CFCC15 poster - Potsdam Institute for Climate Impact Research

Bottom-Up Formation & Stabilisation
of a Grand International Climate Coalition under Rationality
Jobst Heitzig, Potsdam Institute for Climate Impact Research (PIK), Transdisciplinary Concepts & Methods,
Ulrike Kornek, Mercator Research Institute on Global Commons and Climate Change; Kai Lessmann, PIK
[email protected]
Summary
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Observed: shift from Kyoto top-down agreement to Durban bottom-up process of pledges, but slow progress and large uncertainties (Lima)
Economic models had predicted global climate protection “coalition” likely “unstable” due to several obstacles for achieving high levels of cooperation (e.g. Barrett 2005)
Formal analyses of strategic interactions often neglect the time-evolving (“dynamic”) process inherent in negotiations
Here: Dynamic model of bottom-up coalition formation (Fig. 3) under usual assumption of rationality gives much more optimistic results!
Findings
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(similar for most parameter choices and payoff models)
Typically more than one consistent scenario (= assignment of probabilities to transitions)
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a “focal”, more symmetric scenario (Fig. 1c)
● several asymmetric scenarios (with one player being advantaged, Fig. 1ab)
A stable grand (global) coalition always forms after several steps
Closed-membership coalitions, once formed, will not be terminated later (although allowed unilaterally)
Several competing pathways to global cooperation, differing in
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no. of steps needed
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allocation of mitigation costs (players joining later have a bargaining advantage)
Path uncertainty largest in early steps with medium farsighted players, where
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both highly vulnerable and “reluctant” nations (with low mitigation potential)
delay cooperation (chicken-game-like, Fig. 2b players AB)
● both little vulnerable and “eager” nations (with high mitigation potential, Fig. 2b players CD)
compete for forming a coalition with many reluctant players and few other eager players
Surprisingly, strategic interactions do not lead to a stalemate without progress
(which would not form a consistent set of rational expectations)
(a) myopic players
(b) medium farsighted players
(c) very farsighted players
(a) scenario best for player A
(c) scenario best
for player C
(b) scenario best for player B
AC|B A|BC 67 BC
67 AC
(AB)C AB|C 67 BC
(AC)B 33 A
ABC 67 AC
A(BC) A|B|C 33 B
A|B|C AC|B 33 B
A|BC AC|B A(BC) AB|C (AB)C ABC A|B|C 33 A
AB|C ABC (AC)B (AC)B (AB)C A|BC A(BC) Fig. 1: Different consistent scenarios of coalition formation process
between three medium farsighted players (A=USA, B=Europe, C=China, payoff estimates from MICA [5]),
starting with no cooperation (box A|B|C) and producing grand coalitions (right end boxes) with different
probabilities (arrow labels).
(a) If all believe that USA may try to delay cooperation to improve their bargaining position, this indeed gets
a positive probability, leading to an intermediate coalition structure A|BC and then to the “nested” grand
coalition A(BC). (b) Analogous for Europe. (c) If all players believe China will not agree to a non-grand
coalition, it is rational for them to not try to delay cooperation.
Only these three potential scenarios form consistent sets of common expectations in this numeric example.
Model Details
25 C
(ABD)C (AB)CD ●
75 ABD
(AB)D|C A|BCD ((AB)D)C ●
B
ABCD (AB)C|D A
((AB)C)D ACD|B C
●
50 AB
AB|C|D 25 A
AB|CD (AB)(CD) A(B(CD)) D
50 CD
A((BD)C) A(BD)C 50 BD
A|B(CD) A|B|CD A(B(CD)) AB(CD) final stable grand coalition (ACD)B =
B signs an agreement with existing coalition ACD
(AC)(BD) ●
50 BD
25 C
AC|B|D 50 BD
AC|BD 50 AC
50 AC
●
A|BD|C 50 AC
A(CD)|B with
certainty
(A(CD))B (AC)BD (A(BD))C 50 AC
50 BD
50 AC
●
A(BD)|C ABD|C 50 BD
(AC)D|B B
((AC)D)B (AC)B|D (AB)CD 50 BD
A
AC|B|D ●
A|(BD)C Dynamic, stochastic, game-theoretic, similar to [1–3]
Process of international coalition formation under rationality
Over time, nations can form, grow, merge, shrink, split, or terminate coalitions
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existing coalitions assumed to ensure compliance internally (e.g. via [4])
In proportion to bargaining power, players propose changes in coalition structure
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Proposals will be accepted if profitable and undominated by another change (see figure)
Players may farsightedly anticipate and discount later states to some degree
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Uncertainty about proposals leads to unresolvable uncertainty about realised “pathway”
Result: consistent scenario of different branching pathways and their probabilities
Different scenarios represent different consistent common expectations about process
C
50 AB
((AB)D)C ((AC)B)D 50 CD
50 AB
AC|BD D
(AC)(BD) (AB)(CD) 50 CD
Grand coalitions
AB|C|D with “closed membership” treaties
(solidly painted borders)
are typically stable
absorbing states
50 CD
50 AD
A|(BD)C A|BD|C A(BD)|C 50 CD
intermediate state ACD|B =
all but B form a first coalition
A((BD)C) (AB)C|D A((BC)D) 50 BC
Individual
short-term
payoffs
in this state
50 AB
(A(BD))C ((AB)C)D 50 CD
with some
probability
A(BD)C 50 AB
AB|CD A|B|CD 50 AB
(AB)D|C (AD)BC Resulting
discounted
expected
long-term
payoffs
50 AB
B
(AD)C|B A|B|C|D ((AD)C)B (A(CD))B A
C
AD|B|C (AD)B|C 50 AD
((AD)B)C AD|BC A|BC|D A|(BC)D A((BC)D) 46
24
24
24
13
13
46
24
24
24
Some feasible moves are
profitable (w.r.t. long-term payoffs)
but dominated (dotted arrows) :
A subset of its initiators has another
move which they all prefer
initial state A|B|C|D = no cooperation
50 AD
A|B|C|D 50 AC
(A(BC))D A|B(CD) A(BCD) A(B(CD)) 25 A
ABD|C A(CD)|B (ACD)B (A(CD))B 25 B
A|B|CD (ABD)C ABC|D 50 CD
AB(CD) (AB)(CD) AB|CD (ABC)D A((BC)D) A|(BC)D (A(BC))D (AB)CD (AB)D|C Fig. 2: Influence of
farsightedness on
coalition formation
between four players (A,B,C as in
Fig.1, D=India, MICA payoffs [5]).
(a) Myopic players will form the
grand coalition immediately.
(b) Medium farsighted players
(discounting later payoffs at
factor 0.7 per step) may need
two steps, allowing USA or
Europe to delay cooperation.
(c) Very farsighted players (discount
factor 0.95) are patient enough to
even terminate any “asymmetric”
coalition to reach the “symmetric”
grand coalition (box ABCD).
AB|C|D (AB)C|D A(BC)|D A|BCD (AD)BC AD|B|C ABD|C (ABD)C 12
12
38
14
14
Permit buyers
(here: blue) prefer
to join late
Some moves are
profitable but
no-one's favourite
24
24
24
24
24
(dashed arrows)
START
75 BCD
A(CD)|B 25 A
((AB)C)D 0
0
0
14.3
10.3
10.3
Initial state
without coalitions
“Open
membership”
treaties
(dashed borders)
1/3
2/3
Probabilities
(line thickness)
are proportional to total
bargaining power
“Open
membership”
might get
coverted
to “closed
membership”
(exogenous parameter, here: all equal)
of those players
favouring the move
among all undominated moves
might get
terminated
50 AD
A(BC)D (ACD)B 36
18
AB(CD) A(BCD) ACD|B 12
18
50 AB
25 A
75 ACD
12
18
A|(BC)D A(BC)|D A|BC|D 12
A|B(CD) 75 BCD
AD|BC 36
25.7
Terminating
a coalition might be
not short-term but
long-term profitable
A(BCD) A(BC)D 3
5.9
50 CD
50 BC
(AD)(BC) 24
Permit sellers (here: red)
prefer to join early
3
((AC)B)D 25 A
16
7.5
50 BD
((AB)D)C 16
Simple
agreement
24
((AC)D)B i bl e )
o ss
ty
al p babili
ver
o
f s e 5% p r
eo
on ays (2
hw
pat
ACD|B 40
Nested
agreements
72
This move is
short-term but not
long-term profitable
50 BC
50 AC
A(BC)D 16
24
50 AD
50 BD
A(BC)|D 16
Free riders are “bought into” the coalition
6
ABCD ((AD)B)C A|BCD Result of surplus sharing
depends on reference point
(= state before new agreement)
40
(here: blue prefers terminating
the coalition unilaterally)
50 BC
((AD)C)B Given
coalitional
payoff
72
13
50 BC
(AD)(BC) 72
13
(here:
discount factor
= 1/2)
50 CD
(A(BC))D D
72
75 ABD
25 B
A|B|C|D 6
50 AD
24
24
(AD)B|C 25 B
75 ACD
50 CD
50 BC
(AD)C|B ABC|D (ABC)D (AD)BC (AD)C|B (AD)B|C 25 B
ABCD 3
3
36
12
12
12
36
12
12
7.5
5.9
25.7
17.7
15.1
17.1
37
13
13
50 AC
(ACD)B ((AD)C)B (AC)(BD) 25 B
A(BD)C (AC)D|B If a player leaves an
“open membership” coalition,
the rest stay together
75 BCD
((AD)B)C AC|BD A|BD|C 25 A
A|(BD)C (AC)B|D A((BD)C) A(BD)|C 25 B
50 BD
25 C
(AC)BD 72
(A(BD))C AC|B|D 75 ACD
(AC)BD ABC|D (ABC)D 25 B
(AC)D|B ((AC)D)B AD|B|C 75 ACD
75 ACD
(AC)B|D ((AC)B)D A|BC|D AD|BC (AD)(BC) 24
24
24
23.3
99
99
Grand coalitions with “open membership”
treaties (dashed borders) are typically unstable
References: [1] Konishi H, Ray D (2003) Coalition formation as a dynamic process. J Econ Theory 110 (1), 1–41
[2] Hyndman K, Ray D (2007) Coalition formation with binding agreements. Rev Econ Studies 74 (4), 1125–47
[3] Heitzig J (2011) Efficiency in face of externalities when binding hierarchical agreements are possible. Game Theory & Bargaining Theory eJournal 3 (40), 1–16
[4] Heitzig J, Lessmann K, Zou Y (2011) Self-enforcing strategies to deter free-riding in the climate change mitigation game and other repeated public good games. PNAS 108 (38), 15739–15744
[5] Lessmann Kai, Kornek U et al. (2014) The Stability and Effectiveness of Climate Coalitions. Environmental and Resource Economics, 1-26
Fig. 3: Detailed
explanation
of the model
in a fictitious
example
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