parties, whereas there exist contracts that further
restrict transfers (e.g. = S, together with restrictions t 7/54 that are acceptable by
both parties, even though they do not yield ex post efficiency.[10]
In what follows, we shall mostly focus on situations where either utilities are smooth and
the parties want to reach efficiency (a = a*) or relaxing constraints on transfers at the ex
post negotiation stage benefits both parties. In both cases, without loss of generality we
can restrict attention to simple contracts of the form ( , t0).

[5]
The situation would be different if for example subsequent actions had to be taken and the
ultimate outcomes depended jointly upon all actions. Then, allocating future decision rights on
the basis of reported actions might allow the parties to reveal their first choice of action - see
Aghion, Dewatripont and Rey (2000).

[6]
Yet the two parties' strategies in this game may depend upon the negotiated action and also
upon the negotiated transfer.

[7]
We assume that any restriction on transfers binds at every stage of the implementation of
the contract. The reasoning still holds if the restriction only applies to the transfers that are
finally agreed to.

[8]
Given the negotiated transfer t = , reaching requires an
interior solution, which must therefore satisfy this firstorder condition.

[9]
When private benefits are not continuously differentiable, restrictions on transfers may still
be required to satisfy participation constraints without necessarily inducing a loss of efficiency
(see example 2 below).

[10]
More precisely, ex post efficiency could be achieved (e.g. with = S, t0 = 0) if 1/4 wB <
1/2, whereas no contract can induce efficiency if wB < 1/4. In both cases, however, meeting
both parties' participation constraints requires = S, together with additional restrictions on
transfers, of the form T = [0, t], with t [0, t] with t [7/54, wB).
4 The determinants of control allocation
As pointed out in AB, wealth constraints raise two types of issues: they limit the
efficiency of the ex post negotiation game and make it harder to meet one party's
participation constraint ex ante. We consider these two problems in turn.

4.1 Limited wealth and ex post negotiation
In this sub-section we focus on the choice of action that results from ex post Nash
Bargaining and abstract from ex ante participation considerations (assume, for example,
that B1 > b21 and B2 > b21). We first stress that when parties differ in their initial wealth,
giving control to the poorer party enhances the efficiency of the negotiation stage.
To see this, suppose first that one party, say party 2, has very little wealth (w2 ! 0),
whereas the other party is unconstrained (w1 large). Then, allocating control to the poor
party (party 2) leads to the first-best action a*, since it is always in the interest of the rich
2
to compensate the poor for moving from a to a*. That is:


On the other hand, if control rights are allocated to the rich party (party 1), then the
ultimate choice of action will be a1 since party 2 lacks the resources needed to convince
party 1 to move away from her most preferred action. More generally, achieving
efficiency requires giving control to the poorer party whenever the initial wealth
distribution is sufficiently uneven. This, of course, has also some implications with
respect to the distribution of the gains from the partnership.

The following example helps illustrate this point and also allows us to briefly discuss the
role of the two parties' bargaining powers.
Example 2


Let A = [0, 1], and suppose that the private benefit functions b1 and b2 are symmetric and
piecewise linear, defined by:




and:




The ex post efficient action is a* = 1/2 and yields a total utility level:


1 2
while the parties' preferred actions (a = 0, a = 1) yield, for i = j = 1, 2:



We first assume equal bargaining powers: 1 = 2 = 1/2. If control is granted to party 1,
in the absence of any initial transfer t0, the outcome of the negotiation is determined as
follows:


if w2 party 2 is too poor to induce party 1 to take the
efficient action; the outcome of the negotiation in that case is defined by
, and
Using the fact that a < 1/2, and thus and b2(a) =
Ka, the first-order condition with respect to a yields


The corresponding utilities for the two parties are, respectively,




if



then party 2 can afford to bribe party into taking the efficient action but the
negotiated transfer is still constrained by party 2's limited wealth; in that case




finally, if w2 ", wealth constraints play no role; â = a* = ½ and the net
transfer is simply determined by



the utilities for the two parties are then:


Both efficiency and the two parties' utilities increase with party 2's wealth w2 as long as
this party is severely constrained (w2 < w), whereas beyond this threshold increasing w2
has no effect on efficiency but leads to a distribution of gains more favorable to party 1.
Note, however, that db1/dw2 1, so that party 1 cannot gain from transferring wealth to
party 2 through an initial transfer t0.
The outcome of the negotiation when control is granted to party 2 can be derived by
symmetry. Thus, ex post efficiency is achieved iff control is allocated to the poorer party
(party 1, say), whenever


Furthermore, if

so that efficiency cannot be achieved, the ex post outcome is still closer to the first-best
utility level b* when control is allocated to the poorer party, thereby letting the richer
party make the ex post monetary transfers. Note however that the richer party is better
off being granted control.

We now consider the impact of the parties' relative bargaining power on the eventual
choice of action.
The minimal wealth required from party 2 for achieving first-best efficiency when control
is allocated to party 1 is determined by a = a* being a solution to:

Taking the first-order condition with respect to a for a = a* = 1/2 yields:




This is strictly greater than the wealth required from party 1 for achieving
first-best efficiency if control is allocated to party 2, namely:



This suggests that it is easier to ensure ex post efficiency by allocating control to the
party with the lower bargaining power.

4.2 Limited liability and participation constraints
In contrast to ex post efficiency, participation constraints considerations call for allocating
control to the richer party. To see why, consider first the following simple example:
Example 3



Suppose:



Assume first that the initial contract allocates the decision right to party 2( = 2). Then,
since party 2 can offer no transfer to party 1, party 1 cannot hope to get more than



which is lower than his or her reservation level of utility. Hence no contract stipulating =2
would ever be accepted by party 1.




In contrast, allocating the decision right to party 1 can help meet this party's participation
constraint. For example, together with an initial transfer of 100 from party 1 to party 2, it
leads after ex post negotiation of the action choice to:




and thus satisfies both parties' participation constraints. This example thus suggests that,
when at least one party faces wealth constraints, reaching efficient outcomes may
require to allocate the decision right to the least wealth-constrained party.
We now further explore how the interplay between wealth and participation constraints
governs the allocation of control in our more general setting. Assuming that the two
parties' benefits are smooth, if control is allocated to party 1, say, together with an initial
transfer t0 to party 2, if ex post negotiation is efficient the final transfer t from party 1 to
party 2 is equal to:


or equivalently:

Since party 2 must compensate party 1 to convince that party to undertake the efficient
[11]
action, this net transfer is lower than the initial transfer t0. And since the initial transfer
[12]
must itself be feasible, the admissible range for the net transfer is defined by :

To better focus on the role of participation constraints, assume that party 2 is sufficiently
unconstrained (w2 is sufficiently large) that ex post efficiency could always be achieved
by granting control to party 1 (party 2 then bribes party 1 into choosing the efficient
action). Yet, if party 1's wealth is too small, namely if:
party 2 will never accept to sign a contract that allocates decision rights to party 1. To
see this, note that if the contract ( = 1, t0) is accepted and eventually leads to ex post
efficiency (a = a*), the final transfer, given by (4) gives party 2 a level of utility u2 equal to:


A contract granting control to party 1 can therefore be accepted by party 2 only if


w11. In contrast, there exists a feasible transfer t0 such that
which in turn requires w1
the contract ( = 2, t0) is individually rational for both parties and efficient:
Proposition 2


Suppose that: (i) one party, 2, say, is sufficiently unconstrained that it can always bribe the
other party into choosing the efficient action ex post; and:(ii) efficient contracting would
individually rational if the action choice were verifiable. Then, allocating control to party 1
may violate party 2's individual rationality constraint, whereas there always exists a feasible
transfer t0 such that the contract ( = 2, t0) is individually rational for both parties and
efficient.




Proof: If the contract ( = 2, t0) yields ex post efficiency, then the net transfer is given by

and is larger than the initial transfer t0. In addition, the two parties' equilibrium payoffs are
respectively given by:



Such a contract will therefore be individually rational if and only if ui Bi. If party 2 is
sufficiently unconstrained, the relevant constraints are thus the feasibility condition:


and party 2's participation condition:


These two conditions are compatible when:


or:




But this latter condition is trivially satisfied when efficient contracting is individually
rational for party 2 if the action were verifiable.
Thus, allocating control to the least wealth-constrained party, together with an
appropriate transfer towards the poorer party, makes the project acceptable by both
parties and can eventually lead to the efficient action choice a*. Giving instead control to
the poorer party puts that party at an excessive advantage in the negotiation game,
which in turn makes it difficult to meet the other party's participation constraint.
Remark. In the more general case where both parties face (tight) credit-constraints, we
saw on p. 204 that achieving ex post efficiency might require granting control to the
poorer party. However, the above discussion suggests that doing so is more likely to
violate individual rationality.
Whenever ex post efficiency and ex ante participation considerations conflict, in the
sense that there does not exist an individually rational contract that leads to ex post
efficient action choice after renegotiation, the participation constraints should dictate
what the optimal control allocation will be, as suggested by the following example.
Example 2 (contd.)



Consider again our previous example with symmetric piecewise linear utility functions and,
to fix ideas, symmetric bargaining power and reservation utilities:


In addition, suppose that:


so that achieving efficiency is impossible: no party can sufficiently "bribe" the other away
from her preferred action, even if pooling both parties' wealth through initial transfers.




Maximal efficiency if achieved when the controlling party transfers all of her wealth to the
other party. However, while both ( = 1, t0 = w1) and( = 2, t0 = w2) achieve this
maximal efficiency, the latter yields more balanced utility levels:




while




so that[13]


Therefore, whenever
1
granting control to party 1 cannot be acceptable by party 2 (it cannot get more than u 2,
even if party 1 gives away his wealth in exchange for getting control), whereas there
exist contracts granting control to party 2 that are acceptable by both parties. In other
words, ex ante participation dictates that control be allocated to party 2 (the richer party),
[14]
although this does not lead to ex post efficiency.
Remark 2: We saw on p. 205 that allocating control to the party with the lower bargaining
power helps achieve ex post efficiency. The following example suggests that allocating
control to the party with lower bargaining power can also help achieving ex ante
participation.
Example 4



Let:

but with heterogeneous bargaining powers: >> 1. When control is allocated to party 2
2
the participation constraints are:
When 1 (resp. 2) is sufficiently close to zero (resp. to 1), the latter constraint is harder to
satisfy than the participation constraints when control is allocated to party 1, namely:




Remark 3: The above analysis can be easily extended in several interesting directions.
Let us briefly mention two potential extensions:
Monetary benefits When the project yields monetary benefits as well as
private benefits, the additional wealth generated by the project can be
used to soften the impact of limited wealth. In particular, the poorer party
might give up his right to the monetary benefits instead of his right to
control the action choice, as there is substitutability between revenue and
control rights.
Moral hazard If the party who "controls" the project is subject to moral
hazard, this moral hazard is likely to be exacerbated by limited wealth
problems (see, e.g., Sappington 1983 and Aghion and Bolton 1997). This,
in turn, provides another reason for allocating the decision right to the
wealthier party.

[11] 1 1
This is easily checked in the above formula, since b*1 < b 1 and b*2 > b 2.

[12]
In particular, if


then it would not be possible to achieve ex post efficiency by allocating control to party 1,
even with an initial transfer to party 2. Similarly, if

it would not be possible to achieve ex post efficiency by allocating control to party 2.

[13]
We have: u11 u22 = u21 u12 = w2 w1 and




and is thus positive since w1 + w2 <w = KK /(K + K).

[14]
The most efficient acceptable contract is then ( = 2, t0 = w2); a smaller initial transfer (in
w2) increases par ty 2's utility but reduces both party 1's utility and
absolute value, i.e. t0 >
efficiency.
5 Conclusion
In this chapter we have investigated the issue of control allocation in a bilateral
contracting framework with ex post unverifiable actions and limited wealth constraints.
We have shown that the ex post non-verifiability of actions together with the limits that
wealth constraints impose on transfers between the contracting parties, implies that the
optimal contract boils down to an allocation of control rights to one party, together with
an initial transfer from one party to the other, and possibly some contractual restrictions
on the set of feasible transfers. We have turned our attention to the determinants of
control allocation, which we have analyzed in the context of a few selected examples.
These examples suggest, first that ex post efficiency is easier to achieve when control is
allocated to the most wealth-constrained party, whereas ex ante participation constraints
are most easily met when control is allocated to the least wealth-constrained party;
second, that allocating control to the party with lower bargaining power at the
renegotiation stage, helps both in achieving efficiency and meeting participation
constraints.
Our analysis can be extended in several directions. One natural extension would be to
open the "black box" of the bilateral trade between the party in control and the party
making the monetary transfers. More specifically, we have assumed that, at this stage,
the controlling party could credibly commit to changes in action choices in exchange for
suitable monetary transfers; it would be interesting to explicitly analyze the credibility
game between the two parties, for example using a dynamic model of reputation-building.
Another extension would be to explore the interactions between contracting under ex
post unverifiable actions and the strategic interactions between the contracting parties in
a dynamic context, with a view to better understand the organization of firms. Two
companion papers with Mathias Dewatripont (Aghion, Dewatripont and Rey 2000, 2001)
provide preliminary attempts at exploring such a research agenda. The first paper shows
how dividing formal control rights over a sequence of actions can enhance cooperation
by creating "checks and balances"; the second paper shows how delegating real
authority to a subordinate allows this subordinate to build a reputation regarding her
willingness to cooperate in the future.
Notes
1. Closely related to AB is the paper by Dewatripont and Tirole (1994),
which includes an effort variable before the non-contractible action is
chosen and investigates the ability of the action to provide effort
incentives.
2. In Aghion, Dewatripont and Rey (2000), we refer to this type of actions
as actions with contractable control, in contrast to non-verifiable actions
over which the allocation of control is not-verifiable, although control may
can be credibly transfered from one party to the other.
As suggested by Bengt Holmström, one can interpret control allocation as
giving the "key" to access a room, and where only those who enter the room
can observe the action to be taken there. Control allocation (who gets the key)
can then be verifiable, even though the choice of action is not.
3. Note that t refers to the overall net transfer, not to the additional transfer t
t0 negotiated on top of the initial transfer t0.
4. While allowing lotteries (e.g. random control allocations), we shall
assume that the outcome of such lotteries is realized before the
negotiation starts.
5. The situation would be different if for example subsequent actions had to
be taken and the ultimate outcomes depended jointly upon all actions.
Then, allocating future decision rights on the basis of reported actions
might allow the parties to reveal their first choice of action “ see Aghion,
Dewatripont and Rey (2000).
6. Yet the two parties' strategies in this game may depend upon the
negotiated action and also upon the negotiated transfer.
7. We assume that any restriction on transfers binds at every stage of the
implementation of the contract. The reasoning still holds if the restriction
only applies to the transfers that are finally agreed to.
8. Given the negotiated transfer , reaching
requires an interior solution, which must therefore satisfy this first-order
condition.
9. When private benefits are not continuously differentiable, restrictions on
transfers may still be required to satisfy participation constraints without
necessarily inducing a loss of efficiency (see example 2 below).
10. More precisely, ex post efficiency could be achieved (e.g. with = S, t0 =
0) if 1/4 wB < 1/2, whereas no contract can induce efficiency if wB < 1/4.
In both cases, however, meeting both parties' participation constraints
requires = S, together with additional restrictions on transfers, of the
form T = [0, t], with t [0, t] with t [7/54, wB).
1 1
11. This is easily checked in the above formula, since b*1 < b 1 and b*2 > b 2.
12. In particular, if

then it would not be possible to achieve ex post efficiency by allocating control
to party 1, even with an initial transfer to party 2. Similarly, if

it would not be possible to achieve ex post efficiency by allocating control to
party 2.
13. We have: u11 u22 = u21 u12 = w2 w1 and




and is thus positive since w1 + w2 < w = KK /(K + K).
14. The most efficient acceptable contract is then ( = 2, t0 = w2); a smaller
initial transfer (in absolute value, i.e. t0 > w2) increases par ty 2's utility
but reduces both party 1's utility and efficiency.
Complexity and Contract
Chapter 13:
W. Bentley MacLeod
"The time is not here yet, but I hope it is coming when judges realize that the people who
[1]
draft contracts cannot envisage all the things that the future will bring."
1 Introduction
Building upon the work of Simon (1957), Williamson (1975) observes that a fundamental
reason for transaction costs is the impossibility of planning for all future contingencies in
[2]
a relationship. The purpose of this chapter is to explore the conditions under which
such complexity can constrain the set of feasible contracts, and help us better
understand the contracts observed in practice. Specifically, a situation where agents are
asked to make decisions when unforeseen events occur, but cannot renegotiate the
contract is one I call ex post hold-up. In these cases, complexity can have an important
impact upon the form of the optimal contract. The chapter begins by comparing the
structure of the ex post hold-up problem to other contracting problems in the literature
and suggests that a key ingredient in understanding the form of the optimal contract is
the timing of information and actions in a relationship. Secondly, a way to measure
contract complexity is suggested that has empirical implications. Finally, the optimal
governance of contracts facing ex post hold-up when complexity is high depends upon
the degree of correlation in subjective beliefs between the contracting parties.

Beginning with Simon (1951), there is a large literature that takes as given contract
incompleteness due to transaction costs and then explores its implications for efficient
governance. Simon argues that giving one agent authority over another economizes on
transaction costs by allowing one to delay decision-making until after uncertainty has
been resolved. In a similar vein, the property-rights literature, beginning with Grossman
and Hart (1986), argues that problems of contract incompleteness are resolved by an
appropriate reallocation of bargaining power in a relationship through ownership rights.

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