Transaction Costs and the Robustness of the Coase Theorem

Transaction Costs and the Robustness of
the Coase Theorem∗
Luca Anderlini
Leonardo Felli
(Southampton University and
(London School of Economics)
Georgetown University)
January 2001
Abstract.
This paper explores the extent to which the presence of ex-
ante transaction costs may lead to failures of the Coase Theorem. In particular
we identify and investigate the basic ‘hold-up problem’ which arises whenever
the parties to a Coasian negotiation have to pay some ex-ante costs for the
negotiation to take place.
We then show that a ‘Coasian solution’ to this
hold-up problem is not available. This is because a Coasian solution to the
hold-up problem typically entails a negotiation about the payment of the costs
associated with the future negotiation which in turn is associated with a fresh
set of ex-ante costs, and hence with a new hold-up problem.
JEL Classification:
C70, D23, D60, D80.
Keywords:
Transaction Costs, Hold-Up Problem, Coase Theorem, Coasian Nego-
tiation.
Address for correspondence:
Leonardo Felli, London School of Economics,
Houghton Street, London WC2A 2AE, England. E-mail: lfelli@econ.lse.ac.uk.
∗ This paper is a revised version of part of the material contained in a working paper entitled
“Costly Coasian Contracts” (Anderlini and Felli 1998). Both authors acknowledge financial support
from the E.S.R.C. (Grant R000237825). This revision was completed while Leonardo Felli was
visiting the Department of Economics at the University of Pennsylvania. Their generous hospitality
is gratefully acknowledged. We are also grateful to seminar participants at the I.S.E.R. 2000 in Siena
for stimulating comments.

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Transaction Costs and the Coase Theorem
1
1.
Introduction
1.1.
Motivation
The Coase theorem (Coase 1960) has had a pervasive influence on the way economists
and legal scholars think about inefficiencies. It guarantees that provided that property
rights are allocated, fully informed rational agent involved in an inefficient situation
will ensure through negotiation that there are no unexploited gains from trade and
hence an efficient outcome obtains.
In its strongest formulation, the Coase theorem is interpreted as guaranteeing
an efficient outcome regardless of the “way in which property rights are assigned”
(Nicholson (1989, p.725)) and whenever the potential mutual gains “exceed [the]
necessary bargaining costs” (Nicholson (1989, p.726)).1
The predictions entailed by the stronger version of the Coase theorem are startling.
Whenever property rights are allocated, we should observe only outcomes which are
constrained efficient in the sense that all potential gains from trade (net of transaction
costs) are exploited. This clearly contradicts even the most casual observation of
empirical facts. The economic world is full of inefficient situations in which obvious
Pareto improving negotiation opportunities are available but they are left unexploited
by the parties involved.
If we were to believe the predictions of the ‘strong’ Coase theorem, all these
apparent inefficiencies would not be real inefficiencies at all. They should simply be
viewed as the result of transaction costs which are ‘high’ relative to the potential
gains from trade. We take the view that this is not a satisfactory explanation of these
observed facts.
Our aim in this paper is to take issue with this strong version of the Coase Theorem
and show that the impact of transaction costs can extend over and above their size
relative to the potential gains form trade. This stems from the strategic role which
transaction costs may play in a Coasian negotiation. It turns out that a key factor in
determining the strategic role of transaction costs is whether they are payable before
1This stronger version of the Coase theorem does not correspond to what is claimed in Coase
(1960), but it is an interpretation of it which is sufficiently common to have found its way into basic
microeconomic text-books such as the one quoted above.

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Transaction Costs and the Coase Theorem
2
or after the negotiation on the distribution of the unexploited gains from trade takes
place. Our analysis below highlights the impact of ex-ante transaction costs.
The primary effect of ex-ante transaction costs is that they may generate a con-
strained inefficient outcome. In the most basic version of our model the agents may
end up not exploiting any of the potential gains from trade, and hence the poten-
tially beneficial negotiation may not even occur. When the choice of ex-ante costs is
‘gradual’, higher costs paid correspond to a more ‘detailed’ negotiation that allows
the parties to exploit better the potential gains from trade and hence to achieve a
higher surplus from the negotiation. In this case the agents will, in general, end up
leaving part of the potential gains from trade unexploited. In other words, they will
choose to negotiate an agreement which is less detailed than would be optimal, after
the ex-ante costs are taken into account. In its simplest form, the strategic effect
which drives our results below is not hard to outline.
Consider any ‘Coasian negotiation’ with the following features.2 Two agents con-
template entering a negotiation which might yields a surplus of an arbitrary given
size. Moreover, the two agents’ shares of the surplus generated by the negotiation
are exogenously given, say because the extensive form which they must use in the
negotiation is itself exogenously given.
Suppose now that there are ex-ante transaction costs associated with this negoti-
ation. In particular, suppose that the agents must each pay a given cost before the
negotiating phase begins. Then, if the distribution of ex-ante costs is such that one
(or both) agents will not be able to recoup the ex-ante cost given the distribution of
surplus, the negotiation will not take place. This is possible even when the total of
ex-ante costs across the two agents is less than the surplus which the negotiation may
generate so that it would be socially efficient for the agents to pay the ex-ante costs
and negotiate the division of the surplus.
In this paper we model this situation taking the distribution of surplus as ex-
ogenously given, in Anderlini and Felli (1998) and Anderlini and Felli (2001a) we
explore a variety of extensive forms in which the agents are allowed to bargain over
2By this we mean a situation in which the property rights of the agents are sufficiently well
defined to allow them to enter into a negotiating phase, and that there are some un-exploited gains
from trade. This obviously covers an extremely wide variety of possible situations, ranging from
text-book like externalities to complex contingent contracts.

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Transaction Costs and the Coase Theorem
3
the distribution of surplus, provided of course that the ex-ante costs have been paid.
We find that the problem we have described is ‘highly pervasive’ in the sense that in
a whole variety of extensive forms, the agents will not negotiate an agreement even
though it would be socially efficient to do so.
What we have just described is a version of a source of inefficiencies well known
in contract theory as the ‘hold-up problem’ (Grout 1984, Grossman and Hart 1986,
Hart and Moore 1988, among many others). The problem is particularly acute in
our setting since it may be impossible for the negotiating parties to find a ‘Coasian
solution’ to this hold-up problem for the following reasons.
Imagine that the two agents in the negotiation we have described attempt to
resolve the inefficiency in the following (Coasian) way. Before the ex-ante costs are
paid, they negotiate a transfer of money which will compensate the agent who is
unable to recoup the ex-ante cost for his loss, of course contingent on his paying the
ex-ante cost. Provided the sum of ex-ante costs does not exceed the surplus generated
by the negotiation, such transfer can always be arranged so that both agents now
benefit from paying the ex-ante costs and entering the negotiation. However, the
problem which arises now is that the contingent compensating transfer can itself be
viewed as a Coasian negotiation, which may involve a new set of ex-ante costs.
Suppose that the ‘second tier’ negotiation we have described does indeed involve
a new set of strictly positive ex-ante costs. Suppose moreover that the second tier
ex-ante costs must be paid for, and the second tier negotiation must occur, before the
first order costs are paid for and the first order negotiation occurs.3
Then it is possible to show that the ex-ante costs associated with the second tier
negotiation may not be paid. In particular there always exists an equilibrium such
that the contingent compensating transfer is not negotiated and therefore does not
take place. Hence, the ex-ante costs associated with the first tier negotiation will,
in turn, not be paid, and the actual surplus will not materialize. This outcome is of
particular interest since it is the only one which survives when we restrict attention
to ‘renegotiation-proof’ equilibria. In other words if, in a Coasian spirit, we insist
3This is obviously an assumption as such. However, we believe it to be plausible in a wide variety
of cases.

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Transaction Costs and the Coase Theorem
4
that the outcome of negotiation at every stage must yield a (constrained) efficient
outcome, the overall outcome is not efficient and therefore not Coasian at all.
The hold-up problem described above is less pervasive in an environment in which
each party to the negotiation has an incentive to bestow a higher share of the surplus
to his partner for reasons that may have nothing to do with the partner’s payment of
the ex-ante transaction costs. In Section 6 below we consider one of these reasons. If
the size of the surplus shared by the two parties depends on the distribution dictated
by the negotiation, then each party may be willing to leave his counterpart more than
his outside option in the attempt to increase the overall size of the surplus. This may
result in a smaller range of parameter values for which the hold-up problem described
above occurs.
1.2.
Related Literature
It is clear that the original version of the Coase theorem (Coase 1960) explicitly
assumes the absence of any transaction costs or other frictions in the bargaining
process. Indeed, Coase (1992) describes the theorem as a provocative result that was
meant to show how unrealistic is the world without transaction costs.4
Here, we go further by identifying the crucial strategic role played by ex-ante trans-
action costs (as opposed, for instance, to those transaction costs which are payable
ex-post) which may lead to an outcome that is constrained inefficient.
We are certainly not the first to point out that the Coase theorem no longer
holds when there are frictions in the negotiation process. There is a vast literature on
bargaining models where the frictions take the form of incomplete and asymmetric in-
formation. With incomplete information, efficient agreements often cannot be reached
and delays in bargaining may obtain.5 By contrast, the reduced form negotiation that
we consider in our analysis is one of complete information. The source of inefficiencies
in this paper can therefore be traced directly to the presence of transaction costs.
As in our analysis, Dixit and Olson (2000) are concerned with a classical Coasian
public good problem in which they explicitly model the agents’ ex-ante (possibly
4de Meza (1988) provides an extensive survey of the literature on the Coase theorem, including
an outline of its history and possible interpretations.
5See Muthoo (1999) for an up-to-date coverage as well as extensive references on this strand of
literature and other issues in bargaining theory.

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Transaction Costs and the Coase Theorem
5
costly) decisions of whether to participate or not in the bargaining process. In their
setting they find both efficient and inefficient equilibria as opposed to the unique
constrained inefficient equilibrium we derive in our setting. They also highlight the
inefficiency of the symmetric (mixed-strategy) equilibria of their model.
The papers that are closest to the present one are Anderlini and Felli (2001a)
and Anderlini and Felli (2001b). In particular, Anderlini and Felli (2001b) is also
concerned with the hold-up problem generated by ex-ante contractual costs in a model
of a Coasian negotiation and with the inefficiencies it generates. However, while the
parties’ bargaining power is taken as a primitive in the present analysis, in Anderlini
and Felli (2001b) we take as primitive a general formulation of the ‘game forms’ that
define the actual negotiation game played by the parties. We then show that the
inefficiencies generated by the presence of ex-ante transaction costs are robust to this
general formulation of the the protocol followed by the actual negotiation and any
possible associated compensating transfers. In Anderlini and Felli (2001b) we also
interpret our results in a different vein as the ones presented here. In particular, there
we argue that the hold-up problem created by ex-ante transaction costs should be
considered a major source of contractual incompleteness.
Anderlini and Felli (2001a) instead focuses on a specific extensive form of the par-
ties’ negotiation in the presence of ex-ante transaction costs: the alternating offers
bargaining game with complete information with potentially infinite rounds of nego-
tiation in which the players discount the future at a strictly positive rate (Rubinstein
1982). Ex-ante transaction costs are modeled as positive costs that both parties, at
each round of negotiation, must pay to participate to that round of the bargaining
game. In this environment, in Anderlini and Felli (2001a) we show that a whole
plethora of inefficiencies may arise. First, for some values of these costs it is efficient
to reach an agreement but the unique equilibrium outcome is one in which agreement
is never reached. Secondly, even when there are equilibria in which an agreement
is reached, we find that the model always has an equilibrium in which agreement is
never reached, as well as equilibria in which agreement is delayed for an arbitrary
length of time. Finally, the equilibrium in which agreement is never reached is per-
vasive in the sense that if the parties are given the opportunity to renegotiate out of
these inefficient outcomes, the only equilibrium outcome that survives is the one in

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Transaction Costs and the Coase Theorem
6
which agreement is never reached, regardless of the value of the transaction costs.
1.3.
Overview
We begin with a discussion of the possible interpretations of the ex-ante transaction
costs in Section 2. In Section 3 we present the simplest possible model of the basic
hold-up problem associated with a surplus-enhancing negotiation. This problem is
analyzed in the case in which the ex-ante costs associated with the Coasian negotiation
are discrete and are either complements or substitutes. In Section 4 we address the
question of whether a Coasian solution to our basic hold-up problem is plausible.
We do this by analyzing the possibility of a negotiated transfer from one party to the
other before the payment of the transaction costs that are at the origin of the hold-up
problem. We then turn (Section 5) to the analysis of a simple model in which the
agents’ choice of ex-ante costs is continuous. In Section 6 we present a model in which
the size of the surplus available to the parties depends on its distribution. Section 7
offers some concluding remarks. To ease the exposition, we have relegated all proofs
to the Appendix.
2.
Ex-Ante Transaction Costs
We are concerned with Coasian negotiations in which the parties have to incur some
ex-ante transaction costs, before they reach the stage in which the actual negotiation
occurs.
The interpretation of these ex-ante transaction costs which we favor is that of
time spent ‘preparing’ for the Coasian negotiation. Typically, a variety of tasks need
to be carried out by the parties involved before the actual negotiation begins.
In those cases in which the negotiation of an agreement contingent on a state
of nature is concerned, both parties need to conceive of, and agree upon, a suitable
language to describe precisely the possible realizations of the state of nature. The
parties also need to collect and analyze information about the ‘legal environment’ in
which the agreement will be embedded. For instance, in different countries the same
agreement will need to be drawn-up differently to make it legally binding and hence
enforceable.

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Transaction Costs and the Coase Theorem
7
In virtually all settings in which a negotiation is required the parties need to
spend time arranging a way to ‘meet’, and they need to ‘earmark’ some of their time
schedules for the actual meeting.
In many cases, before a meaningful negotiation can start, the parties will need
to collect and analyze background information which may be relevant to their un-
derstanding of the actual trading opportunities. These activities may range from
collecting information about (for instance the credit-worthiness of) the other party,
to actual ‘thinking’ or ‘complexity’ costs incurred to understand the negotiation prob-
lem. We view this type of ex-ante transaction costs as both relevant and important
for the type of effects which we identify in our analysis below. However, it should
be emphasized that our model does not directly apply to this type of costs. This
is because in our model the size of the gains from trade is fixed and known to the
parties. On the other hand, the lack of information and/or understanding of the
negotiation setting which we have just described, would clearly make the size of the
surplus uncertain for the parties involved. We have not considered the case of uncer-
tain surplus for reasons of space and analytical convenience. However, we conjecture
that the general ‘flavor’ of our results generalizes to this case.
We conclude this section with an observation. In many cases the parties to a
negotiation will have the opportunity to delegate to outsiders many of the tasks
which we have mentioned as sources of ex-ante transaction costs. The most common
example of this is the hiring of lawyers. In these cases, the time costs which we have
just discussed will be monetized at an appropriate rate. Abstracting from agency
problems (between the negotiating party/principal and the lawyer/agent), which are
likely to increase the ex-ante costs anyway, our analysis applies, unchanged, to the
case in which the ex-ante transaction costs are payable in money.
3.
Discrete Transaction Costs
3.1.
Perfect Complements
Our model consists of two agents, called A and B, who face a ‘Coasian’ opportunity
to realize some gains from trade. Without loss of generality we normalize the size of
the surplus, which is realized if an agreement is reached, to be one, and we set the
parties’ payoffs in the case disagreement to be equal to zero.

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Transaction Costs and the Coase Theorem
8
In the simple model we analyze in this section, once the negotiating phase is
reached the division of surplus between the two agents is exogenously given and cannot
be changed by the agents. This should be thought of as the result of the agents having
exogenously given bargaining power in the negotiating phase (the extensive form of
the bargaining game they play to divide the surplus is exogenously given).6
Let λ ∈ [0, 1] be the share of the surplus which accrues to agent A if the parties
engage in the negotiation and 1 − λ the share of the surplus which accrues to B.
For the negotiation to start, each agent has to pay a given ex-ante transaction
cost. In other words, the agents reach the negotiating phase only if they both pay
a certain amount before the negotiation begins.7 These costs should be thought of
as representing a combination of the activities necessary for the gains from trade to
materialize which we discussed in some detail in Section 2 above.
Let cA > 0 and cB > 0 be the two agents’ ex-ante costs. Clearly, if cA + cB > 1
then the two agents will never reach the negotiation that yields the unit surplus, but
then neither would a social planner since the total cost of the negotiation exceeds the
surplus which it yields. We are interested in the case in which it would be socially
efficient for the two agents to negotiate an agreement. Our first assumption guarantees
that this is the case.
Assumption 1. The surplus which the negotiation yields exceeds the total ex-ante
costs which are payable for the negotiation to occur. In other words cA + cB < 1.
Our two agents play a two-stage game. In period t = 0 they both simultaneously
and independently decide whether to pay their ex-ante cost. Only if both agents pay
their ex-ante cost at t = 0, do they have the possibility of negotiating an agreement
yielding a surplus of size one at t = 1.8 We simplify the analysis of the game at t = 1
by taking it as a ‘black box’ yielding payoffs of λ to A and 1 − λ to B. If one or
6In Section 6 below, we consider the possibility that the size of the surplus may depend on its
distribution across the agents.
7Notice therefore that we are implicitly assuming that the agents have some endowments of
resources out of which the ex-ante costs can be paid.
8Notice that we are therefore assuming that the two agents’ ex-ante costs are perfect complements
in the ‘technology’ which determines whether the surplus-generating negotiation is feasible or not.
We examine the cases of perfect substitutes, and of strategic complements in Subsections 3.2 and
3.3 below respectively.

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Transaction Costs and the Coase Theorem
9
pay cB
not pay cB
pay cA
λ − cA, 1 − λ − cB
−cA, 0
not pay cA
0, −cB
0, 0
Figure 1: Normal form of the two-stage game with ex-ante costs.
both agents do not pay their ex-ante costs at t = 0, the game at t = 1 is trivial: the
negotiation which yields the unit surplus is not feasible; the agents have no actions
to take and they both receive a payoff of zero.
Throughout the paper, unless otherwise stated, by equilibrium we mean a subgame
perfect equilibrium of the game at hand.
The normal form which corresponds to the two-stage game we have just described
is depicted in Figure 1. From this it is immediate to derive our first two propositions,
which therefore are stated without proof.
Proposition 1. Let a pair of ex-ante costs cA > 0 and cB > 0 satisfying Assumption
1 be given. Then there exists a range of values — namely Λ = [0, cA) ∪ (1 − cB, 1]
— for the distribution parameter λ such that the only equilibrium of the two-stage
game represented in Figure 1 has neither agent paying the ex-ante cost, and therefore
yields the no-agreement outcome.
Proposition 2. Let any value of the distribution parameter λ ∈ [0, 1] be given. Then
there exists a set C = {cA, cB | either cA > λ or cB > 1 − λ and cA + cB < 1} of
pairs of ex-ante costs which satisfy Assumption 1, and such that the only equilibrium
of the two-stage game represented in Figure 1 has neither agent paying the ex-ante
cost, and therefore yields the no-agreement outcome.
We view Propositions 1 and 2 together as implying that in the presence of ex-ante
transaction costs, if the distribution of ex-ante costs across the parties is sufficiently
‘mis-matched’ with the given distribution of surplus, then the ex-ante costs will gen-
erate a version of the hold-up problem which will induce the agents not to negotiate
an agreement even though it would be socially efficient to do so.

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