**4. The unregulated common property: The
prisoner's dilemma revisited**

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**4.1
The role of private contracting: Lessons from the coase theorem**

**4.2
The role of decentralized punishment: Spontaneous co-operation in
repeated PD games**

Theoretical arguments can be put forward to show that the tragedy of the commons is an unduly pessimistic story. They all rest on the idea that purely decentralized mechanisms exist which allow agents to escape perverse equilibria leading to the gradual destruction of local CPRs. Essentially, these arguments call into question Hardin's representation of the pattern of resource exploitation by a one-shot static PD game. To that effect, different theoretical approaches can be followed. First, decentralized contracting processes around use rights may bring about a Pareto-optimal pattern of exploitation through side payments that transform the payoff structure of the original PD game. Second, co-operation may be shown to emerge even within the framework of the PD game provided, however, that allowance is made for repeated interaction over time between different individuals' choices. Third, the payoff structure of the game being played may not be that of the PD, and in these new types of games, collectively rational outcomes become more likely. In the following, an extensive discussion of these different approaches will be undertaken and, in the process, the role of such variables as group size, group homogeneity, trust among agents, and moral norms will be highlighted. (liven the magnitude of the task, this discussion will take place in two steps corresponding to two distinct chapters: the first two aforementioned approaches will be the focus of this chapter while the third one will be the object of the next chapter.

**4.1 The role of private contracting: Lessons
from the coase theorem**

*A simple exposition of the
Coase theorem*

In a celebrated article, Coase argues that, provided rights are well defined, agents will negotiate so as to achieve Pareto-efficiency. The starting-point of his analysis is the reciprocal nature of the damages related to an externality and its correction: 'We are dealing with a problem of reciprocal nature. To avoid harm on B would inflict harm on A. The real question that has to be decided is: should A be allowed to harm B or should B be allowed to harm A? The problem is to avoid the more serious harm' (Coase, 1960: 2). For instance, if, by his activities, a polluter imposes an externality on someone, by asking him to reduce his emission of pollutants, the pollutee also causes a damage to the polluter. Provided that either the polluter's or the pollutee's rights are recognized, they will negotiate and, by comparing their respective costs, choose the efficient course of action. State intervention is not necessary to achieve efficiency. 'It is necessary to know whether the damaging business is liable or not for damage caused since without the establishment of this initial delimitation of rights, there can be no market transactions to transfer and recombine them. But the ultimate result (which maximizes the value of production) is independent of the legal position if the pricing system is assumed to work without costs.' Indeed, 'It is always possible to modify by transactions on the market the initial delimitation of rights. And, of course, if such market transactions are costless, such rearrangements of rights will always take place if it would lead to an increase in the value of production' (ibid. 8, 15).

Coase's work on 'the problem of
social cost' has been interpreted in various ways in the
literature. We concentrate below on one particular version of
what has come to be known as the Coase theorem. According to this
interpretation, *'voluntary negotiation will lead to a fully
efficient outcome' *(Farrell, 1987: 115, our emphasis)
provided: (a) rights are well defined, (ii) transactions are
costless, and (c) there are no income effects. The implications
of this proposition are far-reaching:

- if markets are incomplete, people will negotiate and the efficient outcome will result;
- there is no need for government intervention; and
- the outcome is independent of the initial assignment of rights.

Let us illustrate this with the help of a simple example. Assume that, in a fishery, there are three fishermen, say A, B. and C, each of whom operates only one boat. The production conditions in the fishery are such that the net profits per boat are determined as follows:

Number of boats | 1 | 2 | 3 |

Net profit per boat | $3 | $2 | $1 |

In such a fishery, there is one Pareto optimum, where only two boats are operated. First consider the situation of an unregulated common property, where each fisherman has a right to fish. In the absence of any transaction, each of them will enter the fishery and the tragedy of the commons results. However, such a result is unlikely if transactions are costless. Indeed, A and B (or B and C, or A and C) are ready to pay C (or A, or B) up to $2 if C renounces to make use of his right of access to the fishery. C is ready to sell his right provided he is paid at least $1. The precise amount which will be decided depends in general on the bargaining strength of the partners. In the symmetric game examined here, one may argue that they will agree on $1.33 (that is, the maximum total catch of $4 divided by the number of potential fishermen) so that each fisherman will be indifferent between fishing or not. In any case, by negotiating, the three fishermen achieve Pareto-efficiency.

If, however, instead of being an unregulated common property, the fishery considered above was the exclusive property of A who is able to operate only one boat, the fishery would be underexploited. Fisherman B. or C, would be ready to pay A as much as $2 to have a right of access to the fishing-ground. Once again, if transactions are costless, an agreement will be reached by which agent A will sell to another agent the right to fish on his territory. In other words, provided property rights are well defined, the fishery will always be exploited efficiently. Variation in the system of property rights (private or common property) has the only effect of altering the distribution of income.

The Coase theorem can be applied
to a variety of cases where externalities are involved, and in
most of the problems we are concerned with it merely *implies
that collective action (through regulation) is not needed: *through
negotiation, agents will make up for missing markets. As evident
from the foregoing example, an immediate application of the Coase
theorem—and one that, strangely enough, is never mentioned
in the literature—is that, in an unregulated common property
resource, no tragedy of the commons can ever occur: people will
always be able to negotiate to avoid this inefficient outcome. *There
is no need for any central intervention, whether for the purposes
of taxation or of privatization *of the whole resource domain.
This being said, as will be argued in the following, the Coase
theorem suffers from a number of serious limitations which
considerably restrict its practical relevance.

*The problem of the existence
of a solution to bargaining*

Though in many cases bargaining
may lead to efficiency, there is at least one important class of
problem where it does not. More precisely, Shapley and Shubik
(1969), with the help of the 'garbage game', have shown that, if
there are more than two parties, 'the economy can fail to possess
a core allocation if there are polluters' rights over *private
bads*, such as household garbage' (Dasgupta and Mäler, 1990:
15-16). Let us consider a modified version of Shapley and
Shubik's pollution example: assume there are three herdsman, A,
B. C who also possess their own plot of land L_{A}, L_{B},
L_{C}. The pastures are common property but lie next to
these plots. When a herd grazes, it causes damage to the
adjoining cultivated field. However, there is one field, L_{C},
less intensively cultivated, for which the damage caused by a
herd is less important, equal to a, while the damage caused on
each of the other two plots, L_{A} and L_{B}, is
equal to b, with b > a.

Let us first consider the case
where each herdsman has the right to let his herd graze close to
any of the cultivated fields, L_{A}, L_{B}, L_{C},
and suppose that side-payments are authorized. If no agreement is
reached, a herdsman, say A, lets his herd graze close to one of
the two plots belonging to the others, L_{B} or L_{C},
causing a damage of b or a. However, he can also negotiate, say,
with C, to the effect that both of them locate their herds close
to L_{B} At most, they risk a loss of b (if B chooses to
place his herd close to L_{A}), that they share together,
C paying e to compensate A. The resulting payoffs to (A,B,C) are
then (-b+e,-2b,-e). However, in this situation, B is ready to
accept from C a compensation smaller than e, say d, so that they
can both form a coalition against A. The resulting payoffs are
(-2b,-b+d,-d). But A can make a counter-offer, for example to
B.... It is easy to verify in this example that no agreement can
satisfy every (group of) herdsmen 'to the point where they
cannot, by violating it, be sure of doing belter' (Shapley and
Shubik, 1969: 541). In other words, though there does exist an
efficient solution in this game, players will not be able to
reach it through bargaining. As a matter of fact, the core is
empty.

Things are however different if, instead of giving to the herdsmen the right to graze their herds wherever they wish, the agriculturalists' exclusive rights to an undamaged harvest are recognized. In that case indeed, it is clear that all three herdsmen will locate their herds close to the field L`. A and B each pay to C a sum between a and b, since otherwise either C will not tolerate that their herds graze close to his field or A and B will find it more interesting to let their animals graze close to their own fields. When the rights are given to the agriculturalists, decentralized bargaining thus results in an efficient solution.

The conclusion is clear: in games involving more than two parties, whether or not an efficient solution will be reached through decentralized bargaining may depend on the initial assignments or rights: as it stands, the Coase theorem is not valid.

Another crucial difficulty with the Coase theorem is its implicit requirement that all parties concerned are in a position to negotiate. However, in many environmental problems, it is the future generations who bear the costs of the externality. It is not at all clear how their interests may be systematically taken into account in the bargaining process.

*The importance of transaction
costs*

There is no doubt that Coase was well aware of the importance of transaction costs for the validity of his theorem.

But this assumed costless market transactions. Once the costs of carrying out market transactions are taken into account it is clear that such a rearrangement of rights will only be undertaken when the increase in the value of production consequent upon the rearrangement is greater than the cost which would be involved in bringing it about.... In those conditions, the initial delimitation of legal rights does have an effect on efficiency with which the economic system operates. One rearrangement of rights may bring about a greater value of production than any other. But unless this is the arrangement of rights established by the legal system, the costs of reaching the same result by altering and combining rights through the market may be so great that the optimal arrangement of rights, and the greater value of production which it would bring, may never be achieved. (Coase, 1960: 15-16)

This argument is particularly important in the case where there are many parties affected by the externality, such as stream pollution by a firm.' Assume that no pollution is the optimal situation. If the potential polluters have a right to clean water, the firm will take measures not to pollute the river: there are no transaction costs in this case. However, if the firm has a right to pollute, the costs of having all the pollutees organized and prepared to contribute financially to the firm's efforts to reduce pollution may simply be prohibitive, and the sub-optimal situation of pollution will obtain and persist.

As noted by Fisher, Demsetz's argument that 'where transaction costs block a private bargaining solution. . . the status quo must be optimal in the sense that the benefits from moving are less than the costs, including the transaction costs' (Fisher, 1981: 182) is not valid. Indeed, in many cases, such as in the pollution example given above, state intervention to the effect of redesigning the allocation of rights may be optimal, even when the transaction costs of such intervention are taken into account. By contrast, the private bargaining solution is not optimal.

In short, the importance and size of transaction costs in private bargaining agreements depend upon the initial delimitation of rights and the number of agents concerned. The State has an important role to play in this respect. First, in designing the initial allocation of rights, it has to take account of the transaction costs which such an allocation will entail in private bargaining. Second, given an initial allocation of rights, public intervention may incur lower transaction costs than private agreements.

*The distributive effects*

As our statement of the Coase theorem has made clear, the theorem bears only upon the issue of efficiency. The distributive effects of private bargaining are completely disregarded, though they may be the most important issue in practice. They may also have an important impact on the outcome of the private bargaining process itself. Indeed, 'when the damaged party is a consumer . . . willingness to pay may differ from required compensation because the former is constrained by the consumer's income.' When income effects are thus taken into account, 'the assignment of property rights will affect resource use' (Fisher, 1981: 184).

*Private information*

The validity of the Coase theorem is seriously challenged when allowance is made for the fact that, in many private bargaining processes, information is not perfect. When there are informational asymmetries, the parties to the bargain often have an incentive to cheat and to give false information in order to manipulate the outcome of the process. In these cases, bargaining is typically inefficient. For instance, 'a potential buyer may value a house more than its prospective seller does, but less than the seller believes "most" buyers do. He would then have trouble persuading the seller to lower the price enough to make the deal' (Farrell, 1987: 115). A well-known problem in the negotiation of self-imposed catch restrictions (or quotas) is the incomplete information about others' past harvesting performances. Depending upon the chosen mechanism for setting individual quotas (that is, for sharing the burden of restrictions), fishermen may be incited to over- or under-report their past records so as to bear the smallest possible burden of restriction. Moreover, as this is common knowledge, everybody becomes suspicious of all statements made by others.-)

The question which arises is whether it is possible for a central authority, when deciding about a project, to induce people to release the true information, even though they know that this information will be used to decide (a) whether the project is worth undertaking and (b) the amount of the contributions each beneficiary will be required to pay. In the case of the commons, the 'project' may typically consist in determining the extent of reduction in total use of the variable factor (fishing effort, size of the herd) to be imposed on the users and the 'contribution' is the reduction each individual agent may be required to accept. It can be shown (see d'Aspremont and Gerard-Varet, 1976, 1979) that there indeed exists such a scheme or 'mechanism' which can be proposed to the players by a mediator and such that these players will be induced to reveal the truth (even though they fully anticipate that such information will be used to decide on their contribution). The following conditions are sufficient to ensure that result:

- there are at least three players, or,
- each player can be of only two possible 'types', a type being determined by the extent of interest an individual agent has in a particular project, or,
- the individual types are independently distributed.

This approach nevertheless suffers from two important limitations. First, the agents are not free to decide whether they will participate or not, even though their participation may actually hurt them. If we require furthermore that each player must be willing to participate in the scheme (the scheme must be 'individually rational'), then it can be shown that, for a whole class of bargaining problems, efficiency cannot be achieved. This fundamental result is due to Myerson and Satterthwaite (1983) and is to be ascribed to the fact that there are almost always losers who are reluctant to join the scheme. To achieve efficiency, a central authority is therefore needed for the purpose of coercing each player to participate. Its role is obviously much more compelling than that of a mediator who is content with centralizing and processing the information dispersed throughout the resource users.

Second, the central authority must commit itself to carrying out the scheme proposed, and this commitment must be credible to all participants, even though they all know that, in some instances, it may not want to carry out the scheme. For instance, the State may offer freedom to a convict who is ready to denounce his accomplices and later regret this move of forgiveness. In other words, the central authority is bound to its promise, and is not free to reconsider its decisions.

Even when these two conditions
are satisfied, the Coase theorem loses much as a decentralization
result when there is private information. Indeed, *a central
authority is needed to achieve efficiency in order to commit
itself to an incentive scheme and to make participation in the
scheme compulsory.*

In a remarkable paper, Joseph Farrell, arguing first that people may not trust the State's commitment to an incentive scheme and, second, that doubts can be expressed about the actual ability of the State to collect and process such information flows, suggests that the comparison to be made is perhaps between the inefficient outcome of a private bargaining process and the inefficient outcome of an uninformed central authority. In other words, a second-best comparison may be what is called for: 'perhaps the Coase theorem should be viewed as a second-best result: property rights are more efficient than some reasonable alternative' (Farrell, 1987: 122).

Let us examine a simple example proposed by Farrell in which an inefficient state outcome is compared to an inefficient private bargaining outcome. The problem is the following: two people, A and B. care about a decision x: x can take on any positive value, but A would prefer it to equal a value a, and B. a value 6, with a < 6 by assumption (think of x as the (unidimensional) location of a collective good, such as an irrigation canal, the timing of a collective action, or the number of boats each fisherman will be allowed to operate). Suppose that the payoffs to A and B in monetary units can be expressed as follows:

A's payoffs: u(x, a) = -a (x - at)^{2}

B's payoffs: v(x,b) = -b (x - b)^{2}.

These functions reflect the fact that A and B receive a negative payoff when x is different from their preferred value (a for A and 6 for B) and, the more x deviates from this value, the higher the disutility.

A problem arises because a and b
are private information: only A knows a and only B knows b.
However, to the outside world, a is uniformly distributed on [a_{-},
a_{+}], and b on [b_{-}, b_{+}], with a_{+}<b_{-}
(the latter assumption means that people are aware that there are
two distinct types of players: even if they are not sure about
the exact value ascribed by each type to the decision variable,
they know that the possible range of such values for one type is
strictly above the possible range for the other type). If a and 6
were public information, the Pareto-efficient decision would be
the one which maximizes u(x, a) + v(x,b):

x* = (b b + a a)/(a + b )

Let us now consider a 'bumbling bureaucrat' who is not able to design an incentive scheme, and must base his decision on public information. His best choice is to set

X^{B} = (a E(a) + b E(b))/(b + a), where
E(.) refers to the expected value of (.). This achieves a good
compromise, but one cannot expect a and b to be equal to their
expected value. The expected loss can be estimated at (a _{2}_{s}_{
a}^{2} + b ^{2}^{s}^{ }_{b}^{2}),
where s ^{2}(.) refers to the variance of
(.).

If, however, A has the right to
choose x, in the absence of any side-payment, she will set x = a.
B expects to lose E(-b (a - b)^{2}). Yet, he can also
offer bribes to A so as to induce A to change his choice of x. In
other words, B can offer a contract to A specifying for each
choice of x a price B will pay to A.

A will always choose the
efficient level of x, x*, if she is offered a contract which
allows her to internalize all the positive externality such a
choice is bound to create. Such a contract specifies that B must
pay to A: p(x) = b ((a_{-}- b)^{2} - (x - b)^{2}),
if A chooses x (for proof, see Farrell, 1987). However, with such
a contract, B looses (-b (a_{-}- b)^{2}), which is
worse than if A sets x = a. Therefore, B will never propose such
a contract.

One can show that, if B maximizes
his payoffs, B will propose a particular contract to A (see
Farrell, 1987: 126-8), such that, for very low values of a, A
will ignore B's bribe and set x = a, and for high values of a, A
will set x = x* - a (a_{+}- a), which is above a but
below x*. The expected welfare loss resulting from this situation
is 4a ^{2}^{s}^{ }2, to be compared with the
loss that can be attributed to the bumbling bureaucrat, that is,
(a
^{2}^{s}^{ }_{a}^{2} + b ^{2}^{s}^{
}_{b}^{2}). If the right to choose x was
given to B. the resulting expected welfare loss would amount to 4b ^{2}^{s}^{
}_{b}^{2}. Therefore, for many values of the
parameters, *'the bumbling bureaucrat outperforms troth
allocations of rights' *(ibid. 128). This important result,
unfortunately demonstrated only in the context of a limited
example, sheds a new light on the validity of the Coase theorem
in the presence of private information. What comes out is that
this theorem is invalid, *even as a second-best theorem: an
inefficient centralized decision-making process yields a better
outcome than private bargaining.*

To summarize, in this section, we have analysed in detail the claim made by Coase following which a centralized intervention is not needed in situations involving externalities since the efficient solution will emerge from private bargaining. This claim is an important one since it applies to any externality, including that which causes the tragedy of the commons: it implies in particular that no policy intervention is required in the situation of unregulated common property, since the agents are free to sell or buy their rights to use the commons. Although the Coase theorem is helpful in calling attention of policy-makers to the potentialities of private bargaining to enhance efficiency, it buffers from a number of severe limitations. In particular, it does not apply, even as a second-best result, to problems involving private information, that is, paradoxically enough, to problems for which a centralized intervention is the most delicate to design and to carry out. Moreover, the negotiation processes involved ate likely to be so costly as to be infeasible except when the number of agents concerned is small.