Chapter 3. International cooperation in environmental protection

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Protection of environmental resources, such as the global climate and biological diversity, is an international public good. It would be expected, therefore, that the pursuit of national self-interest would result in too little protection of resources. But the fact that all countries potentially could be better off if all cooperated to protect these resources equally suggests that countries have incentives to invent institutions that can facilitate cooperation. As discussed in the previous chapter, such institutions do exist; they are IEAs or treaties that establish rules for protecting international environmental resources. More than 140 IEAs have been negotiated, excluding bilateral agreements and European Community directives (Barrett, 1991). The most recent were agreements to protect the global climate and biological diversity signed in Rio de Janeiro in June 1992. An important question is whether such institutions really can be expected to improve environmental protection, given the incentives countries have to free ride. Both the climate change and biological diversity conventions were signed by about 150 countries - virtually all UN member countries. Does that mean that the agreements achieve the full cooperative outcomes, or do they instead merely codify the non-cooperative outcomes?

While both climate change and biological diversity concern shared environmental resources, they differ in one important respect. As noted in the introduction, climate change is a reciprocal externality: if one country emits more carbon, others may retaliate by emitting more too. Most of the other environmental problems discussed in the last section are similar. If one country eases its plant protection, others may respond by easing theirs. If one country increases its tuna harvest, others may do likewise. Biological diversity is more like a unidirectional externality; the costs of conservation fall primarily on tropical rain forest countries, while the benefits are received by the countries belonging to the Organisation for Economic Cooperation and Development. For this reason, these types of environmental problems are treated separately below. It will be seen, however, that the qualitative results are remarkably similar. As indicated in the introduction, the reason is that the provision of compensation for the conservation of biological diversity itself involves a reciprocal externality.

The prisoners' dilemma

The situations discussed here are "mixed-motive games", where countries can be made better off through cooperation, although each country could do better still by defecting from a cooperative agreement. Of particular interest is the "prisoners' dilemma game", because it demonstrates that under certain conditions countries may not be able to sustain a cooperative agreement, even though all countries would be better off if such an agreement were sustained.

The prisoners' dilemma game is illustrated in Figure 1. There are two countries, A and B. Each country must choose an action, Y or N. Any one of four outcomes may result: A and B both choose Y; A and B both choose N: A chooses Y and B chooses N; and A chooses N and B chooses Y. Associated with each of these outcomes is a payoff to countries A and B. The figures in the cells represent these payoffs. The figure on the left is A's payoff, and the figure on the right in each cell is B's payoff. Note that for this game only relative payoff magnitudes matter.

Figure 1 might describe a "game" of abating a pollutant that is known to damage the environment of every country, where a country abates its own emissions by choosing Y and does not by choosing N. The rules of the game are that the two players must choose their actions simultaneously, knowing that the game will not be replayed. The Nash equilibrium is easily calculated. Consider A's decision. If B chooses Y. A's best choice is N. If B chooses N. A's best choice is still N. Hence, A will choose N whatever B chooses (N is a dominant strategy for A). Similarly, B will choose N whatever A chooses. As a result, the equilibrium for this game is that neither country abates its emissions. Both countries have an incentive to cooperate and abate their emissions, however, since both countries do better when Y is chosen than they do in the Nash equilibrium where N,N is the outcome.

How can the outcome Y,Y be sustained? The most obvious way would be to have both countries make binding commitments or commitments in which the penalty for breaking the agreement is so great that neither country would ever want to do so. For example, if in Figure I each party agreed to choose Y or to suffer a penalty of 2 if it instead chose N. the payoffs would be changed so that Y becomes a dominant strategy for both players.

Individuals and firms could commit themselves by signing contracts enforceable by a nation's courts although a cartel agreement between firms is not legal in many countries. In international relations, however, there is no third party to enforce an agreement. If an agreement is broken, the injured country can take the offender to the International Court of Justice - but the offender cannot be made to defend itself before the Court. Furthermore, if the Court finds the defendant guilty and imposes a punishment, the offending country cannot be forced to bear the punishment. In other words, international agreements must be self-enforcing.

FIGURE 1 Illustration of the prisoniers' dilemma game

Self-enforcement is a severe constraint. Indeed, with respect to the prisoners' dilemma, self-enforcement ensures that an international agreement cannot be sustained. However, it turns out that in a richer model, a country can do at least a little better than in the Nash equilibrium.

The self-enforcing IEA

One approach to modelling reciprocal externalities, such as plant protection, international fisheries management and climate change, is to assume that countries that sign an IEA collude by maximizing their collective net benefits.6 These countries do so perhaps taking into account the reactions of nonsignatories. Non-signatories choose their actions on the assumption that their choices will not affect the decisions of other countries. Any country may sign the IEA, and any signatory may withdraw from the agreement. The agreement is stable if no signatory wishes to withdraw and if no non-signatory wishes to accede to the agreement. This notion of stability is consistent with international law, which respects sovereignty and, hence, rules out third-party enforcement of an IEA (Barrett, 1990).

To illustrate the procedure, consider a simple example (Barrett, 1992b) involving a shared resource. The precise nature of the example is not important. It may concern pollution or plant protection or a fishery. What is important is that all countries involved take actions that directly affect the stock of the resource (the abundance of fish, the concentration of a pollutant, the prevalence of a pest). Supposing that the problem concerns pollution, there are i = 1,...,N identical countries with net benefit functions

NB_i = w Q - cq_i²/2, (1)

where Q is total pollution abatement, qj is country i's abatement (i.e. Q = åqj) and w and c are positive parameters. The reciprocal externality is reflected by the presence of Q in i's net benefit function.

If countries do not cooperate, it seems reasonable to assume that each country will maximize its own net benefits, taking the abatement choices of other countries as given. The solution (formally, the Nash equilibrium) involves each country setting its own marginal benefit of abatement equal to its own marginal cost. Each country will choose a level of abatement q₀= w/c, where the subscript o denotes the open access or non-cooperative outcome. In this case, total abatement is given by Q₀ = w N/c. The solution is shown in Figure 2, where the horizontal axis measures total abatement, MC_j denotes country i's marginal abatement cost schedule and MB and MB_j, respectively, denote the global and national abatement benefit schedules.

Figure 2.Non-cooperative and cooperative outcomes

Suppose now that countries cooperate fully. Since all countries are identical, it is reasonable to assume that countries will choose their abatement levels jointly in order to maximize their collective net benefits. This requires that each country set its own marginal cost of abatement equal to the global marginal benefit of abatement. Each country chooses a level of abatement q_c= wN/c, where the subscript c denotes the full cooperative outcome; in this case, Q_c = wN²/c This solution is also shown in Figure 2. It is obvious from the figure that Q_c > Q₀. The outcome Q₀, is not stable, however, because MC_j > MB _j for each country. To improve upon the outcome Q₀, this incentive to free ride must be reduced. One possibility is considered below.

Before turning to free rider deterrence, it should be noted that the extent to which an agreement is able to increase net benefits depends on the nature of the problem at hand. For specification (1 ), it is easy to show that the gap in global net benefits between the non-cooperative and full cooperative outcomes is given by w²N(N - 1)²/2c. The larger c is and the smaller ce is, the smaller the total gains to cooperation are. Calculating the gains to cooperation is important, because in some cases the gains may not be very large. For specification (1), if c is large and w is small, countries would not abate their emissions by much even if they cooperated fully. Hence, failure to cooperate would not reduce well-being dramatically. This is not true if c is small and is large.

Suppose now that a fraction a of the N countries sign an IEA, while the remaining (1- a)N countries do not. Denote the former countries by the subscript s and the latter by the subscript n. Assume that non-signatories behave non-cooperatively by choosing an abatement level where each country's marginal benefit of abatement equals its marginal cost; the solution for specification (1) is q_n = w /c, and Q_n = åq_n=(1- a)Nw/c. Assume further that signatories maximize their collective net benefits by choosing Q_s = å q_s . Formally, signatories perform the following problem:

max w aN(Q_s + Q_n) - cQ_s²/2 a N,

Q_s

the solution to which is q_s = w aN/c, or Q_s = w a²N²/c.

To solve foraN, the stable number of signatories, a stable IEA is defined as one that satisfies the following conditions:

NB_n(a - 1/N) < =NB_s(a) and NB_n(a) >= NB_s(a + 1/N). (2)

That is, a stable IEA is one from which no signatory wishes to withdraw and to which no non-signatory wishes to accede.

Substituting q,, and q into ( I ) yields:

NB_n(a) = w²N( 1 - a + a²N - 1/2N)/c
(3a)

NB_s (a) = w²N( 1 - a + a²N/2)/c
(3b)

NB_n(a - 1/N) = w²N(1 - 3a + 3/2N + a²N)/c
(3c)

NB_s(a + 1/N) = w²N( 1 - 1/2N + a²N/2)/c.
(3d)

Substituting (3a) and (3d) into (2) yields a a>=2/N. Substituting (3b) and (3c) into (2) and solving for the resulting quadratic equation yields 3/N 2 a 2 I/N. Since stability requires that both of these conditions hold, the stable IEA consists of 3 >=aN >= 2 countries. Clearly, if N = 2, then both countries will sign the IEA. Upon substitution, it is easy to show that NB_s (3/N) = NB_n(2/N). If it is assumed that an additional country will join the IEA when NB_s(a + 1/N) = NB_n(a), then the equilibrium IEA will consist of three countries whenever N >= 3.

An illustration of the stable IEA for this specification is shown in Table 2, where NB = å NB_s + å NB_n. Notice that if two countries form an IEA, they each earn 4 000, which is more than the 3 800 they would earn if there were no agreement. However, free riders do even better than signatories; they earn 4 600. If a third country accedes to the agreement, it receives 4 600, which leaves it no worse off than if it had chosen to free ride. If a fourth country acceded to the treaty, however, it would earn 5 600, which is less than it would earn as a free rider (6 200). Similarly, it can be shown that, starting from an agreement consisting of all countries, there is always an incentive to withdraw as long as four or more countries are in the agreement. Hence, the self-enforcing IEA can sustain no more than three countries. The IEA is able to increase global net benefits from 38 000 to 57 200, although this increase falls far short of that associated with the full cooperative outcome.

One problem with this analysis is that it is not obvious how the equilibrium would be arrived at in practice, since each country would prefer to be outside the agreement.This problem can be relieved somewhat by allowing countries to differ. Then, because some countries gain more from acceding to an agreement than others, it is fairly easy to see how the IEA might be formed. Allowing countries to be different - to have different parameter values -- complicates the analysis considerably, however. When countries are identical, any solution concept from cooperative game theory would require that all countries in the IEA adopt the same levels of abatement. When countries are different, this is no longer true; the abatement levels of signatories will depend on the "cooperative game theoretic model" employed.

TABLE 2. Illustration of stability analysis for specification*

*Assumes N = I0, w = 10, w⁺= 0.25.
For a= a⁺ = 0.3, the number of signatories is stable (a⁺ = 10 x 0.3 = 3).

What is more' when countries are different, more than one equilibrium may exist. This serves to indicate the difficulty of analysing IEAs in a rich structure. For the purposes of this paper, however, it is better to concentrate on the fundamental problem of free rider deterrence and to consider only the simple case where all countries are identical.

The specification given by equation (1) permits the stable IEA to be calculated analytically. This is not true of all specifications, and, as Table 3 shows, different specifications yield different results; depending on the functional form and parameter values, the number of signatories to the stable IEA ranges from 0 to N.

What is attractive about this model is that it solves endogenously for the number of signatories, the terms of the agreement reached and the abatement effort by non-signatories. In addition, the IEA is selt-enforcing; signatories do not withdraw from and non-signatories do not accede to the IEA, because it is not in their interest to do so. The mechanism that achieves partial cooperation is simple. If an additional country joins the IEA, the other cooperators abate more, and if one signatory withdraws from the IEA, the remaining cooperators abate less. Hence cooperation is rewarded and free riding punished. These rewards and punishments are credible, because signatories are always maximizing their collective net benefits.

Such rewards and punishments may not be large enough to sustain an IEA consisting of many countries, however. Indeed, the one robust conclusion that emerges from this model of an IEA is that when N is large, an IEA can do little to improve global well-being.

TABLE 3 Model results for different functional specifications

Source:Barrett(1992b)

This is obviously true for the last specification given in Table 2, but it is also true of the first. Analysis of this specification shows that an IEA will be signed by many countries when N is large only when the gap between the non-cooperative and fully cooperative outcomes is very small (Barrett, 1992b). The reason for this general result is that when N is large, the model cannot deliver a large punishment to deter free riding. When N is large, a defection by any one country reduces the net benefits of the remaining signatories by only a small amount. Hence, it is only credible for these countries to inflict a small punishment. But when the marginal abatement cost curve is steep, the incentive to free ride is great. Hence, free riding cannot be credibly deterred. A different model can inflict harsher punishment.