International cooperation for sale

European Economic Review 45 (2001) 1835}1850

International cooperation for sale

Scott Barrett

Paul H. Nitze School of Advanced International Studies, Johns Hopkins University,1740 Massachusetts Avenue, Washington DC, NW 20036, USA

Received 1 July 1998; accepted July 2000

Abstract

This paper shows that strong asymmetry among countries warrants a change in therules of the game of global public goods provision, with the consequence that coopera-tion by some countries is bought by others and aggregate welfare is increased, perhapssubstantially. Side payments on their own have virtually no e!ect on the outcomes thatcan be sustained by self-enforcing cooperative agreements. But when the rules of thegame are changed by strong asymmetry } when some countries are e!ectively &commit-ted' to being non-signatories to an agreement eschewing money transfers } side paymentsbecome the vehicle for increasing participation in a cooperative agreement. � 2001Elsevier Science B.V. All rights reserved.

Keywords: International agreements; Side payments; Public goods

1. Introduction

Cooperative arrangements to supply global public goods like protection ofthe ozone layer are normally codi"ed in international treaties. Every nation maybe better o! if all nations participated in such treaties, but sovereignty entitlesevery nation to choose to participate or not as it pleases. So global public goodswill be under-provided unless free riding can be deterred. It is not enough thata treaty threatens to punish free riders severely. Signatories must also be content

E-mail address: [email protected] (S. Barrett).

0014-2921/01/$ - see front matter � 2001 Elsevier Science B.V. All rights reserved.PII: S 0 0 1 4 - 2 9 2 1 ( 0 1 ) 0 0 0 8 2 - 4

�Carraro and Siniscalco (1993) also consider the possibility that a subset of non-signatories maycommit to paying the remaining non-signatories to cooperate.

�Carraro and Botteon (1997) extend this earlier paper for a special case of asymmetry.

to carry out the threat, should they be called upon to do so. The problem is thatany punishment intended to harm free riders will in the bargain harm thecountries called upon to impose the punishment. The sticks needed to deter freeriding completely will often not be credible (Hoel, 1992; Barrett, 1994, 1999).

Can carrots succeed where sticks fail? Carraro and Siniscalco (1993) showthat they can help, but only if the parties can commit to remaining as signa-tories.� As noted above, however, the rules of international law allow countriesto withdraw from an international treaty, at least after giving su$cient notice;and, as if to rea$rm this freedom, nearly all treaties include an explicit provisionfor withdrawal. Besides, if commitments of this kind could be entered into, onemight ask why all countries would not simply commit to being signatories to anagreement sustaining full cooperation.

Yet, side payments are a feature of some international agreements, perhapsthe most important being the agreement to protect the earth's ozone layer } theMontreal Protocol. Moreover, side payments not only increased participationin this treaty but were intended to have this e!ect (Benedick, 1998). How couldthis be, when Carraro and Siniscalco show that commitment is needed to makeside payments potent? The simple answer is that the side payments in theMontreal Protocol exploit important asymmetries. The rich countries, whichcan expect to gain most from the provision of this global public good, have paidthe poor to accede to this treaty. Carraro and Siniscalco take countries to besymmetric, and in doing so may have overlooked the most important reason formaking side payments.�

Since participation in a treaty is voluntary, at a minimum every country needsto gain from participating, and if participation is to be full when countries areasymmetric this will often require some sharing of the costs of pollutionabatement (MaK ler, 1990). Allocations sustained by international agreementsshould probably also ensure that no coalition of countries can gain by with-drawing, and so it is natural to ask whether the full cooperative outcome lies inthe core of the game. Chander and Tulkens (1994) show that, under certainconditions, there exists a very simple cost-sharing rule that not only lies in thecore but that also sustains full cooperation as an equilibrium, whether countriesare symmetric or asymmetric (see also Chander and Tulkens, 1992, 1997).

This is an astonishing result. But the analysis which gives rise to it rests ona possibly strong assumption: each country is assumed to believe that, should itwithdraw from an agreement sustaining full cooperation, all the other countrieswill choose their pollution abatement unilaterally. However, it may not be in thecollective interests of these other countries to behave in this way (if it is

1836 S. Barrett / European Economic Review 45 (2001) 1835}1850

collectively optimal for N countries to cooperate, why should not it be optimalfor N!1 countries to cooperate, given that one country has chosen not tocooperate)? Put di!erently, only in unusual cases would the threat to play Nashupon a single deviation from the full cooperative outcome be credible. Still,though the Chander}Tulkens analysis may understate the free riding problem,their cost-sharing rule is appealing in a number of important respects and couldpossibly increase participation in a self-enforcing, asymmetric treaty (as notedpreviously, Carraro and Siniscalco prove that, in the absence of commitment,cost sharing would not increase participation in a self-enforcing, symmetrictreaty).

In this paper I combine the most appealing features of this literature andobtain very di!erent results. I begin by analyzing a game in which side paymentsare prohibited. I then show that strong asymmetry among countries justi"esa change in the rules of the game. If countries with a small net bene"t fromcooperation would never accede to a cooperative treaty, either individually oren masse, then they are essentially &committed' to being non-signatories to anagreement without side payments. At the same time, these countries would bewilling to accede, provided they were paid to cooperate. So they would o!ertheir cooperation for sale, and the countries with a relatively large net bene"tfrom cooperation would have an incentive to buy this cooperation. I show that,under certain conditions, such a transaction would take place, that the equilib-rium compensation would just satisfy the participation constraints, that thecountries that are paid to participate would nonetheless receive a surplus fromthe agreement, and that the o!er of side payments would not only increase thenumber of signatories with small net bene"ts but also the number of signatorieswith large net bene"ts.

If countries are only weakly asymmetric, neither type of country can &commit'to being a free rider when side payments are prohibited, and so countries shouldbe treated symmetrically as regards their decision to be a party to an interna-tional treaty. Prohibiting cost sharing under such circumstances, however,seems excessively harsh, so I also consider the implications of assuming thatsignatories invoke the Chander}Tulkens cost-sharing rule. I show that use ofthis rule makes little di!erence to the equilibrium agreement. There may bea change in the composition of the agreement, but there will be no signi"cantchange in the aggregate surplus that can be realized by a self-enforcing treaty.I also show that the Chander}Tulkens cost-sharing rule does not help evenwhen countries are strongly asymmetric. Hence, it is not the making of sidepayments per se that aids international cooperation, or even the making of sidepayments when countries are strongly asymmetric. What really matters is thatstrong asymmetry supports a change in the rules of the game by e!ectively&committing' some countries to being non-signatories to an agreement that doesnot pay for their accession. Side payments are only a vehicle for realizing thegains from cooperation made possible by this change.

S. Barrett / European Economic Review 45 (2001) 1835}1850 1837

What is perhaps most remarkable about these results, and what sets thispaper apart from the earlier literature, is that the side payments mechanism inthe Montreal Protocol emerges as an equilibrium. The &rich' countries pay the&poor' just enough to cover their incremental costs of accession, and no more.These and other policy implications are also discussed in the paper.

2. The model

Asymmetric games of international cooperation are notoriously di$cult towork with and must usually be solved numerically (see Barrett, 1997; Carraroand Botteon, 1997). Here I simplify by assuming that there are only two types ofcountry, that each country faces a binary choice (it either plays Abate orPollute), and that every country's payo! is a linear function of the choices of allother countries. These simpli"cations give us everything we need (the underlyinggame is an asymmetric prisoners' dilemma) while at the same time allowing us toobtain sharp analytical results.

There are N countries, N�of which are of type 1 and N

�of which are of type 2

(N"N�#N

�). If any country of type i (i"1, 2) plays Pollute (Abate) it gets

a payo! ��(��

�):

��"�

�(b

�z�#b

�z�), ��

�"!c#�

�(b

�z�#b

�z�), (1)

where z�is the number of type i countries that play Abate (N

�!z

�countries thus

play Pollute); where, after normalizing, ��"1 and �

�3[0, 1]; and where

b�5b

�'0. According to (1), each of the other countries bene"ts at least as

much when one more type 2 country plays Abate as when one more type 1country does so; each type 2 country bene"ts at least as much as each type 1country from the abatement undertaken by any country; and a country's ownnet bene"t of abatement, !c#�

�b�, is at least as high for a type 2 country as for

a type 1 country. Payo!s are normalized such that countries of either type geta payo! of zero if no country undertakes any abatement.

In the context of stratospheric ozone depletion, we can think of type 1 coun-tries as being &poor' and the type 2 countries as being &rich'. The rich countriesuse far more ozone-depleting substances, so that abatement by a rich countrywill improve the environment more than abatement by a poor country(b

�'b

�). The poor bene"t less from global abatement than the rich, however,

because depletion is less near the equator, because people with darker skin areless likely to get skin cancer, and because people in poor countries havea smaller risk of dying of cancer (�

�'�

�).

If abatement is a prisoners' dilemma game, two further conditions must hold.First, play Pollute must be a dominant strategy for every country; that is

c'b�. (2a)


� It can be shown in a repeated game context that if a treaty can deter a unilateral withdrawal thenit can also deter a unilateral act of non-compliance (Barrett, 1999). In other words, in a repeatedgame framework, the assumption of full compliance does not a!ect the equilibrium. This implies thatthe analysis presented here, though geared to the study of international cooperation problems,applies more broadly.

Second, the aggregate payo! of all N countries must strictly increase in z�and z

�:

��N

�#N

�'c/b

�. (2b)

Assume that these conditions are satis"ed. Then we know that the Nashequilibrium of the one-shot game will be unique; all N countries will playPollute in equilibrium, but all N countries would be strictly better o! if everycountry played Abate instead. What we want to know is: if the rules of the gamewere suitably rewritten, could a better outcome be sustained by a self-enforcingagreement?

3. Equilibria without side payments

Consider to begin the following 2-stage game: in stage 1, all countries choosesimultaneously to be a signatory or a non-signatory; and in stage 2 signatorieschoose jointly whether to play Pollute or Abate (that is, signatories behavecooperatively) while non-signatories simultaneously and independently makethe same choice (that is, non-signatories behave non-cooperatively).

This formulation treats countries symmetrically as regards their decision to bea signatory or a non-signatory (states are sovereign equals under internationallaw). Signatories, however, have an advantage over non-signatories in thismodel: they are assumed to comply fully with an agreement to play Abate(their decision to play Abate, however, is determined endogenously). Thisdistinction may seem arti"cial but it is compatible with international law.Custom insists that countries comply with the agreements they sign up to (sothat we can think of compliance as being enforced outside of the model) but itdoes not expect others to punish a country that fails to implement a unilateraldeclaration.�

Solving the game backwards, it is obvious by (2a) that all non-signatoriesmust play Pollute in equilibrium. The "rst two stages of the game, however, area bit harder to solve.

Let k�denote the number of signatories of type i. Then it can be shown (see the

appendix) that, in equilibrium, signatories will play

zH�"0 if c/b

�'�

�k�#k

�,

zH�"k

�if c/b

�(�

�k�#k

�. (3)


�Notice that, if (4a) holds, then kH�3�2,N

�� since, by (2a), c'�

�b�; if (4b) holds, then kH

�3�2,N

��;

and, if (4c) holds, then kH�3�1,N

�� and kH

�3�1,N

�� since �

�kH�#kH

�'c/b

�5c/b

�'1 and since (4c)

is feasible by (2b).�Technically, the game is not repeated and so there can be no &reactions'. My wording here is

intended to aid intuition.

It remains to solve the stage 1 game. Three types of equilibria are possible (fork�#k

�'0):

c/b�#�

�'�

�kH�'c/b

�, kH

�"0 for �

�N

�'c/b

�, (4a)

kH�"0, c/b

�#1'kH

�'c/b

�for N

�'c/b

�, (4b)

c/b�#�

�'�

�kH�#kH

�'c/b

�, �

�kH�#�

�kH�b�/b

�'c/b

�. (4c)

Depending on the parameters of the problem, the self-enforcing agreement(assuming one exists) may comprise a subset of type 1 or 2 countries ora combination of both types of countries.�

These are &linchpin' equilibria in the sense that, if any signatory were towithdraw from these equilibrium agreements, all the remaining signatorieswould play Pollute.� It will be recalled that Chander and Tulkens (1994) employa similar equilibrium concept. However, they assume that, should any countrywithdraw from an agreement consisting of N countries, then all the remainingsignatories will &respond' by playing Pollute. Here we see that this belief will onlybe con"rmed for the special case where kH

�#kH

�"N.

Of course, for �kH�, kH

�� to be an equilibrium, it is not enough that signatories

cannot gain by withdrawing. Non-signatories must also not be able to gain byacceding. In this model, any country that accedes to an agreement comprisingkH�#kH

�signatories must play Abate. However, the act of accession will not alter

the behavior of the other signatories (nor that of the non-signatories), and weknow from (2a) that an incremental accession must therefore be irrational.

Conditions (4) tell us that a self-enforcing agreement will consist of only onetype of country if countries are su$ciently asymmetric. In the absence of sidepayments, a self-enforcing agreement can only consist of both types of country ifthey are weakly asymmetric.

4. Examples

The following examples illustrate the qualitatively di!erent kinds of equilibriathat can be sustained as self-enforcing treaties. In all of these examples,N

�"N

�"50, c"100, and b

�"6.

Example 1. Suppose, to begin, that the two types of country are stronglyasymmetric. Suppose, in particular, that b

�"3 and �

�"0.5. Then there exists


just one equilibrium, �0, 17�, yielding an aggregate payo! of 5950 (for comparison,the full cooperative outcome yields an aggregate payo! of 23,700). This equilib-rium satis"es (4b). The equilibria de"ned by (4a) and (4c) do not exist.

Example 2. Suppose now that the asymmetry is weaker. In particular, supposethat b

�"3 and �

�"0.75. Then there exist two equilibria, �45, 0� and �0, 17�.

These equilibria satisfy (4a) and (4b), respectively, and support aggregate payo!sof 7312.5 and 7225, respectively (the aggregate payo! in the full cooperativeoutcome is 29,375).

Example 3. Finally, suppose that the two types of countries are nearly symmet-ric. In particular, suppose that �

�"0.99 and b

�"5.95. Then there exist 18

equilibria, each with kH�#kH

�"17 (the equilibria are thus �0, 17�, �1, 16�,

�2, 15�,2, �16, 1� and �17, 0�). Aggregate payo!s range from 8364.4 for �17, 0�to 8449 for �0, 17� (full cooperation yields an aggregate payo! of 49, 521.25).

5. Equilibrium selection

As just shown, when countries are asymmetric there will typically exista multiple of equilibria. Which equilibrium will be selected? If the choice ofwhether to be a signatory or a non-signatory were made simultaneously andindependently, we could not say. However, if one type of country could committo being a non-signatory, then there would exist at most one equilibrium.Suppose, for example, that type 1 countries could commit in this way. Then theequilibrium in all of the above examples would be �0, 17�. The same equilibriumwould be sustained if the decision of whether to be a signatory or a non-signatory were made sequentially, with the type 1 countries choosing "rst, andwith all past choices being publicly observable. But how is the order of play to beestablished? In general, it is impossible to say. However, for a special case theorder of play is obvious.

6. Strong asymmetry

For the special case illustrated by Example 1, where b�

is &big' relative tob�

and where ��

is &small', it is obvious that type 2 countries will move "rst.Since the di!erent types of country are very di!erent, equilibrium (4c) will notexist; and, since �

�N

�( c/b

�, the equilibrium described by (4a) will not exist

either. So long as N�

' c/b�, an agreement consisting of type 2 countries only

will exist.However, this equilibrium is not very compelling. The type 1 countries are

e!ectively side-lined in this game, and yet the type 2 signatories can gain if the


�With rationing, not all type 1 countries will accede.

type 1 countries also play Abate. The rules of the game should allow the type 2countries to pay type 1 countries to accede to the agreement. Consider, then, thefollowing game: in stage 1 every type 2 country chooses to be a signatory ora non-signatory; in stage 2, type 2 signatories collectively choose (i) whetherto play Abate or Pollute and (ii) a money side payment m to be paid to everytype 1 country which agrees to accede to the agreement and play Abate; instage 3 every type 1 country chooses to be a signatory or a non-signatory, underthe conditions laid down above; and in stage 4, all non-signatories of whatevertype choose to play Abate or Pollute.

As above, we solve the game backwards. Since, by (2a), play Pollute isa dominant strategy, all non-signatories will play Pollute in equilibrium. Tosolve the stage 3 game, note that every type 1 country will take as given m, z

�,

and the number of other type 1 countries that play Signatory (Abate). Accessionfor any type i country is rational provided

m5c!��b�. (5)

By assumption, c'b�'�

�b�; so the payment needed to make accession by

a type 1 country individually rational is strictly positive.If (5) is satis"ed, it will be in the interest of every type 1 country to accede;

otherwise, it will not be in the interest of any type 1 country to accede. Assumingthat side payments are not rationed, and denoting an equilibrium of this sidepayments game by two stars, we have�

zHH�

"kHH�

"0 if m(c!��b�,

zHH�

"kHH�

"N�

if m5c!��b�. (6)

In stage 2, type 2 signatories take k�

as given. They choose z�3�0, k

�� to

maximize

��"z�(!c#b

�z�#b

�z�)#(k

�!z

�)(b

�z�#b

�z�)!mz

�. (7)

Assuming for simplicity that c/b�is a non-integer, the solution requires

zHH�

"0 if k�(c/b

�,

zHH�

"k�

if k�'c/b

�. (8)

Type 2 signatories must also choose a money side payment m to maximize (7).By assumption, type 2 signatories anticipate correctly that, if m satis"es (5), thenzHH�

"N�; otherwise zHH

�"0. So type 2 signatories will choose m"c!�

�b�if

and only if the payo! they get by o!ering this side payment to all type 1countries exceeds the payo! they get by not o!ering it. A little algebra shows


� In contrast to this paper, Hoel and Schneider (1997) assume that signatories o!er side paymentsto every non-signatory, irrespective of their type. They "nd that side payments reduce the number ofsignatories that pay others to abate (in the context of this model, they "nd that the number of type 2signatories falls when side payments are o!ered). In the model developed here, this would nothappen; type 2 signatories would not o!er side payments to type 2 non-signatories.

that this implies

mHH"0 if k�(c/b

�!�

�,

mHH"c!��b�

if k�5c/b

�!�

�. (9)

It remains to solve for kHH�

. Recall that this analysis was motivated by the specialcase where b

�was substantially greater than b

�, so that (4c) does not hold. This

implies that c/b�'c/b

�#�

�; and this in turn implies:

zHH�

"0, mHH"0, zHH�

"kHH�

"0 if k�(c/b

�, (10a)

zHH�

"k�, mHH"0, zHH

�"kHH

�"0 if c/b

�!�

�'k

�'c/b

�, (10b)

zHH�

"k�, mHH"c!�

�b�, zHH

�"kHH

�"N

�if k

�'c/b

�!�

�. (10c)

Two types of agreements can thus be sustained (for k�#k

�'0):

kHH�

"0, c/b�#1'kHH

�'c/b

�for c/b

�!�

�'N

�'c/b

�, (11a)

kHH�

"N�, c/b

�#1!�

�'kHH

�'c/b

�!�

�for N

�'c/b

�!�

�. (11b)

The new result is (11b). Provided b�is not too small, the equilibrium agreement

will consist of kHH�

#N�signatories, each of which plays Abate, with the type 2

signatories compensating the type 1 signatories by an amount c!��b�each.

Notice that the provision of side payments increases participation in the equilib-rium treaty by both types 1 and 2 countries. Strong asymmetry &ratchets up' thecooperation problem from one of supplying the public good directly to one ofpaying others to supply the good. More type 2 countries participate in theagreement with side payments because it is only jointly optimal for the requiredpayments to be o!ered if the cost can be spread over a large enough number oftype 2 countries.�

For Example 1, where the two types of countries are strongly asymmetric, theequilibrium agreement with side payments is �50, 33�, and the aggregate payo!is 17,800, or almost three times as large as in the earlier game. Changing the rulesof the game to allow side payments can thus have a dramatic e!ect on theequilibrium when countries are strongly asymmetric.

7. Fair side payments

The assumption that the type 2 signatories can make a take-it-or-leave-it o!erto the type 1 countries may seem jarring. Why should not type 1 signatories


receive a share of the surplus created by their participation? I consider analternative cost-sharing rule in the next section, but for now it is enough toobserve that, when there are more than two players, there will be a di!erencebetween the incremental gain and the total gain received by type 1 players(provided �

�'0). The decision of whether to accede would be guided by the

incremental gain, but the decision to accept the o!er as regards fairness wouldlikely be guided by the total gain. It is easy to show that, provided �

�'0, every

type 1 country is made strictly better o! when side payments are o!ered ascompared to the equilibrium where side payments are prohibited. Indeed, type1 signatories may gain more than type 2 signatories under this arrangement. InExample 1, a type 1 signatory gains 121.5 by the o!er of side payments whereasa type 2 signatory gains 96.8.

8. Cost sharing

Suppose now that countries are weakly asymmetric, as in Examples 2 and 3.Then the sequence of moves just considered no longer seems appropriate. At thesame time, the assumption that side payments cannot be paid seems excessivelyharsh. Even when countries are strongly asymmetric, as in Example 1, it is notobvious that the game analyzed above is the only alternative to the gamewithout side payments. Let us then treat countries as being symmetric as regardstheir accession decision but allow them to share the burden of public goodprovision.

In particular, suppose that signatories adopt the Chander}Tulkens (1994)cost-sharing rule. As compared with the alternatives studied in the literature(like the Nash bargaining solution, used by Carraro and Siniscalco (1993) andthe Shapley value, used by Barrett (1997, and Carraro and Botteon (1997)), theChander}Tulkens rule has a number of advantages: it belongs in the core (moreprecisely, the �- and �-core; see Chander and Tulkens (1994)), has a uniquesolution, and is simple. The rule requires that each signatory bears a share of thetotal cost of providing the public good equal to that country's share of the totalbene"t of the provision to all signatories. Formally,

��"

!c��(z

�#z

�)

��k�#k

�

#��(b

�z�#b

�z�). (12)

Since maximization of the joint payo! of signatories is una!ected by intra-treaty money transfers, the abatement choices of signatories are still givenby (3). Furthermore, equilibria (4a) and (4b) are unchanged by the o!erof side payments. The equilibria given by (4c) do change } though only slightly }when side payments are on o!er. As shown in the appendix, equilibriaconsisting of both types 1 and 2 countries must satisfy one of the following


four conditions:

c/b�#�

�'�

�kH�#kH

�'(c/b

�)(1#kH

�/kH

�), �

�kH�#kH

�'c/b

�#1,

(13a)

c/b�#�

�'�

�kH�#kH

�'c/b

�, (13b)

c/b�#�

�'�

�kH�#kH

�'c/b

�, c/b

�!1'�

�kH�#kH

�,

(c/b�)(kH

�#1)!1'�

�kH�#kH

�, (13c)

c/b�#�

�'�

�kH�#kH

�'c/b

�, c/b

�'�

�kH�#kH

�'c/b

�!1,

c(kH�#kH

�#1)/(b

�kH�#b

�)!1'�

�kH�#kH

�. (13d)

If (13a) or (13b) holds, then the self-enforcing agreement will require that bothtypes of signatory play Abate. If (13a) is satis"ed, a unilateral withdrawal willtrigger only the type 1 signatories to play Pollute. If (13b) holds instead, thena withdrawal would impel all the signatories to play Pollute. Conditions (13c)and (13d) are relevant only for equilibria in which type 2 signatories play Abatebut type 1 signatories play Pollute.

For Example 1, only condition (13c) is satis"ed. The equilibrium agreementconsists of both types of countries but with the &poor' paying the &rich' to playAbate! In particular, (13c) is able to sustain 16 di!erent equilibria. kH

�must be an

even number, and so the equilibria are �2, 16�,�4, 15�,2,�32, 1�. Though sidepayments increase the number of signatories in equilibrium, this is of no realbene"t, for the maximum aggregate net bene"t resulting from the application ofcost sharing is only 5600 } an amount strictly less than the aggregate net bene"twithout cost sharing. Perhaps even more importantly, type 2 signatories doworse with cost sharing as compared to the equilibrium agreement without sidepayments. Though type 1 signatories share the cost of abatement by the type 2signatories, there are fewer type 2 signatories undertaking abatement and thusless abatement being undertaken in aggregate. From a number of perspectives,application of the Chander}Tulkens cost-sharing rule may yield a very un-appealing outcome when countries are strongly asymmetric.

Of the other two examples, only Example 3 yields an equilibrium in whichboth types of country are required by the self-enforcing agreement to playAbate. In this case, only (13b) holds; and there are 16 possible equilibria, rangingfrom �1, 16� to �16, 1�. The total number of signatories is thus precisely thesame as compared to the case without side payments. Since the asymmetries arefor this example very slight, application of the Chander}Tulkens cost-sharingrule has a negligible e!ect on the equilibrium.

The message of this analysis is absolutely clear: allowing for side paymentswhen all countries choose simultaneously to be a signatory or a non-signatorydoes not buy any additional cooperation for the world. Indeed, the analysis


�This means that the provision of side payments would not a!ect participation by type 2countries.

Non-parties include: Afghanistan, Albania, Andorra, Angola, Armenia, Bhutan, Cape Verde,Congo, Djibouti, Eritrea, Guinea-Bissau, Haiti, Iraq, Kyrgyzstan, Palau, Rwanda, San Marino, SaoTomeH Principe, Sierra Leone, and Somalia.

provides a compelling explanation for why the kind of cost-sharing rule pro-posed by Chander and Tulkens (1994), which in their cooperative frameworkseems so appealing, is virtually never used in the real world.

9. The Montreal Protocol

In contrast to the earlier literature, the results reported in this paper areconsistent with the most signi"cant of all international environmental agree-ments: the Montreal Protocol.

Side payments were not included in the original, 1987 agreement. As RichardBenedick (1998, p. 148), the chief US negotiator, later put it, at this stage of thenegotiations most developing countries were &onlookers'. The industrializedcountries stood to gain the most from ozone layer protection. Indeed, for theUS, and possibly for every industrialized country, participation in this agree-ment was a dominant strategy (Barrett, 1990); that is, for these countries, theinequality in (2a) was reversed.� In a sense, the cooperation problem for thesecountries was to provide incentives for developing countries to accede to thetreaty.

Consistent with the theory developed here, the original treaty was amended in1990 to include a provision for compensating developing countries for the&incremental costs' of their participation. The parties agreed on the total com-pensation required for an initial period ($160}$240million for 1991}1993), givenassumptions about participation, and then apportioned this cost according tothe United Nations assessment scale, the obvious focal point. Soon after theamendment was negotiated, the number of developing country parties shot up;today, virtually every country with an e!ective municipal government is a partyto this treaty. It is true that some developing countries rati"ed the treaty beforecompensating payments were negotiated. However, many of these countrieswould have been a!ected by the treaty's trade sanctions. Moreover, the treaty'semission constraints did not bind on the vast majority of developing countries atthis time.

Though the treaty did not prescribe an explicit penalty for failing to contrib-ute to the Multilateral Fund, over the period 1991}1995, compliance with thisaspect of the treaty was nearly full. Of the total arrearage in payments, 99% wasattributable to just seven economies in transition, for whom special conditionsapplied (Benedick, 1998, p. 262).


�See the web page for the Secretariat of the Multilateral Fund for the Implementation of theMontreal Protocol, http://www.unmfs.org/general.htm.

Through June 1999, $973 million has been granted to the Multilateral Fundby 32 industrialized countries. The Executive Committee which manages theFund has approved the expenditure of $936 million, to support more than 2800projects and activities in 116 developing countries (124 developing countriesqualify to receive "nancial assistance). These investments are expected to reducethe consumption (production) of ozone-harming chemicals by more than121,000 (40,000) tons.� By any standard, this is a remarkable achievement.

10. Implications

This paper has obtained a number of results, some negative and somepositive. The important negative result is that side payments on their own havelittle e!ect on international cooperation. Countries &punish' defections when it isin their collective interests to do so, and this decision is not in#uenced directlyby the o!er of side payments. Side payments are transfers between signatories,and group rationality therefore ignores them. It is, of course, for this samereason that Carraro and Siniscalco (1993) obtain their main negative result, thatside payments cannot assist cooperation in symmetric treaties without commit-ment. Chander and Tulkens (1994) get a more pleasing result, but at the cost ofassuming beliefs that will not usually be con"rmed.

The important positive result of the paper is that strong asymmetry betweenplayers warrants a change in the rules of the game, and that this in turn enablesside payments to sustain a vastly superior outcome compared to the agreementwithout side payments. In a sense, strong asymmetry does much the same thingas commitment in Carraro and Siniscalco's (1993) paper, although the &commit-ment' made possible by strong asymmetry is of a di!erent type than theyconsider. Strong asymmetry means that some countries can only lose by acced-ing to an agreement that eschews side payments. With strong asymmetry,countries do not choose to be committed to any particular course of action; thepayo!s of the game simply ensure that these countries are committed.

The real advantage of strong asymmetry is that it is not arbitrary like theassumption of commitment can be (though countries cannot easily enter intocommitments, countries are asymmetric). Moreover, analysis of the equilibriumwith strong asymmetry does not need to appeal to cooperative game theoryand its many alternative solution concepts. So the prediction of themodel developed here deserves to be taken seriously } all the more so, perhaps,because this prediction is also consistent with the example of the MontrealProtocol.


More than this, the model also tells us that the Montreal Protocol is a specialcase. When negotiating the side payments in this agreement, the United Statesinsisted that it be `without prejudice to any future arrangements that may bedeveloped with respect to other environmental issuesa (Benedick, 1998, p. 184).The theory developed here not only explains how side payments came to beimportant to the Montreal Protocol but also why there cannot be a generalsolution to the problem of international cooperation. This, too, is somethingthat the earlier literature has been unable to explain.

Acknowledgements

I am grateful to Carlo Carraro, Parkash Chander, Michael Hoel, HenryTulkens, and two anonymous referees for comments.

Appendix A

Derivation of (3). Since non-signatories will play Pollute, the aggregate payo!of signatories, ��, can be written as

��"[(��k�#k

�)b

�!c]z

�#[(�

�k�#k

�)b

�!c]z

�. (A.1)

Maximization of �� with respect to z�requires

"k�

'

zH�

3�0, k�� if �

�k�#k

�" c/b

�"0 (

(A.2)

for i"1, 2. Assuming for simplicity that c/b�is a non-integer so that (A.2) holds

with strict inequality, the solution requires that all signatories of type i playeither Abate or Pollute. There are three kinds of equilibria: either zH

�"zH

�"0 or

zH�"0, zH

�"k

�or zH

�"k

�, zH

�"k

�. Note that zH

�"k

�, zH

�"0, though feas-

ible, cannot be an equilibrium. This means that, in an agreement consisting ofboth types of countries, if it is optimal for type 1 signatories to play Abate then itmust be optimal for type 2 signatories to play Abate.

Derivation of (13). Suppose to begin that ��k�#k

�'c/b

�. Then a type 1 coun-

try would not accede if ��(b

�k�#b

�k�)'!c�

�(k

�#1#k

�)/[�

�(k

�#1)

#k�]#�

�[b

�(k

�#1)#b

�k�] or c/b

�'[�

�(k

�#1)#k

�]/(k

�#1#k

�),

which holds by our assumptions. Similarly, a type 2 country would not accede,since c/b

�'(�

�k�#k

�#1)/(k

�#k

�#1).

Upon a withdrawal from an equilibrium agreement, two possibilities must beconsidered. Either all the type 1 signatories must play Pollute or all thesignatories of both types must do so, for if neither of these conditions were


satis"ed, then a withdrawal from the agreement would always be individuallyrational. Consider "rst the former possibility. For a withdrawal by a type 1signatory, c/b

�'�

�(k

�!1)#k

�'c/b

�and for a withdrawal by a type 2

signatory, c/b�'�

�k�#k

�!1'c/b

�. A unilateral withdrawal by a country

of either type will then cause all the remaining type 1 signatories to play Polluteif c/b

�#�

�'�

�k�#k

�'c/b

�#1. Given this, a type 1 signatory would not

withdraw if ��k�#k

�'c(k

�#k

�)/(b

�k�); and a type 2 signatory would not

withdraw if ��k�#k

�'c(k

�#k

�)/(b

�k�#k

�). Taken together, these condi-

tions yield (13a).Now suppose that a withdrawal impels all signatories to play Pollute. Then

we have c/b�#�

�'�

�k�#k

�. Withdrawal by a type 1 signatory will therefore

be irrational if ��k�#k

�'c(k

�#k

�)/(b

�k�#b

�k�). Since the RHS of this

inequality cannot exceed c/b�, and since we are considering the case where

��k�#k

�'c/b

�, we know that a type 1 signatory will not withdraw from this

agreement. A similar calculation shows that a type 2 signatory would notwithdraw either. This yields (13b).

There remains one other possibility: there may exist equilibria in whichcountries of both types are signatories but only type 2 signatories play Abate.This requires

c/b�'�

�kH�#kH

�'c/b

�. (A.3)

A type 1 country would prefer not to accede to this agreement if either of thefollowing hold:

c/b�!�

�'�

�kH�#kH

�'c/b

�!�

�, (A.4a)

c(kH�#kH

�#1)/b

�(kH

�#1)!�

�'�

�kH�#kH

�'c/b

�!�

�. (A.4b)

A type 2 country would not want to accede if either of the following hold:

c/b�!1'�

�kH�#kH

�'c/b

�!1, c(kH

�#1)/b

�!1'�

�kH�#kH

�,

(A.5a)

c(kH�#kH

�#1)/(b

�kH�#b

�)!1'�

�kH�#kH

�'c/b

�!1. (A.5b)

A type 1 signatory would be strictly worse o! by withdrawing from agreement(A.3) if

c/b�#�

�'�

�kH�#kH

�'c/b

�. (A.6)

Finally, a type 2 signatory will prefer not to withdraw if either of the followinghold:

c/b�#1'�

�kH�#kH

�'c/b

�, (A.7a)

c/b�#1'�

�kH�#kH

�'c/b

�#1, �

�kH�#kH

�'kH

�c/b

�. (A.7b)


Notice that both (A.7b) and (A.6) cannot be satis"ed. Since (A.6) must besatis"ed, however, (A.7a) must hold. But if (A.6) holds, then so will (A.7a). Inaddition, both (A.4b) and (A.5a) cannot hold. So there exist three possible typesof equilibria. One satis"es (A.3), (A.4a), (A.5a), and (A.6). This is given by (13c).The second satis"es (A.3), (A.4a), (A.5b), and (A.6), and the third satis"es (A.3),(A.4b), (A.5b), and (A.6). However, the conditions needed to sustain these lasttwo types of equilibria can be combined to yield (13d).

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