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 the
rules of the game of global public goods provision, with the consequence that cooperation by some countries is bought by others and aggregate welfare is increased, perhaps
substantially. Side payments on their own have virtually no e!ect on the outcomes that
can be sustained by self-enforcing cooperative agreements. But when the rules of the
game are changed by strong asymmetry } when some countries are e!ectively &committed' to being non-signatories to an agreement eschewing money transfers } side payments
become the vehicle for increasing participation in a cooperative agreement. 2001
Elsevier Science B.V. All rights reserved.
Keywords: International agreements; Side payments; Public goods
1. Introduction
Cooperative arrangements to supply global public goods like protection of
the ozone layer are normally codi"ed in international treaties. Every nation may
be better o! if all nations participated in such treaties, but sovereignty entitles
every nation to choose to participate or not as it pleases. So global public goods
will be under-provided unless free riding can be deterred. It is not enough that
a 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
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S. Barrett / European Economic Review 45 (2001) 1835}1850
to carry out the threat, should they be called upon to do so. The problem is that
any punishment intended to harm free riders will in the bargain harm the
countries called upon to impose the punishment. The sticks needed to deter free
riding completely will often not be credible (Hoel, 1992; Barrett, 1994, 1999).
Can carrots succeed where sticks fail? Carraro and Siniscalco (1993) show
that they can help, but only if the parties can commit to remaining as signatories. As noted above, however, the rules of international law allow countries
to 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 provision
for withdrawal. Besides, if commitments of this kind could be entered into, one
might ask why all countries would not simply commit to being signatories to an
agreement sustaining full cooperation.
Yet, side payments are a feature of some international agreements, perhaps
the most important being the agreement to protect the earth's ozone layer } the
Montreal Protocol. Moreover, side payments not only increased participation
in this treaty but were intended to have this e!ect (Benedick, 1998). How could
this be, when Carraro and Siniscalco show that commitment is needed to make
side payments potent? The simple answer is that the side payments in the
Montreal Protocol exploit important asymmetries. The rich countries, which
can expect to gain most from the provision of this global public good, have paid
the poor to accede to this treaty. Carraro and Siniscalco take countries to be
symmetric, and in doing so may have overlooked the most important reason for
making side payments.
Since participation in a treaty is voluntary, at a minimum every country needs
to gain from participating, and if participation is to be full when countries are
asymmetric this will often require some sharing of the costs of pollution
abatement (MaK ler, 1990). Allocations sustained by international agreements
should probably also ensure that no coalition of countries can gain by withdrawing, and so it is natural to ask whether the full cooperative outcome lies in
the core of the game. Chander and Tulkens (1994) show that, under certain
conditions, there exists a very simple cost-sharing rule that not only lies in the
core but that also sustains full cooperation as an equilibrium, whether countries
are symmetric or asymmetric (see also Chander and Tulkens, 1992, 1997).
This is an astonishing result. But the analysis which gives rise to it rests on
a possibly strong assumption: each country is assumed to believe that, should it
withdraw from an agreement sustaining full cooperation, all the other countries
will choose their pollution abatement unilaterally. However, it may not be in the
collective interests of these other countries to behave in this way (if it is
Carraro and Siniscalco (1993) also consider the possibility that a subset of non-signatories may
commit to paying the remaining non-signatories to cooperate.
Carraro and Botteon (1997) extend this earlier paper for a special case of asymmetry.
S. Barrett / European Economic Review 45 (2001) 1835}1850
1837
collectively optimal for N countries to cooperate, why should not it be optimal
for N!1 countries to cooperate, given that one country has chosen not to
cooperate)? Put di!erently, only in unusual cases would the threat to play Nash
upon 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 could
possibly increase participation in a self-enforcing, asymmetric treaty (as noted
previously, Carraro and Siniscalco prove that, in the absence of commitment,
cost sharing would not increase participation in a self-enforcing, symmetric
treaty).
In this paper I combine the most appealing features of this literature and
obtain very di!erent results. I begin by analyzing a game in which side payments
are prohibited. I then show that strong asymmetry among countries justi"es
a change in the rules of the game. If countries with a small net bene"t from
cooperation would never accede to a cooperative treaty, either individually or
en masse, then they are essentially &committed' to being non-signatories to an
agreement without side payments. At the same time, these countries would be
willing to accede, provided they were paid to cooperate. So they would o!er
their cooperation for sale, and the countries with a relatively large net bene"t
from cooperation would have an incentive to buy this cooperation. I show that,
under certain conditions, such a transaction would take place, that the equilibrium compensation would just satisfy the participation constraints, that the
countries that are paid to participate would nonetheless receive a surplus from
the agreement, and that the o!er of side payments would not only increase the
number of signatories with small net bene"ts but also the number of signatories
with 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 should
be treated symmetrically as regards their decision to be a party to an international treaty. Prohibiting cost sharing under such circumstances, however,
seems excessively harsh, so I also consider the implications of assuming that
signatories invoke the Chander}Tulkens cost-sharing rule. I show that use of
this rule makes little di!erence to the equilibrium agreement. There may be
a change in the composition of the agreement, but there will be no signi"cant
change 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 even
when countries are strongly asymmetric. Hence, it is not the making of side
payments per se that aids international cooperation, or even the making of side
payments when countries are strongly asymmetric. What really matters is that
strong asymmetry supports a change in the rules of the game by e!ectively
&committing' some countries to being non-signatories to an agreement that does
not pay for their accession. Side payments are only a vehicle for realizing the
gains from cooperation made possible by this change.
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S. Barrett / European Economic Review 45 (2001) 1835}1850
What is perhaps most remarkable about these results, and what sets this
paper apart from the earlier literature, is that the side payments mechanism in
the 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 to
work with and must usually be solved numerically (see Barrett, 1997; Carraro
and Botteon, 1997). Here I simplify by assuming that there are only two types of
country, that each country faces a binary choice (it either plays Abate or
Pollute), and that every country's payo! is a linear function of the choices of all
other countries. These simpli"cations give us everything we need (the underlying
game is an asymmetric prisoners' dilemma) while at the same time allowing us to
obtain 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! G (G ):
. G " (b z #b z ),
G "!c# (b z #b z ),
(1)
.
G G where z is the number of type i countries that play Abate (N !z countries thus
G
G
G
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 1
country does so; each type 2 country bene"ts at least as much as each type 1
country from the abatement undertaken by any country; and a country's own
net bene"t of abatement, !c# b , is at least as high for a type 2 country as for
G G
a type 1 country. Payo!s are normalized such that countries of either type get
a payo! of zero if no country undertakes any abatement.
In the context of stratospheric ozone depletion, we can think of type 1 countries as being &poor' and the type 2 countries as being &rich'. The rich countries
use far more ozone-depleting substances, so that abatement by a rich country
will 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 are
less likely to get skin cancer, and because people in poor countries have
a 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)
S. Barrett / European Economic Review 45 (2001) 1835}1850
1839
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 Nash
equilibrium of the one-shot game will be unique; all N countries will play
Pollute in equilibrium, but all N countries would be strictly better o! if every
country played Abate instead. What we want to know is: if the rules of the game
were suitably rewritten, could a better outcome be sustained by a self-enforcing
agreement?
3. Equilibria without side payments
Consider to begin the following 2-stage game: in stage 1, all countries choose
simultaneously to be a signatory or a non-signatory; and in stage 2 signatories
choose jointly whether to play Pollute or Abate (that is, signatories behave
cooperatively) while non-signatories simultaneously and independently make
the same choice (that is, non-signatories behave non-cooperatively).
This formulation treats countries symmetrically as regards their decision to be
a signatory or a non-signatory (states are sovereign equals under international
law). Signatories, however, have an advantage over non-signatories in this
model: they are assumed to comply fully with an agreement to play Abate
(their decision to play Abate, however, is determined endogenously). This
distinction may seem arti"cial but it is compatible with international law.
Custom insists that countries comply with the agreements they sign up to (so
that we can think of compliance as being enforced outside of the model) but it
does not expect others to punish a country that fails to implement a unilateral
declaration.
Solving the game backwards, it is obvious by (2a) that all non-signatories
must play Pollute in equilibrium. The "rst two stages of the game, however, are
a bit harder to solve.
Let k denote the number of signatories of type i. Then it can be shown (see the
G
appendix) that, in equilibrium, signatories will play
zH"0
G
zH"k
G
G
if c/b ' k #k ,
G
if c/b ( k #k .
G
(3)
It can be shown in a repeated game context that if a treaty can deter a unilateral withdrawal then
it can also deter a unilateral act of non-compliance (Barrett, 1999). In other words, in a repeated
game framework, the assumption of full compliance does not a!ect the equilibrium. This implies that
the analysis presented here, though geared to the study of international cooperation problems,
applies more broadly.
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S. Barrett / European Economic Review 45 (2001) 1835}1850
It remains to solve the stage 1 game. Three types of equilibria are possible (for
k #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# kHb /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 or
a combination of both types of countries.
These are &linchpin' equilibria in the sense that, if any signatory were to
withdraw from these equilibrium agreements, all the remaining signatories
would play Pollute. It will be recalled that Chander and Tulkens (1994) employ
a similar equilibrium concept. However, they assume that, should any country
withdraw from an agreement consisting of N countries, then all the remaining
signatories will &respond' by playing Pollute. Here we see that this belief will only
be 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 by
acceding. In this model, any country that accedes to an agreement comprising
kH#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 we
know from (2a) that an incremental accession must therefore be irrational.
Conditions (4) tell us that a self-enforcing agreement will consist of only one
type of country if countries are su$ciently asymmetric. In the absence of side
payments, a self-enforcing agreement can only consist of both types of country if
they are weakly asymmetric.
4. Examples
The following examples illustrate the qualitatively di!erent kinds of equilibria
that 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 strongly
asymmetric. Suppose, in particular, that b "3 and "0.5. Then there exists
Notice that, if (4a) holds, then kH32, N since, by (2a), c' b ; if (4b) holds, then kH32, N ;
and, if (4c) holds, then kH31, N and kH 31, 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.
S. Barrett / European Economic Review 45 (2001) 1835}1850
1841
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 equilibrium 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, suppose
that 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!s
of 7312.5 and 7225, respectively (the aggregate payo! in the full cooperative
outcome is 29,375).
Example 3. Finally, suppose that the two types of countries are nearly symmetric. 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 exist
a multiple of equilibria. Which equilibrium will be selected? If the choice of
whether to be a signatory or a non-signatory were made simultaneously and
independently, we could not say. However, if one type of country could commit
to 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 the
equilibrium in all of the above examples would be 0, 17. The same equilibrium
would be sustained if the decision of whether to be a signatory or a nonsignatory were made sequentially, with the type 1 countries choosing "rst, and
with all past choices being publicly observable. But how is the order of play to be
established? In general, it is impossible to say. However, for a special case the
order of play is obvious.
6. Strong asymmetry
For the special case illustrated by Example 1, where b is &big' relative to
b 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 not
exist; 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
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type 1 countries also play Abate. The rules of the game should allow the type 2
countries to pay type 1 countries to accede to the agreement. Consider, then, the
following game: in stage 1 every type 2 country chooses to be a signatory or
a non-signatory; in stage 2, type 2 signatories collectively choose (i) whether
to play Abate or Pollute and (ii) a money side payment m to be paid to every
type 1 country which agrees to accede to the agreement and play Abate; in
stage 3 every type 1 country chooses to be a signatory or a non-signatory, under
the conditions laid down above; and in stage 4, all non-signatories of whatever
type choose to play Abate or Pollute.
As above, we solve the game backwards. Since, by (2a), play Pollute is
a dominant strategy, all non-signatories will play Pollute in equilibrium. To
solve 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). Accession
for 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. Assuming
that side payments are not rationed, and denoting an equilibrium of this side
payments 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 30, k to
maximize
Q"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 ,
if k 'c/b .
(8)
zHH"k
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), then
zHH"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 1
countries exceeds the payo! they get by not o!ering it. A little algebra shows
With rationing, not all type 1 countries will accede.
S. Barrett / European Economic Review 45 (2001) 1835}1850
1843
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 special
case 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)
HH
HH
k "N , c/b #1! 'k '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 equilibrium treaty by both types 1 and 2 countries. Strong asymmetry &ratchets up' the
cooperation problem from one of supplying the public good directly to one of
paying others to supply the good. More type 2 countries participate in the
agreement with side payments because it is only jointly optimal for the required
payments to be o!ered if the cost can be spread over a large enough number of
type 2 countries.
For Example 1, where the two types of countries are strongly asymmetric, the
equilibrium 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 rules
of the game to allow side payments can thus have a dramatic e!ect on the
equilibrium 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!er
to the type 1 countries may seem jarring. Why should not type 1 signatories
In contrast to this paper, Hoel and Schneider (1997) assume that signatories o!er side payments
to every non-signatory, irrespective of their type. They "nd that side payments reduce the number of
signatories that pay others to abate (in the context of this model, they "nd that the number of type 2
signatories falls when side payments are o!ered). In the model developed here, this would not
happen; type 2 signatories would not o!er side payments to type 2 non-signatories.
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S. Barrett / European Economic Review 45 (2001) 1835}1850
receive a share of the surplus created by their participation? I consider an
alternative cost-sharing rule in the next section, but for now it is enough to
observe that, when there are more than two players, there will be a di!erence
between 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 would
likely 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 as
compared to the equilibrium where side payments are prohibited. Indeed, type
1 signatories may gain more than type 2 signatories under this arrangement. In
Example 1, a type 1 signatory gains 121.5 by the o!er of side payments whereas
a 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 the
same time, the assumption that side payments cannot be paid seems excessively
harsh. Even when countries are strongly asymmetric, as in Example 1, it is not
obvious that the game analyzed above is the only alternative to the game
without side payments. Let us then treat countries as being symmetric as regards
their accession decision but allow them to share the burden of public good
provision.
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) and
the Shapley value, used by Barrett (1997, and Carraro and Botteon (1997)), the
Chander}Tulkens rule has a number of advantages: it belongs in the core (more
precisely, the - and -core; see Chander and Tulkens (1994)), has a unique
solution, and is simple. The rule requires that each signatory bears a share of the
total cost of providing the public good equal to that country's share of the total
bene"t of the provision to all signatories. Formally,
!c (z #z )
G # (b z #b z ).
G "
Q
G k #k
(12)
Since maximization of the joint payo! of signatories is una!ected by intratreaty money transfers, the abatement choices of signatories are still given
by (3). Furthermore, equilibria (4a) and (4b) are unchanged by the o!er
of side payments. The equilibria given by (4c) do change } though only slightly }
when side payments are on o!er. As shown in the appendix, equilibria
consisting of both types 1 and 2 countries must satisfy one of the following
S. Barrett / European Economic Review 45 (2001) 1835}1850
1845
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,
H
H
H
(c/b )(k #1)!1' k #k ,
(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 both
types of signatory play Abate. If (13a) is satis"ed, a unilateral withdrawal will
trigger only the type 1 signatories to play Pollute. If (13b) holds instead, then
a withdrawal would impel all the signatories to play Pollute. Conditions (13c)
and (13d) are relevant only for equilibria in which type 2 signatories play Abate
but type 1 signatories play Pollute.
For Example 1, only condition (13c) is satis"ed. The equilibrium agreement
consists of both types of countries but with the &poor' paying the &rich' to play
Abate! 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 side
payments increase the number of signatories in equilibrium, this is of no real
bene"t, for the maximum aggregate net bene"t resulting from the application of
cost sharing is only 5600 } an amount strictly less than the aggregate net bene"t
without cost sharing. Perhaps even more importantly, type 2 signatories do
worse with cost sharing as compared to the equilibrium agreement without side
payments. Though type 1 signatories share the cost of abatement by the type 2
signatories, there are fewer type 2 signatories undertaking abatement and thus
less abatement being undertaken in aggregate. From a number of perspectives,
application of the Chander}Tulkens cost-sharing rule may yield a very unappealing outcome when countries are strongly asymmetric.
Of the other two examples, only Example 3 yields an equilibrium in which
both types of country are required by the self-enforcing agreement to play
Abate. In this case, only (13b) holds; and there are 16 possible equilibria, ranging
from 1, 16 to 16, 1. The total number of signatories is thus precisely the
same as compared to the case without side payments. Since the asymmetries are
for this example very slight, application of the Chander}Tulkens cost-sharing
rule has a negligible e!ect on the equilibrium.
The message of this analysis is absolutely clear: allowing for side payments
when all countries choose simultaneously to be a signatory or a non-signatory
does not buy any additional cooperation for the world. Indeed, the analysis
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S. Barrett / European Economic Review 45 (2001) 1835}1850
provides a compelling explanation for why the kind of cost-sharing rule proposed by Chander and Tulkens (1994), which in their cooperative framework
seems 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 are
consistent with the most signi"cant of all international environmental agreements: the Montreal Protocol.
Side payments were not included in the original, 1987 agreement. As Richard
Benedick (1998, p. 148), the chief US negotiator, later put it, at this stage of the
negotiations most developing countries were &onlookers'. The industrialized
countries stood to gain the most from ozone layer protection. Indeed, for the
US, and possibly for every industrialized country, participation in this agreement was a dominant strategy (Barrett, 1990); that is, for these countries, the
inequality in (2a) was reversed. In a sense, the cooperation problem for these
countries was to provide incentives for developing countries to accede to the
treaty.
Consistent with the theory developed here, the original treaty was amended in
1990 to include a provision for compensating developing countries for the
&incremental costs' of their participation. The parties agreed on the total compensation required for an initial period ($160}$240 million for 1991}1993), given
assumptions about participation, and then apportioned this cost according to
the United Nations assessment scale, the obvious focal point. Soon after the
amendment was negotiated, the number of developing country parties shot up;
today, virtually every country with an e!ective municipal government is a party
to this treaty. It is true that some developing countries rati"ed the treaty before
compensating payments were negotiated. However, many of these countries
would have been a!ected by the treaty's trade sanctions. Moreover, the treaty's
emission constraints did not bind on the vast majority of developing countries at
this time.
Though the treaty did not prescribe an explicit penalty for failing to contribute to the Multilateral Fund, over the period 1991}1995, compliance with this
aspect of the treaty was nearly full. Of the total arrearage in payments, 99% was
attributable to just seven economies in transition, for whom special conditions
applied (Benedick, 1998, p. 262).
This means that the provision of side payments would not a!ect participation by type 2
countries.
Non-parties include: Afghanistan, Albania, Andorra, Angola, Armenia, Bhutan, Cape Verde,
Congo, Djibouti, Eritrea, Guinea-Bissau, Haiti, Iraq, Kyrgyzstan, Palau, Rwanda, San Marino, Sao
TomeH Principe, Sierra Leone, and Somalia.
S. Barrett / European Economic Review 45 (2001) 1835}1850
1847
Through June 1999, $973 million has been granted to the Multilateral Fund
by 32 industrialized countries. The Executive Committee which manages the
Fund has approved the expenditure of $936 million, to support more than 2800
projects and activities in 116 developing countries (124 developing countries
qualify to receive "nancial assistance). These investments are expected to reduce
the consumption (production) of ozone-harming chemicals by more than
121,000 (40,000) tons. By any standard, this is a remarkable achievement.
10. Implications
This paper has obtained a number of results, some negative and some
positive. The important negative result is that side payments on their own have
little e!ect on international cooperation. Countries &punish' defections when it is
in their collective interests to do so, and this decision is not in#uenced directly
by the o!er of side payments. Side payments are transfers between signatories,
and group rationality therefore ignores them. It is, of course, for this same
reason that Carraro and Siniscalco (1993) obtain their main negative result, that
side payments cannot assist cooperation in symmetric treaties without commitment. Chander and Tulkens (1994) get a more pleasing result, but at the cost of
assuming beliefs that will not usually be con"rmed.
The important positive result of the paper is that strong asymmetry between
players warrants a change in the rules of the game, and that this in turn enables
side payments to sustain a vastly superior outcome compared to the agreement
without side payments. In a sense, strong asymmetry does much the same thing
as commitment in Carraro and Siniscalco's (1993) paper, although the &commitment' made possible by strong asymmetry is of a di!erent type than they
consider. Strong asymmetry means that some countries can only lose by acceding to an agreement that eschews side payments. With strong asymmetry,
countries do not choose to be committed to any particular course of action; the
payo!s of the game simply ensure that these countries are committed.
The real advantage of strong asymmetry is that it is not arbitrary like the
assumption of commitment can be (though countries cannot easily enter into
commitments, countries are asymmetric). Moreover, analysis of the equilibrium
with strong asymmetry does not need to appeal to cooperative game theory
and its many alternative solution concepts. So the prediction of the
model developed here deserves to be taken seriously } all the more so, perhaps,
because this prediction is also consistent with the example of the Montreal
Protocol.
See the web page for the Secretariat of the Multilateral Fund for the Implementation of the
Montreal Protocol, http://www.unmfs.org/general.htm.
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S. Barrett / European Economic Review 45 (2001) 1835}1850
More than this, the model also tells us that the Montreal Protocol is a special
case. When negotiating the side payments in this agreement, the United States
insisted that it be `without prejudice to any future arrangements that may be
developed with respect to other environmental issuesa (Benedick, 1998, p. 184).
The theory developed here not only explains how side payments came to be
important to the Montreal Protocol but also why there cannot be a general
solution to the problem of international cooperation. This, too, is something
that the earlier literature has been unable to explain.
Acknowledgements
I am grateful to Carlo Carraro, Parkash Chander, Michael Hoel, Henry
Tulkens, 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 .
Maximization of with respect to z requires
G
"k
'
G
zH 30, k if k #k
" c/b
G
G
G
"0
(
(A.1)
(A.2)
for i"1, 2. Assuming for simplicity that c/b is a non-integer so that (A.2) holds
G
with strict inequality, the solution requires that all signatories of type i play
either 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 of
both types of countries, if it is optimal for type 1 signatories to play Abate then it
must 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 be
considered. Either all the type 1 signatories must play Pollute or all the
signatories of both types must do so, for if neither of these conditions were
S. Barrett / European Economic Review 45 (2001) 1835}1850
1849
satis"ed, then a withdrawal from the agreement would always be individually
rational. Consider "rst the former possibility. For a withdrawal by a type 1
signatory, 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 Pollute
if 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 not
withdraw either. This yields (13b).
There remains one other possibility: there may exist equilibria in which
countries 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 the
following 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)
(A.5b)
c(kH#kH#1)/(b kH#b )!1' kH#kH'c/b !1.
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 following
hold:
c/b #1' kH#kH'c/b ,
c/b #1' kH#kH'c/b #1,
(A.7a)
kH#kH'kHc/b .
(A.7b)
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S. Barrett / European Economic Review 45 (2001) 1835}1850
Notice that both (A.7b) and (A.6) cannot be satis"ed. Since (A.6) must be
satis"ed, however, (A.7a) must hold. But if (A.6) holds, then so will (A.7a). In
addition, both (A.4b) and (A.5a) cannot hold. So there exist three possible types
of 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 last
two types of equilibria can be combined to yield (13d).
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