A New State of the World
« And one should remember that there is nothing more
difficult to execute, nor more dubious of success, nor
more dangerous to handle that to introduce a new
order of things: for a reformer has all those who
profit from the old system as his enemies, and only
lukewarm allies in all those who might profit from
the new system. These allies are lukewarm partly
from fear of their adversaries, who have the laws in
their favour; and partly from the incredulity of
mankind, who do not truly believe in anything new
until they have had actual experience of it. »
Nicolas Machiavelli, « The Prince »
"Is multilateral international treaty
negotiation
a cooperative or non-cooperative
process?:
The Kyoto Protocol and other examples"
Sylvie Thoron
International Environmental
Agreements
Reduction of atmospheric pollution
Reduction of marine pollution
Conservation and control of marine or
freshwater fisheries
 Conservation of marine mammals
 Conservation of biodiversity…




Public goods: one country’s action on one of
these variables injures or benefits all the other
countries. And this country cannot avoid
engendering this externality.
International environmental
treaties: a modern institution

This generates a free riding problem: regarding only its
own interest, each country has an incentive to overpollute or to over-consume the common resources.

This problem can only be solved by the cooperation of
the different countries  international treaties.

The use of international environmental treaties has
increased significantly, especially since the second world
war.

This growth coincides with the birth of the United
Nations. But the UN is also a consequence of an
increasing demand for this kind of institution.
International treaties
Source: Barret (2003)
The Best of all Worlds:
Negotiation as a cooperative game

N is the set of partners in the negotiation.

Assume that we can incorporate all the elements relevant for
the negotiation in what we call a Characteristic function.

If the purpose of the negotiation is to share some common
resources, the characteristic function attributes to each group
of participants (coalition) S C N, the resources they could
obtain by themselves V(S).

The cooperative game is “super-additive”: what a group of
countries could obtain together is “better” than the sum of
what each one could get on its own.
V(S) + V(T) < V(SUT)

If the purpose of the negotiation is to share the cost to
produce a public good, the characteristic function
attributes to each coalition S C N, the cost which the
countries would bear if they had to produce the public
good by themselves C(S).

The cooperative game is “sub-additive”: the cost a group
of countries would have to bear together is “lower” than
the sum of what each one would have to contribute on
its own.
C(S) + C(T) > C(SUT)
Value and axiomatic approach
A value associates to each cooperative game a « prospect »
which represents what each partner can hope to obtain by
participating in the negotiation.
"At the foundation of the theory of games is the assumption
that the players of a game can evaluate, in their utility scales,
every "prospect" that might arise as a result of a play. In
attempting to apply the theory to any field, one would normally
expect to be permitted to include, in the class of "prospects,"
the prospect of having to play a game. The possibility of
evaluating games is therefore of critical importance.”
Shapley (1953)
A value must be characterized by a set of “Axioms” which are
mathematical properties with an intuitive interpretation.
The Shapley value
Axiomatization
The outcome of the negotiation should satisfy the following
axioms:

Efficiency. The partners share all that they can produce
or the whole cost needed. No loss.

Anonymity. What each partner can obtain or contribute
should not depend on her name.

Additivity. Two negotiations about different objects are
independent: What a partner can obtain as a result of
two negotiations is just the sum of what she can get in
each one.
The Shapley value
i  N,
i  N , v  
n  s !s  1!S  N ,iS vS   vS \ i 
i: a partner
N: the set of partners
V: the characteristic function
n: the size of N
S: the size of coalition S
n!
The Shapley value
Heuristic Description

The partner i’s contribution to group S is her incremental value:
V(SUi) - V(S)

Partners believe in the following principles:
– Each partner must be remunerated at the level of her contribution.
– This contribution depends of course on the coalition the partner joins.
– We need to calculate a kind of average of the different incremental
values.

Players have to meet in a bargaining room to share what they can
obtain all together.

They arrive sequentially and the order in which they do so is
determined by chance, with all arrival orders equally probable.

Each player, when she enters the room, demands and is promised
the amount which her participation contributes to the value of the
coalition already in the room.
Applications of the Shapley value
Cost sharing
 Example: Three properties along a private impasse. How to share
the cost of renewing the road?
C
B
A
O
Applications of the Shapley value
Cost sharing
 Example: Three properties along a private impasse. How to share
the cost of renewing the road?
C
B
A
O
A, B, C
Applications of the Shapley value
Cost sharing
 Example: Three properties along a private impasse. How to share
the cost of renewing the road?
C
B
A
B, C
O
A, B, C
Applications of the Shapley value
Cost sharing
 Example: Three properties along a private impasse. How to share
the cost of renewing the road?
C
B
C
A
B, C
O
A, B, C
Applications of the Shapley value
Cost sharing
 Example: Three properties along a private impasse. How to share
the cost of renewing the road?
C
B
A
O

Most famous example: Investment and pricing policy in 1968-1969
at Birmingham Airport. (Littlechild and Thompson (1974))

The value is the cost of accommodating an aircraft type. Aircraft
types can be ranked by « size ». A bigger aircraft uses a longer
runway.
Environmental Game I
10%
The global target is just a collective
optimum calculated by the scientists.

IPCC

Let the set of partners in the negotiation be a set of three coalitions
of countries N={1,2,3} which want to follow the advice and decrease
their total pollution (TP) by 10 percent.

At the outset, each coalition generates a percentage of the total
pollution TP. Let us assume that each coalition's pollution is,
respectively,
– P₁ = 90,
– P₂ = 160,
– P₃ = 360
Characteristic Function
The environmental game is a cost sharing game.
The three coalitions have to decide how to contribute to decrease the pollution
by 10%.

Consider that, for each coalition, its value is the cost of decreasing its own
pollution by 10%.

The marginal cost is decreasing.
C R   R
For each country:
– The first country has to reduce by 9, its cost to do that is C(1) = 3
– The second country has to reduce by 16, its cost to do that is C(2) = 4
– The third country has to reduce by 36, its cost to do that is C(3) = 6
For each coalition of two countries:
– Countries 1 and 2 have to reduce their joint pollution by 9+16 = 25, the cost to do
that is C(12) = 5
– C(13) = 6.7
– C(23) = 7.2
–
–

For the three countries together
C(123) = 7.8
This game is sub-additive:
C(12) < C(1) + C(2)
C(123) < C(12) + C(3) …
Country 1’s cost to decrease
pollution by 10% = 3
Country 1’s cost to decrease
pollution by 10% = 3
Country 2’s incremental cost
is C(12) – C(1) = 5-3=2
Country 1’s cost to decrease
pollution by 10% = 3
Country 2’s incremental cost
is C(12) – C(1) = 5-3=2
Country 3’s incremental cost
is C(123) – C(12) =
7.8 – 5 = 2.8
Country 1’s cost to decrease
pollution by 10% = 3
Country 2’s cost to decrease
pollution by 10% = 4
Country 2’s incremental cost
is C(12) – C(1) = 5-3=2
Country 1’s incremental cost
is C(12) – C(2) = 5-4=1
Country 3’s incremental cost
is C(123) – C(12) =
7.8 – 5 = 2.8
Country 3’s incremental cost
is C(123) – C(12) =
7.8 – 5 = 2.8
Country 1’s cost to decrease
pollution by 10% = 3
Country 2’s cost to decrease
pollution by 10% = 4
Country 2’s incremental cost
is C(12) – C(1) = 5-3=2
Country 1’s incremental cost
is C(12) – C(2) = 5-4=1
Country 3’s incremental cost
is C(123) – C(12) =
7.8 – 5 = 2.8
Country 3’s incremental cost
is C(123) – C(12) =
7.8 – 5 = 2.8
Country 1’s cost to decrease
pollution by 10% = 3
Country 2’s cost to decrease
pollution by 10% = 4
3
3 2
1
Country 2’s incremental cost
is C(12) – C(1) = 5-3=2
Country 1’s incremental cost 1
is C(12) – C(2) = 5-4=1
2 3
3
Country 3’s incremental cost
is C(123) – C(12) =
7.8 – 5 = 2.8
Country 3’s incremental cost
is C(123) – C(12) =
7.8 – 5 = 2.8
1 1
2
2
The Shapley value of the
environmental game I



Country 1’s Shapley value: 1.48
Country 2’s Shapley value : 2.23
Country 3’s Shapley value : 4.08

Suppose we allocate to each country a reduction in
pollution in proportion to its contribution to the cost. This
gives:

Country 1’s pollution reduction: 11.57 (>9)
Country 2’s pollution reduction: 17.44 (>16)
Country 3’s pollution reduction: 31.91 (<36)



Of course the pollution reduction increases with the
volume of pollution but less than proportionally. The
biggest country reduces its pollution by the smallest
percentage.

Could we use this kind of cooperative game to
evaluate the outcome of a treaty negotiation?

Could we propose the Shapley value to the
delegates as a solution to the negotiation?

And if not, why?

Are we in a cooperative framework?

In a cooperative framework, partners have the
possibility to sign “binding agreements.”
Are the treaties
binding or not binding?

There is a large literature on the problem of compliance.

Most treaties do not incorporate enforcement
mechanisms.

« International lawyers and others familiar with the
operations of international treaties take for granted that
most states comply with most of their treaty obligations
most of the time »
Abram Chayes and Antonia Chayes (1991)

Two interpretations:
– Either the treaties are in fact not far from what the countries
would do without a treaty. Not a big improvement to be made
towards the collective optimum.
– Or the treaties are sustained by informal mechanisms (public
opinion, maintaining reputation).
Example of a successful implementation:
the Montreal protocol on the Ozone layer
depletion (entry into force 1989)
Participation versus Compliance

Even if there is no problem of compliance, or in other
words, if the treaties are binding, the incentive to free
ride remains, generating a participation problem.

Externalities: In the description of Environmental Game
I, the partners do not have the possibility to refuse to
participate in the cost sharing. Otherwise, it may be that
it is much more beneficial to leave to the others the task
of negotiating the decrease of 10%.

The Shapley value for games with externalities is not
efficient (Maskin 2003).
Bilateral treaties

This problem do not occur in the case of bilateral treaties.

Prisoner’s dilemma: cooperation is Pareto-efficient, non-cooperation
is self-enforcing.

Pareto efficiency: a situation in which it is impossible to improve
everybody’s welfare in the same time.

Nash equilibrium: no one wants to change its strategy unilaterally. It
is self-enforcing.
 Problem of compliance
 If the agreement was “binding” the problem would be solved. Each
partner would be willing to be committed to this agreement: both
partners would sign a binding agreement for sure. There is no problem
of participation.
Free riding

Prisoner Dilemma Game
C
c
c
2;2
d
3;-1
d
- 1; 3
R
1; 1
Free riding

Prisoner Dilemma Game
C
c
c
2;2
d
3;-1
d
- 1; 3
R
1; 1
Free riding

Prisoner Dilemma Game
C
c
c
2;2
d
3;-1
d
- 1; 3
R
1; 1
Free riding

Three players
c
c
c
d
d
2 ; 2 ; 2 1.5;2.5;1.5
c
c
d
1.5 ; 1.5 ; 2.5
- 1; 3; 3
3 ; - 1; 3
1;1;1
R
d
2.5 ; 1.5; 1.5 3 ; 3; - 1
d
Free riding

Three players
c
c
c
d
d
2 ; 2 ; 2 1.5;2.5;1.5
c
c
d
1.5 ; 1.5 ; 2.5
- 1; 3; 3
3 ; - 1; 3
1;1;1
R
d
2.5 ; 1.5; 1.5 3 ; 3; - 1
d
Free riding

Three players
c
c
c
d
d
2 ; 2 ; 2 1.5;2.5;1.5
c
c
d
1.5 ; 1.5 ; 2.5
- 1; 3; 3
3 ; - 1; 3
1;1;1
R
d
2.5 ; 1.5; 1.5 3 ; 3; - 1
d
Free riding

Three players
c
c
c
d
d
2 ; 2 ; 2 1.5;2.5;1.5
c
c
d
1.5 ; 1.5 ; 2.5
- 1; 3; 3
3 ; - 1; 3
1;1;1
R
d
2.5 ; 1.5; 1.5 3 ; 3; - 1
d
Multilateral treaties
 There is not only a problem of compliance but
also a problem of participation. Not all the
partners are willing to be committed.

The best situation for a partner is the situation
in which she is not committed and the others
are.

Problem of participation in the case of
multilateral treaties is at least as important as
the problem of compliance.
Multilateral Agreements
Procedure
Two step Procedure
(Vienna Convention on treaty law (1969)):
1.
Negotiation phase which culminates in the
signature of the treaty
 Problem of participation
2.
Ratification phase
 Problem of participation
Outcome of the Negotiation Phase
1. The global objective
In most of the agreements on atmospheric pollution the global objective is
defined as a target and a timetable
1.
Helsinki Protocol on the Reduction of Sulphur Emissions by at least 30
percent (1987)
« Article 2: The Parties shall reduce their national annual sulfur emissions or
their trans-boundary fluxes by at least 30 per cent as soon as possible and at
the latest by 1993, using 1980 levels as the basis for calculation of reductions.»
2.
Montreal Protocol on Substances that Deplete the Ozone Layer: CFCs
(chlorofluorocarbons) Baseline 1986
1.
2.
3.
3.
Freeze 1989
20% in 1993
50% in 1998
Kyoto Protocol of the UNFCCC:
1.
Baseline 1990
- 5.2% of the industrialized countries’ greenhouse gas emissions must be achieved before
the end of the period 2008-2012
Outcome of the Negotiation Phase
2. The different contributions

Protocol on the Reduction of Sulphur Emissions (1985): uniform
target, -30 percent for everybody involved.

Protocol on Further Reduction of Sulphur Emissions (1994): a
differentiation of emission reduction obligations of Parties to the
Protocol.

Montreal Protocol on Substances that Deplete the Ozone Layer:
uniform target for industrialized countries, a 10-year grace period
for developing countries.

Kyoto Protocol of the UNFCCC: limits are country-specific.
Countries included in Annex I to the
Kyoto Protocol
and their emissions targets
Country
Target (1990** - 2008/2012)
EU-15*, Bulgaria, Czech Republic,
Estonia, Latvia, Liechtenstein,
Lithuania, Monaco,
Romania,Slovakia,Slovenia, Switzerland
-8%
US***
-7%
Canada, Hungary, Japan, Poland
-6%
Croatia
-5%
New Zealand, Russian Federation,
*
Ukraine
0
Norway
+1%
Australia
+8%
Iceland
+10%
« The target figures, i.e., assigned amounts, became
highly politicized, and were the most visible element of
the Protocol… Chair Estrada took the initiative to
compile the target figures, due to the explosive nature
of the issue and since the parties made the setting of
their targets dependent upon the targets of others. »
Heike Schröder (1999)
The negotiation was more a contribution game than a
cost sharing game. The global target seems to be more
th result of the negotiation and not a scientific starting
point.
Ratification Phase: Different rules
1.
Not specified: Exceptional. Never the case for treaties on atmospheric
pollution.
2.
Unanimity: All the contracting parties have to ratify before the treaty can
enter into force. Never the case for treaties on atmospheric pollution.
3.
A named set of signatories
International Convention for the Regulation of Whaling (1946) entered into force
after ratification of the Netherlands, Norway, the USSR, the United Kingdom
and the United States.
4.
A minimum number of ratifiers: the most common rule
Vienna Convention for Protection of the Ozone Layer (1985):20 out of 176
signatories
Protocol on the Reduction of Sulphur Emissions (1985): 16 out of 22
5.
A threshold expressed as a proportion of the target
Montreal Protocol (of the Vienna Convention) (1987): 11 states provided these
states account for at least two-thirds of 1986 estimated global consumption of
the controlled substances.
Kyoto Protocol (of the UNFCCC) (1997): 55 states including countries named in
Annex I which account for at least 55 percent of total carbon dioxide
emissions for 1990 of the countries listed in Annex I.
Distribution of emissions of GHG
between Annex 1 countries
(in percentage of Total Pollution in 1990)
Canada
3,3% TP
EU
29,8% TP
Japan
8,5% TP
Russia
17,4% TP
USA
36,1% TP
Total
95,1% TP
Total Annex 1
100%
41,6%TP
Distribution of emissions of GHG in 1990
between Annex I countries
Source: Barret (2003)
Distribution of emissions of GHG in 1990
between EU countries
Distribution of emissions of GHG in 1990
between “other” countries
Distribution of emissions of GHG in 1990
between EIT countries
Given this, how has the ratification process
evolved?
Ratification of the Kyoto Protocol
Calculation in chronological order
Share of
1990
Sum
2001 ratifications (Romania and Czech Republic)
2.48
2.48
Iceland (23rd May)
0.02
2.50
Norway (30th May)
0.26
2.76
Slovakia
0.42
3.18
European Union (15 members) (31st May)
24.23
27.41
Japan (4th June)
8.55
35.96
Latvia (5th July)
0.17
36.13
Bulgaria (15th August)
0.60
36.73
Hungary (21st August)
0.52
37.25
Estonia (14th October)
0.28
37.53
Poland (13th December 2002)
3.02
40.55
Canada (17th December 2002)
3.33
43.88
New Zealand (19th December 2002)
0.19
44.07
Switzerland (Mid 2003)
0.32
44.39
Russia (November 2004)
17.40
61.79 > 55
Kyoto thermometer
Sept.
2004
Nov.
2004
55
Russia
Europe
Europe
Japan
Japan
Canada…
Canada…
Nbr of
signatories
%age of
emissions
Nbr of
signatories
%age of
emissions
Two step procedure of negotiation

Why these two steps? Political acceptability: National delegates
negotiate at the international level but the outcome of the
negotiation needs to be endorsed at the national level.

But this two step procedure is not innocuous for the outcome
of the negotiation.
I It generates new opportunities to free ride: even if the
agreement is binding for the countries which have ratified it,
the signature of the treaty is not binding.
 II It makes the negotiation about the sharing of a global target
difficult.
 III It has an impact on the outcome of the negotiation.

Implications of the two step
procedure II

Assume that the agreement is binding after ratification,
that the “cost sharing game” is sub-additive and that the
countries want to reach a “collective optimum”. These
are the best conditions for a cooperative game, but…

They have to put the cart before the horse.

How can the countries negotiate about how to reach this
collective optimum and how to share a global target if
they do not know how many of them will ratify and will
really participate in the implementation?

This explains why, in this framework, the negotiation
could be more similar to a contribution game than to a
cost sharing game.

A natural way to negotiate would be to sign a more
general agreement and to wait for the minimum level of
participation to be reached to discuss the details of the
implementation.

But of course, this is not possible since the national
institutions would not ratify without knowing what there
are committed to.

And it would not be incentive compatible to fix the global
target in advance and to delay the negotiation about
how to share the cost to achieve this fixed target
between those who ratify. Indeed, the countries would
not have any incentive to ratify.

Another solution would be to propose contingent
contributions. A description of varying contributions,
contingent on the state of progress of the ratification
phase.
Implications of the two step
procedure III
About the Montreal Protocol on protection of the ozone
Layer, Ambassador Richard Benedick (1998), explains
that the U.S. started to propose a very high threshold:
“There was concern that the United States could, in a
situation analogous to its unilateral 1978 action, find
itself bound to the obligations of an "international"
protocol while its major competitors were not. As a
legacy of the domestic debate, some U.S. agencies
insisted on pushing for a proportion of consumption of
90 percent or higher as the trigger for entry into force
and other actions.”
“Such a provision could have proved a formula for delay…”
Article 16: Entry into force would require ratification by at least 11
parties, together constituting at least two-thirds of estimated global
consumption of controlled substances as of 1986.
“Most observers believed that this would provide a sufficient critical
mass to increase the pressure on any potential large holdouts to
join the treaty”
Benedick (1998)
About the Kyoto protocol Heike Schröder (2002) says that:
“The threshold for entry into force was set relatively high in order to
ensure that the most important emitters would be included in the
Protocol.”

When the negotiators choose the minimum participation level they
try to find the right balance between:
– the necessity to guarantee that the ratification phase will not last for
ever and will not be postponed for « too long »,
– and the necessity to fix a threshold high enough to limit the possibilities
of free riding.
Look at Benedick’s quote again:
“Most observers believed that this would
provide a sufficient critical mass to
increase the pressure on any potential
large holdouts to join the treaty”
Benedick (1998)
This, actually, says more.
Tipping Treaties

Barret (2003) speaks about « tipping treaties » when
the minimum participation level plays the role of a
threshold which generates an incentive to ratify for all
the remaining countries.

Why should a high threshold generate an incentive to
ratify for the remaining countries?
– The cost of implementing the agreement decreases if a country
can benefit from the experience of the countries who have
already ratified. Ex: it decreases the cost of developing R&D
projects to find new technologies, new substitutes (Montreal
protocol).
– No country wants to be “the odd man out” (pressure of the
other countries, pressure of public opinion)
– In the Kyoto Protocol, the ratifiers can participate in the
emission permit market (they can de-pollute more efficiently).
Back to the Cooperative Framework

If the minimum participation rule of the ratification
phase could create a tipping treaty, then the game can
be considered as cooperative again.

During the negotiation, the countries know that the
treaty will be fully ratified with a very high probability
and that it will be binding.

Of course there is still a participation problem, but given
the reality of international treaties, the problem is the
full participation, not the participation.

But if we turn back to the cooperative framework the
minimum participation rule still matters.
Cooperative negotiation under
threshold constraints

Should the Shapley value be modified to take into account the two
step procedure?

Even under the assumption of a “tipping treaty”, that is, assuming
that everybody will ratify, the ratification phase matters.

More exactly, what matters is the order in which the different
countries will ratify. Indeed, because the game is sub-additive, the
cost of participation in the treaty implementation decreases when
the number of active participants increases.

There is a second mover advantage.

Assume that the order of ratification is perfectly random.
Anticipations about the order of ratification are very difficult. There
is often a time inconsistency in a country’s declared positions.
– Different people: the delegates who participate in the negotiation are
not the same persons as those who will play a role during the
ratification
– Political changes
« We have moved beyond Cold War definitions of the
United States’ strategic interests. Our foreign policy must
now address a broad range of threats – including damage
to the world’s environment – that transcend countries and
require international cooperation to solve »
Vice President Albert Gore, Jr., letter introducing the US State
Department’s first annual report on the environment and US foreign
policy, Environmental Diplomacy (1997)
A Threshold value
Heuristic Description

The heuristic description of the Shapley value is modified by the
introduction of two rooms: the waiting room and the bargaining room.

The participants arrive sequentially and in a random order in the waiting
room.

But there is nothing to share before the coalition formed by the players in
the waiting room has reached the threshold.

When the last player necessary to reach this threshold enters in the waiting
room, the door is closed from outside and the usual process is followed by
the present players. Players arrive sequentially and in a random order in the
bargaining room. Each player from the waiting room, when she enters the
bargaining room, demands and is promised the amount which her
participation contributes to the value of the coalition.

When the waiting room is empty again, the door of the waiting room is
reopened and the remaining players arrive sequentially and go straight to
the bargaining room in order to demand the amount which their adherence
contributes to the value of the grand coalition.
Three possible rules to define a
threshold

The way the threshold is defined says at which point the
door of the negotiating room is open.

Depending on this definition, the previous description
may or may not differ from the heuristic description of
the Shapley value.

If the threshold is just a number of partners, the rule is
in this case innocuous since all the countries have the
same probability of appearing.

But if the threshold is a named set of partners or even a
proportional rule, the partners do not have the same
“weight” in the negotiation.

Some countries are more involved in the treaty
than the others. They have a leadership
commitment. They wish to be the first ones to
ratify. They are willing to contribute more.

The claim is that the different partners do not
have the same weight in the negotiation
(contrary to what was assumed for the Shapley
value).

And for a country, one way to communicate its
willingness to be a leader in the treaty is
through the minimum participation rule.
Think of a country which is necessary for the
treaty to come into force.
Conclusion

So, what we see from all this is that multilateral
negotiations are more complicated than they must seem
since every phase has an impact on the other phases.

This can be seen from the way in which the different
contributions are assigned.

The answer to the initial question is not clear but there is
some hope that the pressures for cooperative behavior
will be stronger than those for non-cooperative strategic
behavior.

Let’s hope so for our children and grand children.