Strategic bargaining theory

1

• Strategic bargaining theory
• and negotiations on global public goods

Alejandro CAPARRÓS Spanish National Research
Council (CSIC) and University Carlos III
2
The issue

• International negotiations on
• Climate change
• Ozone layer hole
• Biodiversity conservation
• Other (global) environmental issues
• Main common feature
• Prisoners dilemma
• The tragedy of the commons (Hardin, 1968)

3
Main approaches

• The small stable coalitions thesis
  non-cooperative game theory and cartel literature
  results (external and internal stability concept)
• The grand coalition thesis cooperative game
  theory (core concept)
• The negotiations approach bargaining à la
  Rubinstein

4
Motivation for the negotiations approach I

• F.O. Hampson and M. Hart (1995). Multilateral
  Negotiations Lessons from Arms Control, Trade
  and the Environment. JHU Press.
• multilateral negotiation is essentially a
  bargaining process that occurs between different
  coalitions
• Coalitions are defined as the unification of
  the power of resources (or both) of two or more
  parties so that they stand a better chance to
  obtain a desired outcome or of controlling others
  not included in the coalitions. Most
  negotiations when N is large have a tendency to
  break down into negotiations between different
  bargaining sets or coalitions

5
Motivation II

• Characteristics of these international
  negotiations
• Heterogeneous countries are negotiating
• These countries are regrouped in heterogeneous
  coalitions
• G77 and China
• This coalition has been relatively stable in
  climate change negotiations, although it has
  split up in several key moments
• On other issues, as trade negotiations, it
  recently broke down G20, LDC.
• Umbrella Group
• This coalition broke-down during climate change
  negotiations
• European Union

6
Motivation III

• Countries forming a coalition have internal
  meetings, which are closed when important issues
  are treated.
• They set up a common strategy and individual
  negotiators representing the coalition have
  bilateral or multilateral meetings.
• Northern countries are in general (in any case in
  climate change), responsible for the problem and
  ready to move first (climate change), give
  development aid (at least to some extent), accept
  reductions in their current privileges (trade
  negotiations)
• On climate change negotiations, northern
  countries (except USA) have accepted to move
  first, accepting quantitative restrictions to
  emissions (Kyoto Protocol)

7
Motivation IV

• Negotiations take time, several negotiation
  rounds
• United Nations Framework Convention on Climate
  Change, signed in 1992 (ratified by all
  countries)
• Kyoto Protocol, signed in 1997, ratified in
  2001-2004
• Marrakech Accords, signed in 2001, ratified with
  the Kyoto Protocol
• Post-Kyoto climate change agreement, currently
  negotiated
• Information is not complete
• Close meetings of the coalitions

8
Motivation V

• The Presidents of the different COPs have had
  different strategies, e.g., favoring bilateral
  meetings or favoring multilateral meetings.
• Negotiations sometimes fail or have success
  depending on crunch issues e.g. carbon sinks
  in The Hague Bonn.
• Negotiations frequently deal with different
  subjects, which are not necessarily related, e.g.
  climate change negotiations and WTO negotiations.

9
Strategic Bargaining Theory I

• Some papers on international negotiations (on
  global public goods) and strategic bargaining
  theory
• Caparrós, Péreau and Tazdaït, 2004. North-South
  Climate Change Negotiations a Sequential Game
  with Asymmetric Information. Public choice, 121
  (3-4) 455-480.
• Negotiations between coalitions
• Two-three coalitions negotiating
• ? We are now extending the framework to n
  coalitions.
• Infinite time horizon
• Asymmetric information

10
Strategic Bargaining Theory II

• Caparrós, Péreau and Tazdaït, 2005. Bargaining
  with Non-monolithic Players. FEEM Working paper
  95.2005.
• Coalition haves the possibility to split-up
  strategically during the negotiations.
• Camiña and Porteiro, 2004. The Role of Mediation
  in Peacemaking and Peacekeeping Negotiations.
  CORE Discussion Paper 2004/5.
• Mediation, not arbitration, is the role of a
  President of a COP.

11
Strategic Bargaining Theory III

• Manzini and Mariotti, 2005. Alliances and
  negotiations. Journal of Economic Theory.
• Coalitions are negotiating and have internal
  voting rules unanimity or majority
• Issue linkage
• Bac and Raff (1996)
• Fehrstman (1990, 2000)
• Bush and Horstmann (1997, 2002)

12

• North-South Climate Change Negotiations
• a Sequential Game with Asymmetric Information

Caparrós, Péreau and Tazdaït Public choice
(2004), 121 (3-4) 455-480
13
The Model General Characteristics I

• Heterogeneous coalitions are negotiating
• Two in the bilateral version (North vs South),
  three in the multilateral version (South splits
  up)
• Countries inside the coalition are identical
• Simultaneous alternative offers
• The Northern countries coalition (The North)
  starts proposing an amount of transfers to the
  Southern countries coalition (The South)
• Afterwards, alternative sequential offers follow
  (if no agreement is reached)
• Infinite time horizon (or till an agreement is
  reached)

14
The Model II

• The objective function of the coalitions is
  general, depending on the transfers proposed by
  the North to the South to reduce emissions
• Transfers (the sole strategic variable of the
  model) affect
• negatively the welfare of the North
• positively the welfare of the South
• The welfare of the coalition is the sum of the
  welfare of the countries forming it
• The minimum amount of transfers asked by the
  South is decided in an internal vote

15
The Model III

• That is
• Where ? Utility function of the North, U
  Utility function of the South, B abatement
  benefit, C number of countries of the Southern
  coalition, d discount rat ,t transfer, b
  reservation transfer

16
The Model IV

• Asymmetric information
• the North does not know the true type of the
  South, there are two possibilities (for a given
  level of effort)
• Strong requirements (b)
• Weak requirements (b-)
• the South does know the type of the North
• In the multilateral framework we analyze the
  outcome with
• Complementary and,
• Substitutable Southern coalitions.

17
The Model V

• Sequential Equilibrium (Kreps and Wilson, 1982)
• The strategies of both players are optimal in all
  the points of the game, given the believes of the
  North
• For any information set reached the believes of
  the North are given by Bayes law
• The beliefs must be the limit of, at least, a
  sequence of reasonable beliefs (we assume that
  the North has pessimistic believes)

18
Complete Information (Multilateral)

• In general
• the South is interested in negotiating together
  (only one coalition), while
• the North prefers to negotiate with two different
  coalitions
• Taking into account the nature of substitutable
  or complementary of the Southern coalitions
• if they are complementary they are interested in
  acting separately
• if they are substitutable, they are interested in
  acting together

19
Incomplete Information (Bilateral)

• We distinguish Southern coalitions with
• weak (b?) and
• with strong demands (b)
• Using a series of Lemmas, we show that a Southern
  coalition b? has interest in acting as if it were
  a b
• A Southern coalition b? will always suggest a
  counter-offer identical to the one proposed by b
  
• However, for some levels of transfers, b? will
  accept in the first negotiation round

20
Incomplete Information (Bilateral)

• If the offer proposed in the first period
  satisfies
• and the a priori beliefs of the North lower than
  a level g (pltg)
• Separating equilibrium
• b? will accept
• b will reject
• if pgtg, both coalitions obtain the level
  corresponding to b
• Pooling equilibrium
• That is The solution of the game is strongly
  influenced by the a priori believes of the North.
  

21
Incomplete Information (Multilateral)

• We only analyze situations where a delay appears.
• This delay can have two different
  interpretations
• For the North to get information about the
  characteristics of the South
• For the South to dissociate and to show its real
  requirements

22
Incomplete Information (Multilateral)

• Fist case two Southern coalitions with different
  requirements (bj? and bk)
• sub-case 1 acting together they ask b?. They are
  interested in separating themselves if bj? lt ?1
  
• sub-case 2 acting together they ask b. They are
  interested in separating themselves if bj? lt ?2
  
• since ?1 lt ?2, for bj? lt ?1 whatever the claim of
  the union, the Southern groups favor disunity,
  but
• for sub-case 1, bk is confronted with a delay
  while the union would lead to an agreement from
  the first stage,
• for sub-case 2, the negotiation delay is less
  costly for bk than in the previous case, since
  the delay would also appear acting together.

23
Incomplete Information (Multilateral)

• Second case two Southern coalitions with the
  same requirements (both high bj, bk)
• the negotiation will end in the second period
  with or without union
• it shows that each group is interested in acting
  separately when their respective demands,
  although high, are not enough to take a relevant
  part of the benefit (bk lt ?3)
• Third case two Southern coalitions with the same
  requirements (both low bj?, bk?)
• the delay can take place when the groups act
  jointly and require b (the delay can be
  interpreted as the means to affirm high demands)
• The paper discusses also other configurations.

24
Incomplete Information (Multilateral)

• When the Southern groups form a union (when they
  are substitutable) the delay favors the North.
• That delay corresponds to the time necessary for
  it to acquire the relevant information concerning
  the demands of the groups.
• When the Southern groups act separately
  (complementary coalitions), the delay has several
  interpretations
• E.g. if one of the two Southern groups is of type
  b, while the other is of type b?, the delay
  corresponds to the time necessary for b to
  dissociate from b?.

25
Incomplete Information (Multilateral)

• In general, in the multilateral framework, the
  information asymmetry reinforces
• the negotiation power of the complementary
  coalitions, which will generally act separately
• reduces that of the substitutable coalitions,
  which will generally act together.
• When both groups are of type bi, the conditions
  of complementarity-substitutability with
  asymmetric information are identical to those
  obtained with complete information.
• On the contrary, when at least one of the groups
  is of type bi? , the conditions of
  complementarity (substitutability) are wider
  (more restrictive).

26
Conclusions I

• Objective determine the different forms that
  international negotiations to enlarge the Kyoto
  Protocol to include the developing countries
  might take.
• The framework developed is wide enough to
  represent most of the international negotiations
  between the North and the South, as long as
• the North is willing to transfer money (or other
  economic advantages) in exchange of some
  commitment by the Southern countries
• data about the North are more accurate than data
  about the South.

27
Conclusions II

• In a bilateral framework, the asymmetry of
  information is not always beneficial for the
  South
• the North may delay the moment of an agreement to
  obtain information about the characteristics of
  the Southern coalition,
• compared to complete information, the South will
  pay a negotiation cost due to the delay.
• In a multilateral framework, the information
  asymmetry reinforces
• the negotiation power of the complementary
  coalitions, which will generally act separately,
• reduces that of the substitutable coalitions,
  which will act together.

28
Applied Conclusions

• Developing countries are interested in becoming
  complementary by setting at an early stage
  (pre-game) of the negotiations a high minimum
  level of ratification for the agreement to come
  into force (as for the Kyoto Protocol).
• If the southern coalitions become complementary
• they will act separately,
• the agreement will not be reached in the first
  negotiation period,
• the delay can be interpreted as the time needed
  by the coalition with strong demands to
  dissociate from the coalition with weak demands.

29

• Generalization to C southern countries/coalitions

Work in progress
30
Generalization The Model I

• The North (N) negotiates with C southern
  countries, which can form coalitions.
• All C southern countries are identical. We denote
  ci the number of countries in coalition i
• t is the transfer proposed by the North (N) and
  ei is the effort provided by coalition i
• To simplify, we
• normalize the payoffs setting the minimum
  requirements (bi) equal to zero
• assume that the North always starts the
  negotiations
• assume perfect information.

31
Generalization The Model II

• Two stages
• Stage 1 the C countries form n coalitions.
• Provisional criterion maximization of aggregated
  welfare of the Southern countries
• Simultaneous choice of coalition structure
• Stage 2 The n coalitions negotiate with the
  North
• Simultaneous negotiation
• Sequential negotiation
• In both cases, time between offers tends to zero
  (e.g. we are in negotiations within a COP)

32
Generalization The Model III

• The utility function of the Southern coalitions
  can be written as
• And that of the North

33
Generalization The Model IV

• We consider that the Southern coalitions can be
• Perfectly complementary, when the North needs to
  reach an agreement with all of them.
• Perfectly substitutable, when an agreement with a
  subset of the coalition structure suffices to
  have benefits for the North.
• Partially substitutable, when there exist a
  minimum number of signatories (S) needed to have
  positive benefits for the North.

34
Generalization Preliminary Results

• With simultaneous as well as with sequential
  negotiations the three following statements hold
• When the efforts of the countries are perfectly
  complementary, Southern countries will act
  separately.
• When the efforts of the countries are perfectly
  substitutable, Southern countries will act
  together, regrouped in a single coalition.
• If there is a minimum number of participants
  1ltSltC, the countries will regroup in the maximum
  number of coalitions that ensures that all
  coalitions are needed to reach S.

35
Generalization Example I

• Total number of Southern countries needed (or
  percentage of emissions) C 100.
• S 55
• S 67
• S 30

36
Thank you for your attentionE-mail
acaparros_at_ieg.csic.es