Self-Enforcing International Environmental Agreements and Altruistic Preferences

Schop , Ma k
A icle — Published Ve sion
Sel -En o cing In e na ional En i onmen al Ag eemen s
and Al uis ic P e e ences
En i onmen al and Resou ce Economics
P o ided in Coope a ion wi h:
Sp inge Na u e
Sugges ed Ci a ion: Schop , Ma k (2024) : Sel -En o cing In e na ional En i onmen al Ag eemen s
and Al uis ic P e e ences, En i onmen al and Resou ce Economics, ISSN 1573-1502, Sp inge
Ne he lands, Do d ech , Vol. 87, Iss. 9, pp. 2309-2359,
h ps://doi.o g/10.1007/s10640-024-00885-8
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h ps://doi.o g/10.1007/s10640-024-00885-8
1 3
Sel ‑En o cing In e na ional En i onmen al Ag eemen s
andAl uis ic P e e ences
Ma kSchop 1
Accep ed: 10 May 2024 / Published online: 25 June 2024
© The Au ho (s) 2024
Abs ac
This pape analyses he e ec s o al uism on he o ma ion o clima e coali ions in he
s anda d wo-s age game o sel -en o cing in e na ional en i onmen al ag eemen s wi h
iden ical coun ies. Al uism implies ha each coun y alues, o some ex en , e e y o he
coun y’s wel a e when deciding on i s coali ion membe ship and emissions policy. In he
Nash [S ackelbe g] game, he inge [coali ion] coun ies exploi he al uism o he coa-
li ion [ inge] coun ies so ha al uism dec eases [inc eases] he coali ion size. In any
case, global emissions and global wel a e a e close o he non-coope a i e alues. How-
e e , al uism na ows he gap be ween he indi idually op imal emissions and he socially
op imal emissions, so al uism inc eases global wel a e. The e ec s o al uism on he
o ma ion o clima e coali ions c ucially depends on i s modelling: I al uism a ec s he
membe ship decision bu no he policy decision, o i each coali ion coun y is mo e al u-
is ic owa d o he coali ion coun ies han owa d inge coun ies, al uism can s abilise
la ge coali ions up o he g and coali ion. Finally, al uism can s abilise small coali ions bu
des abilises la ge coali ions wi h asymme ic coun ies.
Keywo ds Clima e coali ion· Clima e policy· Mo al beha iou · Social no ms
JEL Classi ica ion C72· D64· Q54· Q58
1 In oduc ion
The Pa is Ag eemen , nego ia ed by 196 pa ies a he 2015 Uni ed Na ions Clima e
Change Con e ence, aims o limi global wa ming o well below 2°C compa ed o p e-
indus ial le els (UN 2015). Al hough he e is hus b oad consensus on he in e na ional
goal o clima e policy, a con inua ion o cu en policies would esul in global wa ming
o abou 3°C abo e p e-indus ial le els (UN 2023).1 Consequen ly, he Pa is Ag eemen
wi h i s na ionally de e mined con ibu ions does no cons i u e an e ec i e in e na ional
* Ma k Schop
ma k.schop @ e nuni-hagen.de
1 Depa men o Economics, Uni e si y o Hagen, Uni e si ä ss . 41, 58097Hagen, Ge many
1 I cu en policies con inue h ough 2030 and he implied ca bon p ice in 2030 inc eases wi h he
global g ow h a e h ough 2100, he e is a 50% [4%] median chance o limi ing global wa ming o 2.7°C
2310
M.Schop
1 3
en i onmen al ag eemen in e ms o he in e na ional poli ical na a i e. On he o he
hand, some wo ld egions ha e in oduced a he high ca bon p ices despi e acing nega i e
social cos s o ca bon (see Table1). Al hough hese ca bon p ices a e s ill well below he
global social cos o ca bon (418/ CO2 om Ricke e al. 2018), his beha iou can ha dly
be explained wi h pe ec sel ishness.2
Ins ead, i may e lec he impo an e ec s o al uis ic alues on en i onmen al beha -
iou ound in he psychological li e a u e (see, e.g., Die z e al. 2005; S eg 2016; Lades
e al. 2021).3 In pa icula , he e is e idence ha clima e policy nego ia o s ha e social
p e e ences ega ding bu den-sha ing ules: I clima e policy nego ia o s om ich coun-
ies we e pe ec ly sel ish, hey would suppo he g and a he ing ule, i.e. equal pe cen -
age educ ion o emissions, and oppose he egali a ian ule, i.e. equal pe capi a emissions.
Howe e , g oss domes ic p oduc pe capi a is no posi i ely [nega i ely] co ela ed wi h
suppo o he g and a he ing [egali a ian] ule (Lange e al. 2007; Meulemann and Zie-
gle 2015). Fu he mo e, clima e policy nego ia o s om indus ialized coun ies s a e ha
he egali a ian ule should be he mos impo an bu den-sha ing ule in in e na ional cli-
ma e ag eemen s (Kes e nich e al. 2021). These esul s sugges ha clima e policy nego-
ia o s a e no d i en by pe ec sel ishness.4
This pape analyses he o ma ion o clima e coali ions wi h al uis ic p e e ences.
In pa icula , each coun y alues, o some ex en , e e y o he coun y’s wel a e when
deciding on i s coali ion membe ship a he i s s age o he game and emissions policy a
he second s age o he game. In o de o be able o compa e ou esul s wi h he s anda d
li e a u e (Ca a o and Siniscalco 1993; Ba e 1994), we apply he canonical model o
sel -en o cing in e na ional en i onmen al ag eemen s wi h iden ical coun ies, conca e
u ili y om own emissions and con ex cos s om global emissions. Wi hou al uis ic
p e e ences, he s anda d (Nash o S ackelbe g) game wi h linea -quad a ic emissions
bene i s and linea ma ginal emissions damages p edic s ei he small o ine ec i e clima e
coali ions.5 Beyond he linea -quad a ic case, Ba e (2013) and Nkuiya e  al. (2015)
show ha clima e h esholds can s abilise he g and coali ion, Nkuiya (2020) inds ha
2 Wi h s a egic clima e policy, e ms-o - ade e ec s could explain pa o he gap be ween egional ca bon
p ices and egional social cos s o ca bon (Ma kusen 1975; Hoel 1996). Fu he mo e, he p esence o an
in e na ional ca bon ma ke wi h endogenous pe mi choice (Helm 2003; Hol sma k and Wei zman 2020)
incen i ises egions wi h low aba emen cos s o mi iga e emissions and sell pe mi s, which can educe
global emissions and aise global wel a e. This has been shown o an exogenous ca bon ma ke wi h an
endogenous clima e coali ion (Al ami ano-Cab e a and Finus 2006; Lessmann e al. 2014), an endogenous
ca bon ma ke wi hou clima e coali ion (Ca bone e al. 2009; Hol sma k and Mid ømme 2021) and an
endogenous ca bon ma ke wi h an endogenous clima e coali ion (Yu and Wu 2022).
3 Fu he examples include Ko chen and Moo e (2007) and Ziegle (2020) [Engle e al. (2022) and And e
e al. (2024)], who ind ha al uis ic alues a e signi ican ly posi i ely co ela ed wi h pa icipa ion in
g een-elec ici y p og ams [p o-clima e dona ions].
4 Hje pe e al. (2011) a gue ha he abili y- o-pay ule, in e ms o g oss domes ic p oduc pe capi a,
“has he g ea es po en ial o se e as a basis o ag eemen in nego ia ions on alloca ing mi iga ion
commi men s” because i is suppo ed by many and opposed by ew clima e nego ia o s. Fu he mo e, i is
no opposed by any clima e nego ia o om indus ialized coun ies.
5 In he Nash game wi h linea -quad a ic emissions bene i s and quad a ic emissions damages, Finus
(2001,p. 232) inds ha clima e coali ions consis o no mo e han wo coun ies. In he S ackelbe g game
wi h linea -quad a ic emissions bene i s and quad a ic emissions damages, Finus (2001,p. 232) inds ha
Foo no e 1 (con inued)
[2°C] abo e p e-indus ial le els (UN 2023,Chap e 4.5, Appendix C). Howe e , he e y high emissions
scena io o he IPCC (2021), which bes e lec s he cumula i e emissions om 2005 o 2020 (Schwalm
e al. 2020), e en p edic s a empe a u e inc ease o 4.4 °C abo e p e-indus ial le els (median; i h o
nine y- i h pe cen ile: 3.3–5.7°C) by he end o he cen u y (IPCC 2021,Chap e 4.3).
2311
Sel ‑En o cing In e na ional En i onmen al Ag eemen s and…
1 3
clima e coali ions can be la ge and e ec i e wi h isoelas ic emissions bene i s in he
S ackelbe g game, and Ecke and Nkuiya (2022) show ha con ex ma ginal emissions
damages can s abilise la ge coali ions up o he g and coali ion in he Nash game. Wi h
gene al unc ional o ms, he second s age o he Nash game and he S ackelbe g game
ha e been analysed in de ail by Bay amoglu e al. (2018) and Finus e al. (2021a, 2021b),
espec i ely. Finally, Finus e al. (2023) show ha he s able coali ion is always weakly
la ge in he S ackelbe g game han in he Nash game.6
We dis inguish be ween he coali ion coun ies aking he inge coun ies’ emissions as
gi en (Nash game) and aking he eac ion o he inge coun ies’ emissions in o accoun
(S ackelbe g game) when choosing hei own emissions. In bo h cases, al uism educes
each inge coun y’s emissions and aises global ma e ial wel a e, i.e. global wel a e in he
absence o al uis ic p e e ences. Fu he mo e, we ge he ypical esul s ha global emis-
sions dec ease and each inge coun y’s emissions and ma e ial wel a e inc ease wi h he
coali ion size in he Nash game and abo e a c i ical coali ion size in he S ackelbe g game.
By con as , he e ec o al uism on he equilib ium coali ion size depends c ucially on
he game s uc u e.
In he Nash game wi h linea -quad a ic emissions bene i s and quad a ic emissions
damages, al uism weakly educes he coali ion size, and clima e coali ions consis o no
mo e han wo coun ies. The di ec e ec o al uism, namely smalle global emissions
and la ge global ma e ial wel a e o a la ge coali ion size, makes i wo hwhile o all
o he coun ies i some coun y joins he coali ion. Howe e , he indi ec e ec o al uism,
namely smalle global emissions and la ge global ma e ial wel a e o a gi en coali ion
size, makes i less cos ly o all o he coun ies i some coun y does no join he coali ion.
This indi ec e ec ou weighs he di ec e ec o small coali ion sizes and explains he
small clima e coali ion in equilib ium.
In he S ackelbe g game wi h linea -quad a ic emissions bene i s and quad a ic emis-
sions damages, al uism weakly aises he coali ion size, and clima e coali ions can consis
o up o six coun ies. In his case, he coali ion coun ies ake ad an age o he inge
coun ies’ al uism by becoming less ambi ious in he igh agains clima e change, expec -
ing he inge coun ies o eac by educing hei emissions mo e han hey would wi hou
al uism. Howe e , he coali ion coun ies a e no much mo e ambi ious in he S ackelbe g
equilib ium han in he business-as-usual scena io wi hou coali ion o ma ion.
These esul s sugges ha al uism canno s abilise la ge and e ec i e clima e coali-
ions. Howe e , al uism na ows he gap be ween he indi idually op imal emissions and
he socially op imal emissions, so al uism inc eases global wel a e. Thus, al uism a ec -
ing he membe ship decision and he policy decision appea s o be mo e o a subs i u e
han a complemen o la ge clima e coali ions.
The economic li e a u e has de eloped and es ed se e al heo ies o impe ec
sel ishness. In he case o al uis ic p e e ences (Becke 1974), one can dis inguish be ween
pu e al uism, i.e. u ili y om o he s’ u ili y alues (Becke 1981), pa e nalis ic al uism,
i.e. u ili y om o he s’ consump ion bundles (Pollak 1988), and impu e al uism, i.e.
u ili y o wa m glow om gi ing o he s (And eoni 1990). Alge and Weibull (2010) show
ha pu e al uism used in his pape is e olu iona y s able, and And eoni e al. (2010)
6 Wi h linea aba emen bene i s, Ka p and Simon (2013) ind ha a coali ion o wo o less [ h ee o mo e]
coun ies is s able wi h s ic ly con ex [conca e] ma ginal aba emen cos s in he Nash game.
clima e coali ions a e ei he small o ine ec i e, and Diaman oudi and Sa ze akis (2006,p. 254) ind ha
clima e coali ions consis o no mo e han ou coun ies when cons aining he pa ame e space o ensu e
non-nega i e emissions.
Foo no e 5 (con inued)
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M.Schop
1 3
summa ize he signi ican e idence o al uism in economic expe imen s. O he heo ies
comp ise ecip ocal ai ness (Rabin 1993), inequali y a e sion (Feh and Schmid 1999;
Bol on and Ocken els 2000) and Kan ian beha iou (Alge and Weibull 2013; Roeme
2015).
These heo ies ha e also been applied in he li e a u e on sel -en o cing in e na ional
en i onmen al ag eemen s. Buchholz e al. (2018) and Nybo g (2018) analyse he e ec s
o ecip ocal ai ness when coun ies decide on hei membe ship in he coali ion and on
hei emissions. They ind ha ecip ocal ai ness can s abilise he g and coali ion, bu i
can also s abilise an in e io coali ion ha is ei he weakly la ge (Nybo g 2018) o e en
weakly smalle (Buchholz e al. 2018) han he in e io coali ion wi hou ecip ocal ai -
ness. Lange and Vog (2003) inco po a e inequali y a e sion à la Bol on and Ocken els
(2000) in o he canonical model o sel -en o cing in e na ional en i onmen al ag eemen s
and ind ha su icien ly la ge inequali y a e sion can s abilise he g and coali ion. By con-
as , Vog (2016) applies inequali y a e sion à la Feh and Schmid (1999) and inds no
s able coali ion wi hou ans e s in his nume ical model wi h he e ogeneous coun ies.
Recen ly, Eichne and Pe hig (2022) and Ulph and Ulph (2023) analysed he e ec s o
Kan ian o mo al beha iou when coun ies decide on hei membe ship in he coali ion
and on hei emissions. They ind ha membe ship mo alism expands he clima e coali ion,
and emissions mo alism can expand he clima e coali ion only in he p esence o membe -
ship mo alism.
Closes o ou pape is ande Pol e al. (2012), who analyse he e ec s o al uism
a ec ing he membe ship decision bu no he policy decision. They ind ha his kind o
pa ial al uism expands he clima e coali ion. We ex end hei model in o di e en di ec-
ions. Fi s , we conside al uism on bo h s ages o he game. Second, we analyse no only
he Nash game bu also he S ackelbe g game. Thi d, while hey sol e hei model nume i-
cally wi h he e ogeneous coun ies, we sol e ou model analy ically wi h homogeneous
coun ies. Fo h, we eplica e hei esul s analy ically o discuss he di e ences om ou
esul s.7
Finally, we pe o m wo model ex ensions. Fi s , we analyse he e ec s o communi y
al uism, ha is, we dis inguish be ween in-g oup al uism and ou -g oup al uism. In his
case, al uism can s abilise la ge coali ions up o he g and coali ion. Second, we analyse
he e ec s o al uism wi h linea clima e damages and asymme ic coun ies. In his case,
al uism can s abilise small coali ions bu des abilises la ge coali ions.
Table 1 La ges ca bon p icing schemes ep esen ing
22%
o global
CO2
emissions
P ice: The Wo ld Bank (2023), SCC (social cos o ca bon): Ricke e al. (2018)
$/ CO2EU GBR CAN USA KOR ZAF CHN ARG MEX JPN KAZ UKR
P ice 73 58 38 28 19 10 10 5 4 2 1 1
SCC
−4
−4
−8
48
−1
3 24 3 12 6
−1
−1
7 Daube (2019) and Goussebaïle e  al. (2023) analyse he e ec s o al uism on clima e policy wi h
mul iple coun ies. Daube (2019) shows ha al uis ic p e e ences lead o a pa ial in e naliza ion o he
clima e ex e nali y in he non-coope a i e solu ion, and o a ull in e naliza ion o he clima e ex e nali y
in he coope a i e solu ion i and only i he al uis ic p e e ences o all coun ies coincide. Goussebaïle
e al. (2023) analyse he e ec s o al uis ic o eign aid on clima e change mi iga ion and ind ha paying
ans e s be o e aba ing emissions incen i ises de eloping coun ies o choose e icien clima e change
mi iga ion and leads o he social op imum i al uis ic p e e ences a e su icien ly la ge. Howe e , bo h
pape s abs ac om coali ion o ma ion.

2313
Sel ‑En o cing In e na ional En i onmen al Ag eemen s and…
1 3
The emainde o he pape is o ganized as ollows: Sec .2 in oduces he model, and
cha ac e ises he social op imum and he business-as-usual scena io. Sec ion3 analyses
he e ec s o al uism on he Nash game o coali ion o ma ion. This sec ion also includes
a compa ison wi h he model o ande Pol e al. (2012). Sec ion4 analyses he e ec s
o al uism on he S ackelbe g game o coali ion o ma ion wi h he coali ion coun ies as
S ackelbe g leade s and he inge coun ies as S ackelbe g ollowe s. Sec ion5 discusses
which ealms o decision making migh be in luenced by social p e e ences. Sec ion6 pe -
o ms ou wo model ex ensions. Sec ion7 concludes.
2 Model
Conside a model wi h
n≥3
iden ical coun ies.8 Each coun y
i∈N
de i es consump ion
bene i s
B(ei)
om i s emissions
ei
, whe e
B(0)
≥
0
,
B′>0
and
B′′ <0
, and aces clima e
damages
D(e)
om global emissions
e
∶=
∑i∈N
e
i
, whe e
D(0)=0
,
D′>0
and
D′′ >0
.
Then, each coun y’s ma e ial wel a e unc ion is
Wi=B(ei)−D(e)
. Fu he mo e, each
coun y is al uis ic such ha i alues i s own ma e ial wel a e by 1 and e e y o he coun-
y’s ma e ial wel a e by
𝛼∈[0, 1]
.9 Thus, he al uism pa ame e
𝛼=0
implies pe ec ly
sel ish coun ies, while
𝛼=1
implies pe ec ly al uis ic coun ies. Then, each coun y’s
mo al wel a e is
whe e
W∶= ∑i∈NWi
is global ma e ial wel a e, and he global mo al wel a e is
Consequen ly, he socially op imal emissions (SO) a e independen o he al uism pa ame-
e
𝛼
, while he indi idually op imal emissions, i.e. he business-as-usual emissions (BAU),
a e no (Daube 2019, Resul s 4 and 5). In pa icula , he socially op imal alues and he
indi idually op imal alues coincide o
𝛼=1
. In AppendixA.1, we p o e ha global
emissions dec ease and global ma e ial wel a e inc eases wi h he al uism pa ame e in
he indi idually op imal solu ion. Consequen ly, he ela i e global emissions
eBAU ∕
e
SO
dec ease and he ela i e global ma e ial and mo al wel a e
WBAU ∕WSO =VBAU ∕VSO
inc ease wi h he al uism pa ame e .
In he u he cou se o he pape we analyse he wo-s age game o sel -en o cing en i-
onmen al ag eemen s. A he i s s age o he game, coun ies decide on hei membe -
ship in he coali ion. The eby, in e nal [ex e nal] s abili y implies ha no coun y will lea e
[join] he coali ion i his educes i s mo al wel a e (D’Asp emon e al. 1983). A he sec-
ond s age o he game, he e is a coali ion o m coun ies, and coun ies decide on hei
(1)
V
i=Wi+𝛼
∑
j∈N�i
Wj=(1−𝛼)Wi+𝛼W
,
(2)
V
∶=
∑
i∈N
Vi=
∑
i∈N
[
Wi+𝛼
∑
j
∈
N
�
i
Wj
]
=[1+𝛼(n−1)]W
.
8 We assume iden ical coun ies o analy ical ac abili y wi h con ex clima e damages. In eali y,
coun ies bene i di e en ly om own emissions and su e di e en ly om global emissions. Fo an
analysis wi h asymme ic coun ies and linea clima e damages, see Sec .6.2.
9 Ins ead, i each coun y alues i s own ma e ial wel a e by 1 and e e y o he coun y’s mo al wel a e
by
𝛾∈[0, 1∕n]
, hen each coun y’s mo al wel a e unc ion is
V
i=Wi+𝛾
∑j∈N�i
Vj=

Wi+𝛼
∑j∈N�i
W
j
wi h

Wi=Wi∕(1+𝛾)
and
𝛼 =𝛾∕[1−𝛾(n−1)] ∈ [0, 1]
, and ou esul s do no change. Fo an analysis wi h
communi y al uism (g ea e deg ee o in-g oup al uism han ou -g oup al uism), see Sec .6.1.
2314
M.Schop
1 3
emissions. The eby, each inge coun y maximizes i s mo al wel a e (1), and each coali-
ion coun y
i∈M
maximizes he sum o he coali ion coun ies’ mo al wel a e
Compa ing (1) and (3), each inge coun y’s policy weigh s i s own ma e ial wel a e by
1−𝛼
and global ma e ial wel a e by
𝛼
, while each coali ion coun y’s policy weigh s he
coali ion’s ma e ial wel a e by
1−𝛼
and global ma e ial wel a e by
𝛼m
. In he ollowing
we dis inguish be ween wo game concep s. In Sec .3, we analyse he Nash game, and in
Sec .4, we analyse he S ackelbe g game wi h he coali ion coun ies as S ackelbe g lead-
e s and he inge coun ies as S ackelbe g ollowe s. The espec i e game is hen sol ed by
backwa d induc ion.
3 Nash Game
A he second s age o he Nash game, each inge coun y
i=
maximizes i s mo al wel-
a e (1) o e i s emissions
e
, aking he o he coun ies’ emissions as gi en, which yields
Each inge coun y equa es ma ginal emissions bene i s o i s own ma ginal emissions
damages
D�(e)
, plus all o he coun ies’ ma ginal emissions damages weigh ed by he
al uism pa ame e
𝛼(n−1)D�(e)
.
Fu he mo e, each coali ion coun y
i=c
maximizes he sum o he coali ion coun ies’
mo al wel a e (3) o e i s emissions
ec
, aking he o he coun ies’ emissions as gi en,
which yields10
Fo
𝛼=0
, each coali ion coun y equa es ma ginal emissions bene i s o he coali ion
coun ies’ ma ginal emissions damages
mD�(e)
. Fo
𝛼>0
, al uism implies ha each coali-
ion coun y accoun s o all o he coun ies’ ma ginal emissions damages ia
1+𝛼(n−1)
,
bu i also implies ha all o he coali ion coun ies accoun o each coali ion coun y’s
ma ginal emissions bene i s ia
1+𝛼(m−1)
. No e ha
B�
(e
)=B
�
(e
c
)=nD
�
(e
)
o
𝛼=1
,
so he Nash equilib ium and he social op imum hen coincide. In he ollowing we ocus
on
𝛼∈[0, 1)
.
Di e en ia ing (4) and (5) yields he slopes o he agg ega e eac ion unc ions
(3)
∑
i
∈M
Vi=
∑
i∈M
[
Wi+𝛼
∑
j∈N�i
Wj
]
=(1−𝛼)
∑
i∈M
Wi+𝛼mW
.
(4)
B�
(e
)=[1+𝛼(n−1)]D
�
(e)≤nD
�
(e)
.
(5)
B
�(ec)=
1+𝛼(n−1)
1+𝛼(m−1)
mD�(e)≤nD�(e)
.
(6)
R
�
∶=
d(n−m)e
dme
c
=− (n−m)[1+𝛼(n−1)]D��(e)
(n−m)[1+𝛼(n−1)]D��(e)−B��(e
)∈ (−1, 0)
,
(7)
R
�
c∶=
dme
c
d(n−m)e
=− m
2
[1+𝛼(n−1)]D
��
(e)
m2[1+𝛼(n−1)]D��(e)−[1+𝛼(m−1)]B��(e
c
)∈ (−1, 0)
.
10 The second-o de condi ions a e ul illed.
2315
Sel ‑En o cing In e na ional En i onmen al Ag eemen s and…
1 3
Consequen ly, emissions a e s a egic subs i u es, and he slopes o he agg ega e eac ion
unc ions ce e is pa ibus inc ease in absolu e e ms wi h he al uism pa ame e . In ui i ely,
al uism implies ha coun ies eac mo e sensi i e o o he coun ies’ emissions changes.
Fu he mo e, we in e
Consequen ly, each inge coun y’s emissions a e g ea e han each coali ion coun y’s
emissions. In AppendixA.2.1, we p o e11
P oposi ion 1 (Compa ison o Nash equilib ium and BAU)
•
ec
<e
BAU
i
<e
and
e<eBAU
,
•
V >Vc
,
•
W
>W
c
,W
BAU
i
.
(8) implies ha he coali ion coun ies a e ce e is pa ibus mo e ambi ious in he igh
agains clima e change han a BAU. This esul s in smalle coali ion coun y’s emissions
and global emissions, which aises he ee- ide incen i es and leads o g ea e inge
coun y’s emissions. Each inge coun y’s emissions being g ea e han each coali ion
coun y’s emissions implies
V >Vc
and
W >Wc
. Finally, global emissions being smalle
and each inge coun y’s emissions being g ea e han a BAU implies
W
>W
BAU
i
and,
hus,
V
>V
BAU
i
i
Wc
≥W
BAU
i
o i
𝛼
is su icien ly small.
To p epa e he analysis o he i s s age o he Nash game, we p o e in AppendixA.2.212
Lemma 1 (E ec s o coali ion size and al uism on emissions and wel a e)
•
de
dm
>
0
,
de
dm
<
0
and
dW
dm
>
0
,
•
de
d𝛼
<
0
,
de
d𝛼
<
0
and
dW
d𝛼
>
0
.
F om he i s bulle o he lemma, we ge he ypical esul s ha each inge coun y’s
emissions inc ease bu global emissions dec ease wi h he coali ion size, so ee- ide
incen i es end o inc ease as he coali ion ge s la ge . The esul ing highe consump ion
bene i s and lowe clima e damages imply ha each inge coun y’s ma e ial wel a e
inc eases wi h he coali ion size and, hus, ha
V
inc eases wi h he coali ion size i
Wc
inc eases wi h he coali ion size o i
𝛼
is su icien ly small.
The second bulle o he lemma e eals ha each inge coun y’s emissions and global
emissions dec ease wi h he al uism pa ame e and ha global ma e ial wel a e inc eases
wi h he al uism pa ame e . Consequen ly, he ela i e global emissions
e∕eSO
dec ease
and he ela i e global ma e ial and mo al wel a e
W∕WSO =V∕VSO
inc ease wi h he
al uism pa ame e . Finally, we p o e in AppendixA.2.2 ha he slope o he inge coun-
ies’ agg ega e eac ion unc ion inc eases in absolu e e ms wi h he al uism pa ame e
o
D′′′ ≤0
and
B��� =0
. This slope co esponds o he leakage a e o he inge coun ies
(8)
B�
(ec)
B
�(e
)=m
1+𝛼(m−1)∈(1, m]
.
11 Fo
𝛼=0
, he esul s o P oposi ion1 ha e been p o en by Bay amoglu e al. (2018,p. 110) o he
aba emen game.
12 Fo
𝛼=0
, he esul s o Lemma 1 ha e been p o en by Bay amoglu e  al. (2018, p. 110) o he
aba emen game.
2316
M.Schop
1 3
|
R
′
|
, and he highe his leakage a e, he g ea e ce e is pa ibus he ee- ide incen i es in
he Nash game (Ca a o and Siniscalco 1993).
Now we u n o he i s s age o he Nash game. Fi s no e ha
V (m)>Vc(m)
om
P oposi ion1 implies ha i a coali ion is ex e nally uns able, i.e.
Vc(m+1)
≥
V (m)
, hen
he co esponding expansion o he coali ion is accompanied by a Pa e o imp o emen , i.e.
V (m+1)>Vc(m+1)
≥
V (m)>Vc(m)
. Fo he de ailed s abili y analysis, we use he
ollowing speci ica ion wi h linea -quad a ic emissions bene i s and quad a ic emissions
damages
We cons ain he pa ame e space o ensu e non-nega i e emissions o all
m∈[2, n]
,
which gi es an uppe bound o d. In pa icula , we o mula e he ollowing
Assump ion 1
d
≤

d∶=
4b
(n−1)2
.
This assump ion is necessa y and su icien o non-nega i e emissions o all
m∈[2, n]
wi h
𝛼=0
.13 In AppendixA.2.3, we hen p o e
P oposi ion 2 (S abili y o coali ions wi h policy al uism) Conside he speci ica ion (9)
and suppose al uism a ec s he membe ship decision and he policy decision.
• Ei he he coali ion
m=2
is s able o no coali ion is s able.
• The coali ion
m=2
is [no ] s able o
𝛼=0
,
n≥12
and
d≤

d
[𝛼=0
,
n<12
and
d=

d]
.
• The coali ion size weakly dec eases wi h
𝛼
.
F om he i s bulle o he p oposi ion, we ge he pessimis ic esul ha a bes a
coali ion o wo coun ies is s able. The esul om he second bulle o he p oposi ion
ha
m=2
is s able o
𝛼=0
when he e is a su icien ly la ge numbe o coun ies may
seem coun e in ui i e. In ac , he e a e wo coun e ailing e ec s o n on he in e nal
s abili y condi ion. On he one hand, he condi ion o
m=2
o be s able becomes s ic e
as n inc eases o gi en pa ame e alues a,b,d and
𝛼
, since he numbe o inge coun ies
inc eases wi h n, which aises ma ginal clima e damages, educes each coali ion coun y’s
emissions and, hus, he bene i s o emaining in he coali ion. On he o he hand, he
condi ion o
m=2
o be s able also becomes s ic e as d inc eases, since each coali ion
[ inge] coun y’s emissions dec ease [inc ease] wi h he damage pa ame e , which e lec s
Ba e ’s (1994) pa adox o coope a ion. These conside a ions imply ha he uppe bound
o d o ensu e non-nega i e emissions dec eases wi h n, i.e.
𝜕
d∕𝜕n<0
, which elaxes
he in e nal s abili y condi ion. This indi ec e ec o n on he in e nal s abili y condi ion
ou weighs he di ec e ec o
m=2
and
𝛼=0
, which explains why he coali ion
m=2
(9)
B(ei)=aei−
b
2
e2
i,D(e)=
d
2
e2, wi h a,b,d>
0.
13 Assump ion1 is also su icien o non-nega i e emissions o all
m∈[2, n]
wi h
𝛼≥0.75
. Fu he mo e,
d
≤
b𝛼
2
∕{(1−𝛼)[1+𝛼(n−1)−√1+𝛼(n−1)]
2
}
is necessa y and su icien o non-nega i e emissions
o all
m∈[2, n]
wi h
𝛼∈(0, 0.75)
.
2323
Sel ‑En o cing In e na ional En i onmen al Ag eemen s and…
1 3
u n ends o inc ease wi h he al uism pa ame e om P oposi ion5. Via his mechanism,
al uism could s abilise la ge coali ions.
Fo he de ailed s abili y analysis, we use speci ica ion (9). We cons ain he pa ame e
space o ensu e non-nega i e emissions o all
m∈[2, n]
, which gi es an uppe bound o d
simila o he Nash game. In pa icula , we o mula e he ollowing
Assump ion 2
d
≤


d∶=
4b
n(n−4)
.
This assump ion is necessa y and su icien o non-nega i e emissions o all
m∈[2, n]
wi h
𝛼=0
.26 In AppendixA.3.5, we hen p o e27
P oposi ion 6 (S abili y o coali ions) Conside speci ica ion (9) wi h
n≥7
and
d≤


d
.
• Some unique coali ion
m∈(m,m+2)
is s able.
• Some unique coali ion
m∈{2, 3}
is s able o
𝛼=0
.
• The coali ion size weakly inc eases wi h
𝛼
.
• Some unique coali ion
m∈{2, 3, 4, 5, 6}
is s able o
𝛼>0
.
Con a y o he Nash game, P oposi ion6 e eals ha al uism s abilises la ge coali ions.
Howe e , he coali ion ne e comp ises mo e han six coun ies. Mo e impo an ly, he
coali ion is always smalle han
m=m+2
. Since he S ackelbe g equilib ium and BAU
coincide o
m=m
, he emissions- educing and wel a e-enhancing e ec s o he coali ion
size om Lemma2 a e negligible. In ac , he small coali ions s em om cons aining he
pa ame e space o ensu e non-nega i e emissions o
m∈[2, n]
, which gi es an uppe bound
o d/b and, hus, o
m
. F om P oposi ion5, his uppe bound inc eases wi h he al uism
pa ame e , which is he d i ing o ce o la ge coali ions wi h han wi hou al uism.
We use a nume ical example o demons a e he e a e economies in which he coali-
ion is la ge wi h han wi hou al uism. Figu e3 depic s each coali ion coun y’s minimal
emissions28 (le -hand side igu e) and he in e nal s abili y condi ion ( igh -hand side ig-
u e) o
m=3
(solid cu e) and o
m=4
(dashed cu e) dependen on
𝛼
. In he nume -
ical example, each coali ion coun y’s emissions a e posi i e o all
m∈[2, n]
. Fu he -
mo e,
m=3
becomes s able o
𝛼≥0.223
, and
m=4
becomes s able o
𝛼≥0.839
. Thus,
he e a e economies in which he coali ion is la ge wi h han wi hou al uism. Finally,
Fig.4 shows ha global emissions dec ease and global ma e ial wel a e inc eases wi h he
al uism pa ame e in he nume ical example. Fu he mo e, as he coali ion ge s la ge a
𝛼=0.223
and a
𝛼=0.839
, global emissions jump downwa ds and global ma e ial wel a e
jumps upwa ds, bu hese jumps a e (almos ) no isible.
26 Assump ion2 is also su icien o non-nega i e emissions o all
m∈[2, n]
wi h
𝛼≥0.5
.
27 Fo
𝛼=0
, he esul s o P oposi ion6 ha e been p o en by Diaman oudi and Sa ze akis (2006,p. 261).
Fo
n∈{5, 6}
, hey show ha some unique coali ion
m∈(m,m+3)
wi h
m∈{2, 3, 4}
[
m∈{2, 3}
] is
s able o
n=5
[
n=6
].
28 Using
ec(m(𝛼),𝛼)
wi h
m(
𝛼
)=a g min ec(m,
𝛼
)
.

2324
M.Schop
1 3
5 Discussion
The p e ious sec ions ha e shown ha al uism a ec ing he membe ship decision and
he policy decision leads o small (P oposi ion2) o ine ec i e (P oposi ion6) clima e
coali ions. By con as , al uism a ec ing he membe ship decision only ( ande Pol e al.
2012) can s abilise he g and coali ion (P oposi ion3).29 Gi en ha he e ec s o al uism
Fig. 3 Each coali ion coun y’s minimal emissions (le -hand side igu e) and he in e nal s abili y
condi ion ( igh -hand side igu e) o
m=3
(solid cu e) and o
m=4
(dashed cu e) dependen on
𝛼
wi h
n=100, a=100, b=1
and
d=
1
∕4500
Fig. 4 Global emissions (le -hand side igu e) and global ma e ial wel a e ( igh -hand side igu e)
dependen on
𝛼
wi h
n=100, a=100, b=1
and
d=1∕4500
29 This was shown o he Nash game, bu since he s able coali ions a e always weakly la ge in he
S ackelbe g game han in he Nash game (Finus e al. 2023), his also applies o he S ackelbe g game.
2325
Sel ‑En o cing In e na ional En i onmen al Ag eemen s and…
1 3
on he o ma ion o clima e coali ions c ucially depends on i s modelling, his sec ion
discusses which ealms o decision making migh be in luenced by social p e e ences in
gene al.30
We s a by looking a wha assump ions he li e a u e on sel -en o cing in e na ional
en i onmen al ag eemen s wi h social p e e ences makes and how i jus i ies hem.
Fi s , he li e a u e inco po a ing inequali y a e sion (Lange and Vog 2003; Lange
2006; Vog 2016; Rogna and Vog 2022) conside s social p e e ences a bo h s ages
o he game and a gues ha go e nmen s in e es ed in e-elec ion mus ake (median)
o e s’ ai ness p e e ences in o accoun in na ional policy and in e na ional nego ia-
ions. Second, he li e a u e inco po a ing ecip ocal ai ness (G üning and Pe e s 2010;
Nybo g 2018) also conside s social p e e ences a bo h s ages o he game.31 Nybo g
(2018,p. 707) a gues ha al hough g oups may ac di e en ly han indi iduals, pol-
icy make s and ea y nego ia o s end o be ecip ocal when he gene al popula ion is
ecip ocal, and end o ac ecip ocally when he median o e is ecip ocal. Thi d, he
li e a u e inco po a ing Kan ian e hics (Eichne and Pe hig 2022; Ulph and Ulph 2023)
allows o di e en mo al beha iou a he wo s ages o he game. Ne e heless, Eich-
ne and Pe hig (2022,pp. 18–19) a gue ha mo al beha iou a jus one s age o he
game o di e en mo al beha iou a he wo s ages o he game appea s o be implausi-
ble, and Ulph and Ulph (2023,p. 12) “ ecognise ha he e is a s ong a gumen ha an
agen should ake he same mo al s ance o all decisions.” Howe e , he la e a gue ha
go e nmen s decide on coali ion membe ship, while bo h go e nmen s and indi iduals
decide on domes ic emissions h ough public policy and p i a e beha iou , espec i ely,
such ha he “decisions in ol e somewha di e en agen s”, which migh explain di e -
en mo al beha iou a he wo s ages o he game. Finally, an de Pol e al. (2012,p.
114) a gue ha “agen s may hold di e en p e e ences when ac ing in di e en social
si ua ions, o example as consume s o as ci izens.” They hen dis inguish be ween
he decision abou he echnology employed and he domes ic egula ions adop ed o
a homo economicus wi h “pe sonal well-being unc ions” (Nybo g 2000,p. 305), and
he decision abou he membe ship in he coali ion o a homo poli icus wi h “subjec i e
social wel a e unc ions” (Nybo g 2000,p. 305).
To sum up, mos o he li e a u e assumes ha indi idual social p e e ences a ec
bo h s ages o he game ia he median o e (o because policy make s and ea y nego-
ia o s end o ha e he same social p e e ences as he gene al popula ion). On he o he
hand, aken oge he , ande Pol e al. (2012) and Ulph and Ulph (2023) p o ide good
a gumen s ha social p e e ences could be di e en a he wo s ages o he game: I
he e is a dis inc ion be ween homo economicus and homo poli icus and i homo eco-
nomicus can in luence domes ic emissions, hen social p e e ences migh be mo e p o-
nounced a he membe ship s age han a he policy s age. Howe e , no e ha he ci ed
li e a u e (and he p esen pape ) abs ac s om indi idual decisions and assumes ha
coun ies o go e nmen s decide on bo h coali ion membe ship and domes ic emissions.
In his case, all decisions a e made by ci izens a he han by consume s, and he e
should be no quali a i e di e ence be ween social p e e ences a he wo s ages o he
game.
30 We owe his sec ion o an anonymous e iewe who sugges ed o discuss which ealms o decision
making migh be in luenced by al uis ic p e e ences.
31 InBuchholz e al. (2018) coun ies a e ecip ocal when hey decide on hei membe ship in he coali ion,
bu he emissions policy inside and ou side he coali ion is exogenously gi en.
2326
M.Schop
1 3
Howe e , s a egic delega ion could be ano he a gumen o di e en social p e e ences
a di e en game s ages. The li e a u e on s a egic delega ion shows ha s a egic o e s
elec policy make s who ca e less abou global public goods when policy make s ba gain
o e hei p o ision. The eby, Buchholz e al. (2005) and Loepe (2017) assume ha policy
make s decide on he coope a i e ba gaining ou come and on he non-coope a i e ba gain-
ing de aul (s ong delega ion), while Segendo (1998) and G aziosi (2009) also conside
policy make s deciding on he coope a i e ba gaining ou come bu median o e s deciding
on he non-coope a i e ba gaining de aul (weak delega ion), which leads o di e en p e -
e ences a di e en game s ages.32 Spyche and Winkle (2022) in oduce s a egic delega-
ion in o he s anda d wo-s age game o sel -en o cing in e na ional en i onmen al ag ee-
men s. They dis inguish be ween weak delega ion, i.e. elec ed policy make s decide on
coali ion membe ship bu median o e s decide on emissions policy, and s ong delega ion,
i.e. elec ed policy make s decide a bo h s ages o he game. While weak delega ion does
no inc ease coali ion size bu does inc ease global emissions, s ong delega ion can s abi-
lise he g and coali ion and he eby b ing abou he social op imum. These esul s sugges
ha s a egic delega ion can pay o . In his con ex , Lange and Schwi plies (2017) a gue
ha he e is indeed s a egic delega ion in clima e policy because he social p e e ences o
clima e nego ia o s and he gene al popula ion di e in ha he o me a e mo e likely o
suppo bu den-sha ing ules wi h low economic cos s o hei egions han he la e .
6 Ex ensions
This sec ion pe o ms wo model ex ensions. The i s subsec ion shows ha a small deg ee
o communi y al uism can s abilise he g and coali ion. The second subsec ion e eals ha
al uism can s abilise coali ions o wo coun ies bu ends o des abilise coali ions o h ee
o mo e coun ies wi h linea clima e damages and asymme ic coun ies.33
6.1 Communi y Al uism
In his subsec ion, we conside communi y al uism. In pa icula , we dis inguish be ween
ou -g oup al uism
𝛼
and in-g oup al uism
𝛽>𝛼
. The psychological li e a u e has de el-
oped and es ed wo heo ies in pa icula o he p e e ence o in-g oup membe s o e
ou -g oup membe s (Ballie e al. 2014): The social iden i y heo y assumes ha indi idu-
als iden i y hemsel es wi h hei membe ships in social g oups (Taj el e al. 1979), while
he heo y o bounded gene alized ecip oci y assumes ha g oups con ain indi iduals
wi h coope a i e epu a ions, which induces indi ec ecip oci y (Yamagishi and Kiyona i
1999). Cheikbossian (2021a) shows ha in-g oup al uism is e olu iona y s able, Cheik-
bossian (2021b) inds ha a combina ion o in-g oup al uism and ou -g oup al uism can
be e olu iona y s able, and Ballie e al. (2014) summa ize he signi ican e idence o in-
g oup al uism (and agains ou -g oup spi e) in psychological expe imen s.
32 While Buchholz e  al. (2005) and G aziosi (2009) ind ha s a egic o ing cancels he gains o
in e na ional coope a ion, Segendo (1998) inds ha weak [s ong] delega ion inc eases [dec eases] he
gains o in e na ional coope a ion, and Loepe (2017) inds ha he esul s depend on he ype o global
public goods.
33 We owe his sec ion o an anonymous e iewe who sugges ed o ex end he analysis o communi y
al uism and asymme ic coun ies.
2327
Sel ‑En o cing In e na ional En i onmen al Ag eemen s and…
1 3
In he ollowing, we i s analyse communi y al uism in he Nash game hen epo he
e ec s o communi y al uism in he S ackelbe g game. In he Nash game o coali ion o -
ma ion, each inge coun y does no belong o a g oup, such ha i s mo al wel a e (1) and
i s i s -o de condi ion (4) do no change. By con as , each coali ion coun y belongs o
he clima e coali ion, such ha i s mo al wel a e becomes
Thus, communi y al uism ce e is pa ibus inc eases he weigh o he coali ion’s ma e ial
wel a e. Rea anging he co esponding i s -o de condi ion yields34
whe e he nume a o e lec s he al uis ic p e e ences o he espec i e coali ion coun y
o all o he coun ies’ clima e damages, and he denomina o e lec s he al uis ic p e e -
ences o all o he coali ion coun ies o he espec i e coali ion coun y’s consump ion
bene i s. Communi y al uism educes he ela i e impo ance o he inge coun ies’ cli-
ma e damages, which ce e is pa ibus inc eases he coali ion’s emissions. Howe e , om
(4) and (17), we in e
Consequen ly, each inge coun y’s emissions a e s ill g ea e han each coali ion coun-
y’s emissions. In Online Appendix B.1.1, we p o e ha he i s bulle and he hi d bul-
le o P oposi ion1 also hold wi h communi y al uism: Each coali ion coun y consumes
less han a BAU, which educes global emissions and, hus, ma ginal clima e damages,
such ha each inge coun y consumes mo e han a BAU. Consequen ly, he ma e ial wel-
a e o each inge coun y is g ea e han ha o each coali ion coun y and g ea e han
ha a BAU. Howe e , and in con as o he case wi hou communi y al uism, he mo al
wel a e o each coali ion coun y can be g ea e han ha o each inge coun y i he
ma e ial wel a e o each coali ion coun y is posi i e, because hen communi y al uism
ce e is pa ibus inc eases he o me bu does no a ec he la e . In pa icula , we ha e
V −Vc=(1−𝛼)(W −Wc)−(𝛽−𝛼)(m−1)Wc
, which ce e is pa ibus dec eases wi h he
deg ee o communi y al uism and wi h he coali ion size i
Wc>0
. This wel a e e ec o
communi y al uism can educe he ee- ide incen i es.
To analyse he policy e ec o communi y al uism, we p o e in Online Appendix
B.1.135
Lemma 4 (E ec s o communi y al uism on emissions and wel a e)
(16)
∑
i
∈M
Vi=∑
i∈M
[
Wi+𝛽∑
j∈M�i
Wj+𝛼∑
j∈N�M
Wj
]
=[1−𝛼+(𝛽−𝛼)(m−1)]
∑
i∈M
Wi+𝛼mW
.
(17)
B
�(ec)=
1+𝛼(n−m)+𝛽(m−1)
1+𝛽(m−1)
mD�(e)≤nD�(e)
,
(18)
B
�
(ec)
B�(e
)=m
1+𝛼(n−1)
1+𝛼(n−m)+𝛽(m−1)
1+𝛽(m−1)∈(1, m]
.
34 The second-o de condi ions a e ul illed.
35 Fu he mo e, we he e p o e ha Lemma1 also holds wi h communi y al uism.
2328
M.Schop
1 3
•
de
d
𝛽
<
0
,
de
c
d
𝛽
>
0
and
de
d𝛽
>
0
,
•
dW
d
𝛽
<
0
and
dW
c
d𝛽
>
0
,
•
dV
c
d
𝛽
>
0
and
d(V
−V
c
)
d𝛽
<
0
o
Wc≥0
(su icien ).
Ce e is pa ibus, communi y al uism does no a ec each inge coun y’s consump-
ion, see (4), bu inc eases each coali ion coun y’s consump ion, see (17). Thus,
ec
inc eases, which inc eases global emissions and, hus, ma ginal clima e damages, such
ha
e
dec eases. Consequen ly, each inge coun y’s ma e ial wel a e dec eases, while
he inc ease in each coali ion coun y’s consump ion bene i s ou weighs he inc ease in he
clima e damages, such ha i s ma e ial wel a e inc eases. This policy e ec o communi y
al uism aises each coali ion coun y’s mo al wel a e and educes he di e ence be ween
he mo al wel a e o each inge coun y and each coali ion coun y i
Wc
≥
0
. Fu he -
mo e, i educes each inge coun y’s mo al wel a e
V =(1−𝛼)W +𝛼W
i
𝛼
is su i-
cien ly small, such ha he dec ease in
W
ou weighs he po en ial inc ease in W.
Taken oge he , he sign o each coali ion coun y’s ma e ial wel a e plays an impo an
ole o he e ec s o communi y al uism on he ee- ide incen i es. This also becomes
clea when we look a he (in e nal) s abili y condi ion o he g and coali ion:
Fi s no e ha he g and coali ion maximizes global ma e ial wel a e om
Vc(n)=[1+𝛽(n−1)]Wc(n)
as in he case wi hou communi y al uism. Now conside
𝛽=1
. Then,
Vc(n)
is maximized global ma e ial wel a e W(n), and
V (n−1)
is non-maxi-
mized global ma e ial wel a e
W(n−1)
minus he coali ion’s ma e ial wel a e weigh ed by
1−𝛼
. Thus, he g and coali ion is s able i
Wc(n−1)≥0
. By con as , i
Wc(n−1)<0
,
he g and coali ion need no be s able. Fo example, conside
𝛼=0
. Then,
V (n−1)
is
equal o he inge coun y’s ma e ial wel a e
W (n−1)
, and his ma e ial wel a e can
exceed maximized global wel a e W(n) i
Wc(n−1)<0
. Howe e , i can be shown ha
Wc(n−1)>0
holds wi h speci ica ion (9) when he e is a su icien ly la ge numbe o
coun ies (
n≥9
). Then, he emissions policy o one inge coun y is ela i ely unimpo -
an o he ma e ial wel a e o many coali ion coun ies. In his case, he g and coali ion is
s able o
𝛽=1
.
No e ha
Wc(n)
is always non-nega i e because he g and coali ion could choose
ec
=0
and, hus,
B(0)≥0
and
D(0)=0
. Consequen ly, in-g oup al uism inc eases each coun-
y’s mo al wel a e in he g and coali ion. Fu he mo e, i educes each inge coun y’s
ma e ial wel a e, bu aises each coali ion coun y’s ma e ial wel a e wi h any o he coali-
ion, such ha he e ec on each inge coun y’s mo al wel a e is in gene al ambiguous.
Howe e , in Online Appendix B.1.1 we p o e ha his e ec is de ini ely nega i e i he e
is only one inge coun y. Then, in-g oup al uism inc eases he emissions o so many
coali ion coun ies ha he co esponding inc ease in clima e damages and dec ease in
he inge coun y’s consump ion bene i s ou weigh he inc ease in he coali ion coun y’s
consump ion bene i s. To sum up, in-g oup al uism inc eases he s abili y o he g and
coali ion.
Finally, ou -g oup al uism does no a ec each coun y’s mo al wel-
a e in he g and coali ion, bu i educes global emissions and inc eases global
(19)
V
c
(n)−V
(n−1)
=(1−𝛽)Wc(n)+𝛽W(n)−
[
(1−𝛼)W (n−1)+𝛼W(n−1)
]
=W(n)−(1−𝛽)(n−1)W
c
(n)−
[
W(n−1)−(1−𝛼)(n−1)W
c
(n−1)
].

2329
Sel ‑En o cing In e na ional En i onmen al Ag eemen s and…
1 3
ma e ial wel a e wi h any o he coali ion, see Lemma1. Thus, i also ends o inc ease
V (n−1)=W (n−1)+𝛼(n−1)Wc(n−1)
i
Wc(n−1)>0
. Consequen ly, i can be
shown ha ou -g oup al uism inc eases he inge coun y’s mo al wel a e wi h speci ica-
ion (9) when he e is a su icien ly la ge numbe o coun ies (
n≥10
). In his case, ou -
g oup al uism dec eases he s abili y o he g and coali ion. We p o e ou esul s in Online
Appendix B.1.1 and summa ize hem in
P oposi ion 7 (S abili y o g and coali ion wi h communi y al uism) Conside
speci ica ion (9).
• The in e nal s abili y condi ion o he g and coali ion inc eases wi h
𝛽
, and i dec eases
wi h
𝛼
o
n≥10
and
d≤

d
(su icien ).
• The g and coali ion is s able o
𝛽=1
,
n≥6
and
d≤

d
(su icien ).
Thus, communi y al uism can s abilise he g and coali ion and he eby b ing abou he
social op imum. Figu e5 depic s h esholds o
𝛽−𝛼
o he g and coali ion o be s able
dependen on
𝛼
in he Nash game (le -hand side igu e) o di e en alues o he clima e
damage pa ame e d.36 When his pa ame e is small, emissions policy is de e mined
mainly by ma ginal emissions bene i s a he han ma ginal clima e damages, so ha he
di e ence be ween he emissions and he e o e he ma e ial wel a e o each inge coun y
and each coali ion coun y is small, which educes ee- ide incen i es and s abilises he
g and coali ion. Figu e5 shows ha he g and coali ion can be s able e en wi h a small
di e ence be ween in-g oup al uism and ou -g oup al uism o less han 0.03.37 No e
ha communi y al uism does no change he g and coali ion’s emissions policy, so i s
s abilizing e ec elies on he wo se emissions policy o he inal inge coun y (policy
e ec ) and on he inc eased mo al wel a e o each coali ion coun y o a gi en emissions
policy (wel a e e ec ).38
Finally, we epo he e ec s o communi y al uism in he S ackelbe g game. Since
he esul s a e simply a combina ion o hose in he S ackelbe g game wi hou commu-
ni y al uism and hose in he Nash game wi h communi y al uism, we delega e he ull
analysis o Online Appendix B.1.2. Fi s , he e is a unique h eshold coali ion
m∈(1, n)
whe e he S ackelbe g equilib ium and BAU coincide in e ms o emissions and ma e ial
wel a e. I
WBAU
i
≥
0
, hen
Vc
(m)≥V
BAU
i
and
V
(m)≤V
BAU
i
o
m≤m
, such ha all coali-
ion
m≤m
a e ex e nally uns able, and he coali ion
m=⌊m+1⌋≥2
is in e nally s able
as in he case wi hou communi y al uism.39 Second, communi y al uism inc eases each
coali ion coun y’s emissions and global emissions, and i dec eases each inge coun y’s
36 Fo
n=100
and
d∕b>3.75∕10,000
, each coali ion coun y’s minimal emissions become nega i e o
ce ain combina ions o
𝛼
and
𝛽
.
37 Coinciden ally, his is consis en wi h he nume ical analysis o ande Pol e al. (2012), who ind ha
he g and coali ion is s able o
𝛼=0
and
𝛽≥0.03
o
𝛼≤0.024
and
𝛽=0.06
and uns able o
𝛼≥0.036
and
𝛽=0.06
.
38 Finally, we an se e al examples o ind o he possible s able coali ion sizes. The e a e economies in
which no coali ion is s able, only he coali ion
m=2
is s able, only he g and coali ion is s able, o some
coali ion
m≥2
and he g and coali ion a e s able. We did no ind an example in which he coali ion
m=2
is s able in he case wi hou communi y al uism and no coali ion is s able in he case wi h communi y
al uism. Howe e , he e a e economies in which only he coali ion
m=2
is s able in bo h cases, and in which
global mo al wel a e is smalle wi h han wi hou communi y al uism due o he highe emissions damages.
39 By con as , i
WBAU
i
<
0
, hen
Vc
(m)<V
BAU
i
and
V
(m)=V
BAU
i
, such ha he coali ion
m=m−1
is
ex e nally s able.
2330
M.Schop
1 3
emissions as in he Nash game. Consequen ly,
m
inc eases wi h
𝛽
, which can s abilise
la ge coali ions. Fu he mo e, communi y al uism dec eases each inge coun y’s mo al
wel a e, and i inc eases each coali ion coun y’s mo al wel a e i
Wc≥0
as in he Nash
game, which hen s abilises la ge coali ions. In pa icula , in-g oup [ou -g oup] al uism
inc eases [dec eases] he in e nal s abili y condi ion o he g and coali ion [when he e is a
su icien ly la ge numbe o coun ies] as in he Nash game. Fu he mo e, i can be shown
ha he condi ion o he g and coali ion o be s able is laxe in he S ackelbe g game han
in he Nash game. Howe e , Fig.5 shows ha he h esholds o
𝛽−𝛼
o he g and coali-
ion o be s able dependen on
𝛼
in he S ackelbe g game ( igh -hand side igu e) a e close
o hose in he Nash game (le -hand side igu e).
6.2 Asymme ic Coun ies
In his subsec ion, we conside asymme ic coun ies in e ms o consump ion bene-
i s
Bi(ei)
and clima e damages
Di(e)
. Wi h con ex clima e damages
D′′
i>0
(o aba e-
men bene i s), he esul s o p e ious li e a u e on coali ion s abili y wi h asymme ic
coun ies a e based on nume ical analyses (Ba e 1997; Bo eon and Ca a o 2001;
McGin y 2007; Bakalo a and Eyckmans 2019; McGin y 2020). In o de o ob ain ana-
ly ical esul s, we hus ely on linea clima e damages
D��
i=0
in his subsec ion. This
implies ha each inge coun y has a dominan s a egy, such ha he Nash game and
he S ackelbe g game coincide. Fu he mo e, we ocus on he case wi hou ans e s.
In such a amewo k wi h wo ypes o coun ies, Fuen es-Albe o and Rubio (2010)
show ha a coali ion o a mos h ee coun ies is s able i ei he clima e damages o
emissions bene i s a e symme ic. Pa lo a and DeZeeuw (2013) con i m his esul and
show ha he same holds i clima e damages and emissions bene i s a e posi i ely co -
ela ed. By con as , i clima e damages and aba emen cos s a e nega i ely co ela ed, a
Fig. 5 Th esholds o
𝛽−𝛼
o he g and coali ion o be s able dependen on
𝛼
in he Nash game (le -
hand side igu e) and in he S ackelbe g game ( igh -hand side igu e) wi h
n=100, a=100, b=1
and
d=1∕10,000
(solid cu e),
d=2.375∕10,000
(dashed cu e) and
d=3.75∕10,000
(do ed cu e)
2331
Sel ‑En o cing In e na ional En i onmen al Ag eemen s and…
1 3
coali ion o all coun ies wi h low clima e damages and wo coun ies wi h high clima e
damages can be s able. Finus and McGin y (2019) ex end his analysis by allowing o
any ype o coun ies. They show ha he g and coali ion can be s able i clima e dam-
ages and aba emen cos s a e nega i ely co ela ed.
Following an de Pol e al. (2012), we conside a unique al uism pa ame e o
de i e he gene al e ec s o al uism on he o ma ion o clima e coali ions. Fu he -
mo e, we abs ac om communi y al uism o check he obus ness o ou main model
wi h linea clima e damages and asymme ic coun ies. Wi h a unique al uism pa am-
e e and wi hou communi y al uism, each coun y’s mo al wel a e unc ion is s ill
gi en by (1), and he global mo al wel a e unc ion is s ill gi en by (2). Consequen ly,
he socially op imal emissions always maximize global ma e ial wel a e, and he indi-
idually op imal emissions maximize global ma e ial wel a e i and only i
𝛼=1
. In
AppendixA.1, we p o e ha global emissions dec ease and global ma e ial wel a e
inc eases wi h he al uism pa ame e in he indi idually op imal solu ion as in he main
model. Consequen ly, he ela i e global emissions
eBAU ∕eSO
dec ease and he ela i e
global ma e ial and mo al wel a e
WBAU ∕WSO =VBAU ∕VSO
inc ease wi h he al uism
pa ame e .
In he coali ion o ma ion game, each inge coun y’s mo al wel a e is s ill gi en by
(1), and he sum o he coali ion coun ies’ mo al wel a e is s ill gi en by (3). Rea anging
he co esponding i s -o de condi ions yields
Consequen ly, conside ing wo ex an e iden ical coun ies, he emissions o he coun y
ou side he coali ion a e g ea e han hose o he coun y inside he coali ion, which means
ha also he ma e ial and mo al wel a e o he coun y ou side he coali ion a e g ea e
han hose o he coun y inside he coali ion. In Online AppendixB.2.1, we p o e40
P oposi ion 8 (Compa ison o Nash equilib ium and BAU wi h asymme ic coun ies)
•
ei
<e
BAU
i
o all
i∈M
,
ei
=e
BAU
i
o all
i∉M
and
e<eBAU
,
•
Vi
>V
BAU
i
o all
i∉M
and
V>VBAU
,
•
Wi
>W
BAU
i
o all
i∉M
and
W>WBAU
.
(21) implies ha he coali ion coun ies a e ce e is pa ibus mo e ambi ious in he igh
agains clima e change han a BAU. This esul s in smalle emissions inside he coali ion,
(20)
B
�
i(ei)=(1−𝛼)D�
i(e)+𝛼
∑
j
∈
N
D�
j(e)≤
∑
j
∈
N
D�
j(e),∀i∉M
,
(21)
B
�
i(ei)=
(
1
−
𝛼
)∑
j∈MD
�
j
(
e
)+
𝛼m
∑
j∈ND
�
j
(
e
)
1+𝛼(m−1)
=(1−𝛼)D�
i(e)+𝛼�
j∈N
D�
j(e)
+(1−𝛼)
∑
j∈M�iD�
j(e)+𝛼(m−1)
∑
j∈N�iD�
j(e)
1+𝛼(m−1)≤
�
j∈N
D�
j(e),∀i∈M
.
40 Fo
𝛼=0
, he esul s o P oposi ion8 ha e been p o en by Finus and McGin y (2019,p. 544) o he
aba emen game wi h linea bene i s and quad a ic cos s.
2332
M.Schop
1 3
while he inge coun ies’ dominan s a egies imply ha he emissions ou side he coali-
ion do no change, such ha global emissions a e smalle han a BAU. Smalle global
emissions and cons an inge coun y’s emissions imply
Wi
>W
BAU
i
o all
i∉M
. The
emaining esul s a ise om he supe addi i i y o he game, i.e.
∑
j∈MVj≥
∑
j∈MV
BAU
j
:
Supe addi i i y implies
W>WBAU
, which in u n implies
Vi
>V
BAU
i
o all
i∉M
and
V>VBAU
.
To p epa e he analysis o he i s s age o he Nash game, we p o e in Online Appen-
dix B.2.241
Lemma 5 (E ec s o coali ion size and al uism on emissions and wel a e wi h asymme ic
coun ies)
• I ano he coun y joins he coali ion, hen each coali ion coun y’s emissions dec ease,
each inge coun y’s emissions do no change and global emissions dec ease. Fu he -
mo e, each inge coun y’s ma e ial and mo al wel a e inc ease, and global ma e ial
and mo al wel a e inc ease.
•
de
i
d𝛼
<
0
o all
i∈N
and
dW
d𝛼
>
0
.
The i s bulle o he lemma e eals ha he compa ison be ween Nash equilib ium and
BAU om P oposi ion8 can be ans e ed o he compa ison be ween he equilib ium
wi h some coali ion M and he equilib ium wi h some smalle coali ion
M∖i
: The la ge he
coali ion, he mo e i igh s agains clima e change, which leads o smalle emissions o he
o iginal coali ion membe s, o smalle emissions o he new coali ion membe and, hus, o
smalle global emissions. The ma e ial wel a e o each inge coun y inc eases, because
i s consump ion bene i s do no change, bu i s clima e damages dec ease. Supe addi i i y
implies ha global wel a e inc eases, which in u n implies ha he mo al wel a e o each
inge coun y and global mo al wel a e inc ease.
The second bulle o he lemma e eals ha each coun y’s emissions dec ease and
global ma e ial wel a e inc eases wi h he al uism pa ame e . Consequen ly, he ela-
i e global emissions
e∕eSO
dec ease and he ela i e global ma e ial and mo al wel a e
W∕WSO =V∕VSO
inc ease wi h he al uism pa ame e as in he main model wi h symme -
ic coun ies and con ex clima e damages.
Fo he i s s age o he game, we use he ollowing speci ica ion
In Online Appendix B.2.3, we hen p o e
P oposi ion 9 (S abili y o coali ions wi h asymme ic coun ies) Conside he
speci ica ion (22).
• Suppose
bi=b
and
di=d
o all
i∈N
. Then, any coali ion wi h h ee membe s is s a-
ble o
𝛼=0
, and any coali ion wi h wo membe s is s able o
𝛼>0
.
(22)
Bi(ei)=aiei−
b
i
2
e2
i,Di(e)=die, wi h ai,bi,di>
0.
41 Fo
𝛼=0
, he esul s o Lemma 5 ha e been p o en by Finus and McGin y (2019, p. 544) o he
aba emen game wi h linea bene i s and quad a ic cos s.
2339
Sel ‑En o cing In e na ional En i onmen al Ag eemen s and…
1 3
Sol ing o
e
,
ec
and
e
yields
whe e
No e ha 𝜕
[
𝜕2
]
e
c
Ω
1+𝛼(m−1)
m>
0
. Fo
𝛼=0
,
e
c
Ω
1+𝛼(m−1)
is minimal a
m
=
n+1
2
, and hen
e
c
Ω
1+𝛼(m−1)
is
non-nega i e i and only i
d
≤

d∶=
4b
(n−1)
2 , which is hus an uppe bound o d. Using his
uppe bound in (A.34) yields
Fo
𝛼>0
,
e
c
Ω
1+𝛼(m−1)
is minimal a
and hen
e
c
Ω
1+𝛼(m−1)
is non-nega i e i and only i
Using (A.33), (A.34) and (A.35) yields
(A.31)
a
−bec=
1+𝛼(n−1)
1+𝛼(m−1)
mde
,
(A.32)
e=(n−m)e +mec.
(A.33)
e
=
1+𝛼(m−1)+m(m−1)(1−𝛼)[1+𝛼(n−1)]
d
b
Ω
a
b
>
0,
(A.34)
e
c=
1+𝛼(m−1)−(n−m)(m−1)(1−𝛼)[1+𝛼(n−1)]
d
b
Ω
a
b,
(A.35)
e
=
1+𝛼(m−1)
Ω
na
b
>
0,
Ω ∶=
1+𝛼(m−1)+[1+𝛼(n−1)]{[1+𝛼(m−1)]n+(1−𝛼)m(m−1)}
d
b
>
0.
e
c=
a
4b2Ω{{𝛼(m−1)[(n−1)(n−m)(4𝛼−3)+(m+3)(n−m)+(m−1)2]
+(n+1−2m)2
}
d+(n−1)2[1+𝛼(m−1)](
d−d)
}
>0⟸d≤
d∧𝛼≥3∕
4.
m
=1+
√
1+𝛼(n−1)−1
𝛼
=n+1
2−𝛼(n−1)2∕2
2
√
1+𝛼(n−1)+2+𝛼(n−1)
∈
�
1, n+1
2
�,
d
≤𝛼
2
b
(1−𝛼){1+𝛼(n−1)−
√
1+𝛼(n−1)}2
.

2340
M.Schop
1 3
The in e nal s abili y condi ion eads
whe e
(A.36)
V
=[1+𝛼(n−m−1)]
[
ae −
b
2e2
−
d
2e2
]
+𝛼m
[
aec−
b
2e2
c−
d
2e2
]
=a2
2bΩ2[1+𝛼(n−1)]{[1+𝛼(m−1)]2−[1+𝛼(m−1)]{[1+𝛼(m−1)][n2−2m
2
−2n+2m−2𝛼(n−1)(n−m)] − 2𝛼m2(n−m)}d
b+(1−𝛼)2[1+𝛼(n−1)]m(m
−1){m2+2n−m−𝛼(m−1)(n2−nm −2n+m)}
(
d
b)
2
},
(A.37)
V
c=[1+𝛼(n−m)]
[
ae −
b
2e2
−
d
2e2
]
+[1+𝛼(m−1)]
[
aec−
b
2e2
c−
d
2e2
]
=V −a2
2bΩ
2n2(m−1)(1−𝛼)2[1+𝛼(n−1)]2[m+1+𝛼(m−1)]
(
d
b)
2
.
(A.38)
V
c(m)−V (m−1)=
a2n2(m−1)(1−𝛼)2[1+𝛼(n−1)]2
(
d
b
)2
2bΩ(m)
2
Ω(m−1)
2Φ(m)
,
(A.39)
Φ(
m) ∶= −[1+𝛼(m−1)][m−3+𝛼(m−2)
2
]−[1+𝛼(n−1)]{2[(n−m)(m−1)+(
m
−3)3+6(m−3)2+11(m−3)+4]+2𝛼{(n−m)[2(m−2)2+5(m−2)+1]
+(m−2)[(m−2)3+4(m−2)2+6(m−2)+2]} + 𝛼2(m−2)[2(n−m)(m2
+m−3)+(m−1)(m−2)] + 2𝛼3(n−m)(m−1)(m−2)2}d
b−[1+𝛼(n−1)]
2
⋅{[n(m+1)+m(m−1)2][n+m(m−3)] + 𝛼{(n−m)2[2(m−2)2+10(m−2)
+3]+2(n−m)[(m−2)4+7(m−2)3+16(m−2)2+14(m−2)+2]+m2(m
−2)2}+𝛼2(n−m)(m−2){(n−m)[(m−2)2+9(m−2)+6]+2(m−2)3+8
⋅(m−2)2+12(m−2)+4}+𝛼3(n−m)(2n−2m+1)(m−1)(m−2)2}(d
b)2
<0⟸m≥3,
2341
Sel ‑En o cing In e na ional En i onmen al Ag eemen s and…
1 3
such ha all coali ions
m≥3
a e in e nally uns able, which p o es he i s bulle o he
p oposi ion. Fu he mo e,
which p o es he second bulle o he p oposi ion. Finally,
whe e
such ha
m=2
is in e nally s able i
d
b
,
𝛼
and n a e su icien ly small. Since all coali ions
m≥3
a e in e nally uns able om (A.39), and he condi ion o
m=2
o be s able
(A.40)
Φ(
2)�𝛼=0=1−2(n−4)d
b−(n−2)(3n+2)
�
d
b
�2
⋛
0
⟺
d
b
⋚2
√
n2−3n+3−n+4
3n
2
−4n−4
,
(A.41)
=
(n−1)
4
16b2
{
(n−12)
4
+36(n−12)
3
+438(n−12)
2
+1860(n−12)+817
(n−1)4d
2
+2(n−3)2+16
(n−
1
)
2(
d−d)d+(
d−d)2
}
>0⟸n≥12 ∧d≤
d,
(A.42)
=−
(n−1)4
16b2{
(
11−n
n−3
)4
+16
(
11−n
n−3
)3
+66
(
11−n
n−3
)2
+88
(
11−n
n−3
)
+5
32(n−1
n−3)4d
2
−2(n−3)2+16
(n−
1
)
2(
d−d)d−(
d−d)2
}
<0⟸n≤11 ∧d=
d,
(A.43)
Φ(2)
1+
𝛼
=1−2[n−4+𝛼(n−2)]
(1+
𝛼
)∕[1+
𝛼
(n−1)]
d
b
−(n−2)[3n+2+𝛼(3n−2)]
(1+𝛼)∕[1+𝛼(n−1)]
2
(
d
b)2
,
(A.44)
𝜕(
Φ(2)
1+𝛼
)
𝜕
(
d
b)
<0⟸n≥
4,
(A.45)
𝜕(
Φ(2)
1+𝛼
)
𝜕𝛼 =−
2(n−2)[(n+1)(3n−4)+(2+𝛼)𝛼(n−1)(3n−2)]
(1+𝛼)2∕[1+𝛼(n−1)] (d
b)
2
−2(n−2)[n−3+(2+𝛼)𝛼(n−1)]
(
1
+𝛼)
2
d
b
<0⟸n≥3,
(A.46)
𝜕(
Φ(2)
1+𝛼
)
𝜕n=−
2[3n−2+6𝛼(n2−n−1)+𝛼2(6n2−15n+8)]
(1+𝛼)∕[1+𝛼(n−1)] (d
b)
2
−2[1+2𝛼(n−2)+𝛼2(2n−3)]
(
1
+𝛼)
d
b
<0⟸n≥2,
2342
M.Schop
1 3
becomes s ic e as
𝛼
inc eases om (A.45), he coali ion size weakly dec eases wi h
𝛼
,
which p o es he hi d bulle o he p oposi ion.
◻
E ec s o Al uism on heIn e nal S abili y Condi ion
F om (11), he di ec e ec o al uism on he in e nal s abili y condi ion eads
which is posi i e i
(
m−1)dWc(m)
dm
+(n−m)
dW
(m)
dm
>
0
. Using (4), (5) and (A.21) yields
such ha
𝜕[
Vc(m)−V (m−1)
]
𝜕𝛼
>
0
o
m∈{2, n}
. Using speci ica ion (9), i can be shown ha
𝜕[
Vc(m)−V (m−1)
]
𝜕𝛼
>
0
o
m∈[2, n]
. The co esponding Maple ile is a ailable on eques .
F om (12), he indi ec e ec s o al uism on he in e nal s abili y condi ion ead
Using (4), (5) and (A.21) yields
and
(A.47)
𝜕[
Vc(m)−V (m−1)
]
𝜕𝛼
=
[
(m−1)W
c
(m)+(n−m)W
(m)
]
−
[
(m−1)W
c
(m−1)+(n−m)W
(m−1)
],
(A.48)
(
m−1)dWc(m)
dm+(n−m)
dW
(m)
dm
=(m−1)[B�(ec)dec
dm−D�de
dm]+(n−m)[B�(e )
de
dm−D�de
dm]
=D�{(m−1)[1+𝛼(n−1)
1+𝛼(m−1)mdec
dm−de
dm]+(n−m)[[1+𝛼(n−1)]
de
dm−de
dm
]}
=
(m−1)(e −ec)+(n−m){[2−m+𝛼(m−1)]de
dm−[1+𝛼(n−1)]−1de
dm}
[
1
+
𝛼
(n−
1
)]
−1
[
1
+
𝛼
(m−
1
)]∕D
�,
(A.49)
(
1−𝛼)
dWc(m)
d𝛼
+𝛼
dW(m)
d𝛼
−
[
(1−𝛼)
dW
(m−1)
d𝛼
+𝛼
dW(m−1)
d𝛼
].
(A.50)
(
1−𝛼)
dW
c
(m)
d𝛼+𝛼
dW(m)
d𝛼
=(1−𝛼)[B�(ec(m))
dec(m)
d𝛼−D�de(m)
d𝛼]
+𝛼[mB�(ec(m))
dec(m)
d𝛼+(n−m)B�(e (m))
de (m)
d𝛼−nD�de(m)
d𝛼
]
=[1+𝛼(n−1)]D�[m
dec(m)
d𝛼+𝛼(n−m)
de (m)
d𝛼−de(m)
d𝛼]
= −(1−𝛼)[1+𝛼(n−1)](n−m)D�de (m)
d𝛼
>0
2343
Sel ‑En o cing In e na ional En i onmen al Ag eemen s and…
1 3
such ha
(
1−𝛼)
d
Wc
(
m
)
d𝛼
+𝛼dW(m)
d𝛼
>
0
and
(
1−𝛼)dW (2−1)
d𝛼
+𝛼dW(2−1)
d𝛼
=[1+𝛼(n−1)] dW
BAU
i
d𝛼
>
0
om Appendix A.1. Using speci ica ion (9), i can be shown ha
(
1−𝛼)
dW
(m−1)
d𝛼
+𝛼dW(m−1)
d𝛼
>
0
o
m∈[2, n−2]
. The co esponding Maple ile is a ail-
able on eques .
P oo o P oposi ion 3
Wi hou al uis ic p e e ences a he second s age o he game, he emissions o a gi en
coali ion size a e gi en by subs i u ing
𝛼=0
in o (A.33), (A.34) and (A.35), and he
ma e ial wel a e le els o a gi en coali ion size a e gi en by subs i u ing
𝛼=0
in o
(A.36) and (A.37). Using hese esul s, he in e nal s abili y condi ion eads
whe e
whe e
Ni∶= n−i
and
Mi∶= m−i
. F om (A.39) and (A.53),
Φ(m)|𝛼=0=𝜑(m)|𝛼=0
, and
om he p oo o P oposi ion2,
Φ(2)|𝛼=0>0
o
n≥12
, which p o es he second bulle o
(A.51)
(
1−𝛼)
dW
(m−1)
d𝛼
+𝛼
dW(m−1)
d𝛼
=(1−𝛼)[B�(e (m−1))
de (m−1)
d𝛼
−D�de(m−1)
d𝛼]
+𝛼[(m−1)B�(ec(m−1)) dec(m−1)
d𝛼
+(n−m+1)B�(e (m−1))
de (m−1)
d𝛼
−nD�de(m−1)
d𝛼
]
=[1+𝛼(n−1)]D�{[1+𝛼(n−m)]
de (m−1)
d𝛼
+𝛼(m−1)2
1+𝛼(m−2)
dec(m−1)
d𝛼
−de(m−1)
d𝛼}
=−
(1−𝛼)[1+𝛼(n−1)]D�
1+𝛼(
m
−2)
{
[𝛼(m−2)(n−m)−1]
de (m−1)
d𝛼
+de(m−1)
d𝛼
}
,
(A.52)
V
c(m)−V (m−1)=(1−𝛼)Wc(m)+𝛼W(m)−
[
(1−𝛼)W (m−1)+𝛼W(m−1)
]
=
(1+2𝛼)n2(m−1)a2
2b(d
b)2
[
1+(m2+n−3m+2)d
b]
2
[
1+(m2+n−m)d
b]
2𝜑(m),
(A.53)
𝜑
(m) ∶= 𝛼
1+2𝛼
{
4N3+3+2[2N2
3+N3(2M2
2+4M2+13)+2M3
2+9M2
2+7M2+9]
d
b
+[7N2
3+N3[4M3
2+22M2
2+22M2+34]+4M5
2+23M4
2+54M3
2+85M2
2
+50M2+27](d
b)2}−{m−3+2[(n−m)(m−1)+(m−3)(m2+2)+4]d
b
+[n−m+m(m−2)][(n−m)(m+1)+m(m2−m+2)]
(
d
b
)
2
}
,
2344
M.Schop
1 3
he p oposi ion. F om (A.53),
𝜑(m)
inc eases wi h
𝛼
1+2𝛼
and, hus, wi h
𝛼
, which p o es he
hi d bulle o he p oposi ion. Fu he mo e,
which p o es he hi d bulle o he p oposi ion. Fu he mo e,
whe e
Ψ>0
o
n≥4
and
m≥3
. The co esponding Maple ile is a ailable on eques .
𝜑(m)≤0
o some
m≥3
implies
𝜕𝜑(m)
𝜕m
<
0
and, hus,
𝜑(m)<0
o all
m≥m
. Fu he -
mo e,
𝜑(m)≥0
⟺
Vc(m)−V (m−1)≥0
⟺
V (m−1)−Vc(m)≤0
. Thus, an in e -
nally s able coali ion m implies an ex e nally uns able coali ion
m−1
. Consequen ly, he e
is a mos one in e nally and ex e nally s able coali ion, which p o es he i s bulle o he
p oposi ion. Finally, no e ha
(A.54)
𝜑
(n)=(n−1)4
16b2
{
50N
5
2+305N
4
2+720N
3
2+790N
2
2+358N2+17
(1+2𝛼)(n−1)4
⋅[𝛼−4
7+
N3(5N2
3+24N3+8)
7(10N3
3+55N2
3+100N3+56)]d2
+
2(10N3
2+33N2
2+36N2+9)
(1+2𝛼)(n−1)2
⋅[𝛼−4
7+5n3+11n2−9n+33
7(10N3
2+33N2
2+36N2+9)](
d−d)d
+2N2+1
1
+
2𝛼
[
𝛼−4
7+n+9
7
(
2
N2+
1
)]
(
d−d)2
}
>0⟸𝛼≥4
7∧d≤
d
,
(A.55)
=−
n
2
(n−2)(2n
2
−3n+2)
1+2𝛼
[
3
7−𝛼+n
2
+2n+8
7(2n2−3n+2)
](
d
b
)2
−
2(2N3
2+7N2
2+8N2+2)
1+2𝛼[3
7−𝛼+
N3
6+12N2
6+38N6+4
7(2N3
2+7N2
2+8N2+2)]
d
b
−2N2+1
1
+
2𝛼
[
3
7−𝛼+
N12
7
(
2
N2+
1
)]
<0⟸𝛼≤3
7∧n≥12,
(A.56)
𝜕𝜑
(m)
𝜕m=
{
1+2(n−m+3m2−7m+3)d
b+ [(n−m)2+(6m2−6m−2)(n−m)+5m4
−14m3+14m2−8m](d
b)2}/{m−3+2[(m−1)(n−m)+(m−3)(m2+2)
+4]d
b+[n−m+m(m−2)][(m+1)(n−m)+m(m2−m+2)]
(
d
b
)
2
}
𝜑(m
)−Ψ,
(A.57)
W
={b
2
−b[n(n−2)−2m(m−1)]d−m(m−1)
2
(n−m)d
2
}na
2
2b[b+(m
2
+n−m)d]
2
,

2345
Sel ‑En o cing In e na ional En i onmen al Ag eemen s and…
1 3
such ha
[
1+𝛼(n−1)]
𝜕W
𝜕m
=
𝜕V
𝜕m
>
0
.
◻
S ackelbe g Game
De i a ion o (13)
The i s -o de condi ion o (3) eads
Subs i u ing (4) and ea anging yields (13). The second-o de condi ion o (3) eads
which is ul illed i
D′′′ ≤0, B′′′ ≥0
.
P oo o P oposi ion4
F om (4), (6) and (13), he equilib ium is cha ac e ised by
Fi s di e en ia ing (A.61), (A.62) and (A.63) wi h espec o
𝜃
yields
(A.58)
𝜕
W
𝜕
m=[(4m−2)(n−m)+(m−1)
2
]n
2
ad
2
2[b+(m2+n−m)d]2ec+(m−1)
4
n
2
(n−2)a
2
d
3
2(n−1)2b[b+(m2+n−m)d]
3
⋅
[
2
(
n−m
m−1)
3
+(4n−1)
(
n−m
m−1)
2
+(n−1)
(
n−m
m−1)
+n2
n−2]
>0,
(A.59)
[
1+𝛼(m−1)]
{
B�(ec)− m[1+𝛼(n−1)]
1+𝛼(m−1)D�
[
1+
d(n−m)e
de
c]
+𝛼m(n−m)
1+𝛼(m−1)B�(e )
de
de
c}
=
0.
(A.60)
[
1+𝛼(m−1)]{B��(ec)− m[1+𝛼(n−1)]
1+𝛼(m−1)D��[1+
d(n−m)e
dec]
2
+𝛼m(n−m)
1+𝛼(m−1)B��(e )(de
dec)
2
−m
1+𝛼(m−1){[1+𝛼(n−1)]D�−𝛼B�(e )} (n−m)[1+𝛼(n−1)]
{(n−m)[1+𝛼(n−1)]D�� −B��(e )}2
⋅
[
B��(e )D���
[
1+
d(n−m)e
de
c]
−D��B���(e )
de
de
c]}
<0,
(A.61)
B
�
(e
)=[1+𝛼(n−1)]D
�,
(A.62)
B�(ec)=[1+𝛼(n−1)]𝜃D�,
(A.63)
e=mec+(n−m)e .
(A.64)
B
��(e )
de
d𝜃
=[1+𝛼(n−1)]D�� de
d𝜃,
(A.65)
B
��(ec)
de
c
d𝜃
=[1+𝛼(n−1)]
[
𝜃D�� de
d𝜃
+D�
],
2346
M.Schop
1 3
Sol ing o
de
d𝜃
,
de
d𝜃
and
dec
d𝜃
yields
No e ha
𝜃
=1⟺e
=e
c
=e
BAU
i
. Thus,
𝜃⋛
1⟺e
⋛
e
BAU
i⋛
e
c
∧e
BAU ⋛e
.
Second di e en ia ing
Vi
and
Wi
wi h espec o
𝜃
and using (4), (6), (13), (A.67), (A.68)
and (A.69) yields
(A.66)
d
e
d𝜃
=m
dec
d𝜃
+(n−m)
de
d𝜃
.
(A.67)
de
d𝜃=m[1+𝛼(n−1)]
2
D
��
D
�
B��(e
c
)B��(e
)−[1+𝛼(n−1)][(n−m)B��(e
c
)+m𝜃B��(e
)]D�� >
0,
(A.68)
d
ec
d𝜃=−
[1+𝛼(n−1)]{(n−m)[1+𝛼(n−1)]D
��
−B
��
(e )}D
�
B��(e
c
)B��(e
)−[1+𝛼(n−1)][(n−m)B��(e
c
)+m𝜃B��(e
)]D�� <
0,
(A.69)
d
e
d
𝜃=m[1+𝛼(n−1)]B
��
(e )D
�
B��(e
c
)B��(e
)−[1+𝛼(n−1)][(n−m)B��(e
c
)+m𝜃B��(e
)]D�� <
0.
(A.70)
dV
d𝜃=[1+𝛼(n−m−1)]B�(e )
de
d𝜃+𝛼mB�(ec)
dec
d𝜃−[1+𝛼(n−1)]D�de
d𝜃
=[1+𝛼(n−1)]D�{(1−𝛼)
de
d𝜃+𝛼[(n−m)
de
d𝜃+m𝜃
dec
d𝜃]−de
d𝜃}
=
𝛼m[1+𝛼(n−1)]2{(n−m)[1+𝛼(n−1)]D�� −B��(e )}(D�)2
B��(ec)B��(e )−[1+𝛼(n−1)][(n−m)B��(ec)+m𝜃B��(e )]D��
⋅
{
(1−𝛼){[1+𝛼(n−1)]D�� −B��(e )}
𝛼{(n−m)[1+𝛼(n−1)]D�� −B��(e
)} +1−𝜃
}
(A.71)
=
𝛼m[1+𝛼(n−1)]
2
{(n−m)[1+𝛼(n−1)]D
��
−B
��
(e )}(D
�
)
2
B��(ec)B��(e )−[1+𝛼(n−1)][(n−m)B��(ec)+m𝜃B��(e )]D��
⋅
{
(1−𝛼){[1+𝛼(n−1)]2D�� −B��(e )}
𝛼[1+𝛼(m−1)]{(n−m)[1+𝛼(n−1)]D�� −B��(e )} +
𝜃−𝜃
},
(A.72)
d
Vc
d𝜃=𝛼(n−m)B�(e )
de
d𝜃+[1+𝛼(m−1)]B�(ec)dec
d𝜃−[1+𝛼(n−1)]D�de
d𝜃
=[1+𝛼(n−1)]D�{(1−𝛼)𝜃dec
d𝜃+𝛼[(n−m)
de
d𝜃+m𝜃dec
d𝜃]−de
d𝜃}
=
[1+𝛼(m−1)][1+𝛼(n−1)]2{(n−m)[1+𝛼(n−1)]D�� −B��(e )}(D�)2(
𝜃−𝜃)
B��(e
c
)B��(e
)−[1+𝛼(n−1)][(n−m)B��(e
c
)+m𝜃B��(e
)]D��
,
2347
Sel ‑En o cing In e na ional En i onmen al Ag eemen s and…
1 3
(A.70) [(A.73)] yields
dV
d𝜃
>
0
[
dV
d
𝜃
>
0
and
d
W
d
𝜃
>0
]
o
𝜃≤1
, which implies
V
<V
BAU
i
[
V<VBAU
and
W<WBAU
] o

𝜃<1
. (A.71) [(A.74)] yields
dV
d𝜃
>
0
[
dV
d𝜃>
0
and
d
W
d𝜃>0
]
o
𝜃≤
𝜃
, which implies
V
>V
BAU
i
[
V>VBAU
and
W>WBAU
] o

𝜃>1
. (A.72) yields
dV
c
d𝜃
⋛
0
o
𝜃⋚
𝜃
, which implies
Vc
>V
BAU
i
o

𝜃≠1
. (A.75) implies
W ⋛
W
BAU
i
o

𝜃⋛1
.
(A.76) yields
dW
c
d𝜃
<
0
o
𝜃≥
𝜃
, which implies
Wc
>W
BAU
i
o

𝜃<1
. Finally, (A.77)
implies
V ⋛
V
c
and
W ⋛
W
c
o

𝜃⋛1
.
Thi d suppose
e≤eSO
. Then, he igh -hand sides o (4) and (13) would be smalle
han
nD�(eSO)
, such ha he le -hand sides would ha e o be smalle han
B�
(e
SO
i)
,
implying
ec
,e
<e
SO
i
and con adic ing
e≤eSO
. Thus,
e>eSO
.
◻
(A.73)
d
V
d𝜃=[1+𝛼(n−1)] dW
d𝜃=[1+𝛼(n−1)]
{
(n−m)B�(e )
de
d𝜃+mB�(ec)
dec
d𝜃−nD�de
d𝜃
}
=[1+𝛼(n−1)]D�{[1+𝛼(n−1)][(n−m)
de
d𝜃+m𝜃
dec
d𝜃]−nde
d𝜃}
=m[1+𝛼(n−1)]3{(n−m)[1+𝛼(n−1)]D�� −B��(e )}(D�)2
B��(ec)B��(e )−[1+𝛼(n−1)][(n−m)B��(ec)+m𝜃B��(e )]D��
⋅{−
(1−𝛼)(n−1)B��(e )
[1+𝛼(n−1)]{(n−m)[1+𝛼(n−1)]D�� −B��(e
)} +1−𝜃}
(A.74)
=
m[1+𝛼(n−1)]
3
{(n−m)[1+𝛼(n−1)]D
��
−B
��
(e )}(D
�
)
2
B��(ec)B��(e )−[1+𝛼(n−1)][(n−m)B��(ec)+m𝜃B��(e )]D��
⋅
{
(1−𝛼)(n−m){[1+𝛼(n−1)]2D�� −B��(e )}
[1+𝛼(m−1)][1+𝛼(n−1)]{(n−m)[1+𝛼(n−1)]D�� −B��(e )} +
𝜃−𝜃
},
(A.75)
dW
d𝜃
=B�(e )
de
d𝜃
−D�de
d𝜃
>
0,
(A.76)
dW
c
d𝜃=B�(ec)
de
c
d𝜃−D�de
d𝜃=D�
{
[1+𝛼(n−1)]𝜃
de
c
d𝜃−de
d𝜃
}
=−
[1+𝛼(n−1)]2{(n−m)[1+𝛼(n−1)]D�� −B��(e )}(D�)2
B��(ec)B��(e )−[1+𝛼(n−1)][(n−m)B��(ec)+m𝜃B��(e )]D��
⋅
{
𝛼m(n−m){(n−m)[1+𝛼(n−1)]2D�� −B��(e )}
[1+𝛼(m−1)][1+𝛼(n−1)]{(n−m)[1+𝛼(n−1)]D�� −B��(e )} +𝜃−
𝜃
},
(A.77)
d(V
−V
c
)
d
𝜃
=(1−𝛼)
d(W
−W
c
)
d
𝜃
=(1−𝛼)
[
B�(e )
de
d
𝜃
−B�(ec)
dec
d
𝜃]
>
0.
2348
M.Schop
1 3
P oo o P oposi ion5
To ally di e en ia ing (4), (13) and
e=mec+(n−m)e
yields
whe e
Sol ing o
de
,
dec
and
de
yields
whe e
(A.78)
B��
(e
)de
=[1+𝛼(n−1)]D
��
de+(n−1)D
�
d𝛼
,
(A.79)
B��
(ec)dec=𝜆ede−𝜆e
de +𝜆mdm+𝜆𝛼d𝛼
,
(A.80)
de=mdec+(n−m)de +(ec−e )dm,
𝜆e∶= 1+𝛼(n−1)
1+𝛼(m−1)mD�� 𝛼(n−m)[1+𝛼(n−1)]D
��
−B
��
(e )
(n−m)[1+𝛼(n−1)]D�� −B��(e )
+1+𝛼(n−1)
1+𝛼(m−1)mD�(1−𝛼)(n−m)[1+𝛼(n−1)]B��(e )
[(n−m)[1+𝛼(n−1)]D�� −B��(e )]2D��� >0⟸D��� ≤0,
𝜆
e ∶= 1+𝛼(n−1)
1+𝛼(m−1)mD�(1−𝛼)(n−m)[1+𝛼(n−1)]D��
[(n−m)[1+𝛼(n−1)]D�� −B��(e )]2B���(e )⋛0⟺B��� ⋛0,
𝜆
m∶= 1+𝛼(n−1)
[1+𝛼(m−1)]2D�1−𝛼
[(n−m)[1+𝛼(n−1)]D�� −B��(e )]2{𝛼(n−m)2[1+𝛼(n−1)]
2
⋅[D��]2−[n+𝛼(m2+n−2m)][1+𝛼(n−1)]D��B��(e )+[B��(e )]2]} >0,
𝜆𝛼∶= n−m
[1+𝛼(m−1)]2mD�1
[(n−m)[1+𝛼(n−1)]D�� −B��(e )]2{[1+𝛼(n−1)][1+𝛼(
m
−1)][1+2𝛼(n−1)+𝛼2(n−1)(m−1)][(n−m)[1+𝛼(n−1)]D�� −B��(e )]D��(1
−
𝜃)∕(1−𝛼)+[1+𝛼(n−1)][1+𝛼(n−1)(m2−1)+𝛼(n−1)(m+2)]D��B��(e )
+[B��(e
)]2}>0⟸
𝜃≤1.
(A.81)
𝜆de
=[1+𝛼(n−1)]D��[m𝜆m−(e −ec)B��(ec)]dm
− {(n−1)[m𝜆
e
−B��(e
c
)]D�−m[1+𝛼(n−1)]D��𝜆
𝛼
}d𝛼
,
(A.82)
𝜆de
c
= −{[1+𝛼(n−1)]D��[(n−m)𝜆m+(ec−e )𝜆e ]−B��(e )[𝜆m+(ec−e )𝜆e]}d
m
+ {(n−1)[(n−m)𝜆e−𝜆e
]D�− {(n−m)[1+𝛼(n−1)]D�� −B��(e )}𝜆𝛼}d𝛼,
(A.83)
𝜆de
=B��(e )[m𝜆m−(e −ec)B��(ec)]dm
− {(n−1)[m𝜆e
−(n−m)B��(ec)]D�−mB��(e )𝜆𝛼}d𝛼
,
2355
Sel ‑En o cing In e na ional En i onmen al Ag eemen s and…
1 3
Thus,

m
is minimal o
𝛼=0
and
n=7
wi h

m=1.96
, and i is maximal o
𝛼=1
and
n→∞
wi h

m=5
.
m∈(m,m+2)
and
m≤

m
hen imply
m∈{2, 3}
o
𝛼=0
and
m∈{2, 3, 4, 5, 6}
o
𝛼>0
. This p o es he second bulle o he p oposi ion and he ou h
bulle o he p oposi ion, espec i ely. Fu he mo e,
such ha
m=3
is in e nally uns able o
𝛼=0
,
n≥26
and
d≤


d
. Finally,
such ha
𝜙(3)
dec eases wi h d/b, and inc eases wi h
(d∕b)3
and
(d∕b)4
, which
implies ha
𝜙(3)
is posi i e i and only i d/b is g ea e han some unique h eshold
d∕b=[a g 𝜙(3)=0]
. Figu e6 shows ha he de i a i e o his h eshold wi h espec o
𝛼
is nega i e o
n∈[7, 25]
. This p o es he hi d bulle o he p oposi ion.
◻
(A.106)
𝜕
m
𝜕n
=16𝛼(n−1)
2
−8𝛼(n−1)(n−2)−4n(n−2)
[(n−2)2+4𝛼(n−1)]2⋛0
⟺𝛼⋛n−2+
√
(n−2)(5n−2)
4(n−1)
∈[0.576, 0.809]
.
(A.107)
𝜙(3)|
𝛼=0
=−8d
b+(n2+10n−23)(d
b)2
+2(n−1)2(n−2)(d
b)3
+(n−2)2(n−3)2(d
b)4
=− d
16b4{(N6
26 +122N5
26 +5951N4
26 +145224N3
26 +1778248N2
26 +8867520N26
+2064240)d3+2n(n−4)(2N4
26 +174N3
26 +5587N2
26 +78148N26 +399316)(

d−d)d
2
+n2(n−4)2(5N2
26
+226N
26
+2519)(

d−d)2d+2n3(n−4)3(

d−d)3},
(A.108)
𝜙
(3)=−2𝛼−2[1+𝛼(n−1)][4+(2n−11)𝛼+(2n−6)𝛼2]
d
b+[1+𝛼(n−1)]2[n2+10
n
−23 +(2n2−28n+68)𝛼−(3n2−24n+29)𝛼2](d
b)2
+(n−2)[1+𝛼(n−1)]3
⋅[2(n−1)2+(8n2−10n−20)𝛼+(n−3)(6n−26)𝛼2](d
b)3
+(n−3)(n−2)2
⋅[1+𝛼(n−1)]4[n−3+4(n−1)𝛼+(5n+7)𝛼2]
(
d
b)
4
,

2356
M.Schop
1 3
Supplemen a y In o ma ion The online e sion con ains supplemen a y ma e ial a ailable a h ps:// doi. o g/
10. 1007/ s10640- 024- 00885-8.
Acknowledgemen s I would like o hank Ma c Lende s, Julia Komm i z and pa icipan s o he EAERE
2023 and he V S 2023 o help ul commen s. Mo eo e , he commen s om h ee anonymous e iewe s
signi ican ly imp o ed his a icle.
Funding Open Access unding enabled and o ganized by P ojek DEAL.
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Re e ences
Alge I, Weibull JW (2010) Kinship, incen i es, and e olu ion. Am Econ Re 100(4):1725–1758
Alge I, Weibull JW (2013) Homo Mo alis-p e e ence e olu ion unde incomple e in o ma ion and
asso a i e ma ching. Econome ica 81(6):2269–2302
Fig. 6 De i a i e o
d∕b
wi h
espec o
𝛼
o
n∈[7, 25]
2357
Sel ‑En o cing In e na ional En i onmen al Ag eemen s and…
1 3
Al ami ano-Cab e a J-C, Finus M (2006) Pe mi ading and s abili y o in e na ional clima e
ag eemen s. J Appl Econ 9(1):19–47
And e P, Bone a T, Chop a F, Falk A (2024) Mispe cei ed social no ms and willingness o ac agains
clima e change. SAFE Wo king Pape No. 414
And eoni J (1990) Impu e al uism and dona ions o public goods: a heo y o wa m-glow gi ing. Econ
J 100(401):464–477
And eoni J, Ha baugh WT, Ves e lund L (2010) Al uism in expe imen s. In: Du lau SN, Blume LE
(eds) Beha iou al and expe imen al economics. The New Palg a e Economics Collec ion, Palg a e
Macmillan, London, pp6–13
Bakalo a I, Eyckmans J (2019) Simula ing he impac o he e ogenei y on s abili y and e ec i eness o
in e na ional en i onmen al ag eemen s. Eu J Ope Res 277(3):1151–1162
Ballie D, Junhui W, De D eu CKW (2014) Ing oup a o i ism in coope a ion: a me a-analysis. Psychol
Bull 140(6):1556–1581
Ba e S (1994) Sel -en o cing in e na ional en i onmen al ag eemen s. Ox Econ Pap 46:878–894
Ba e S (1997) He e ogeneous in e na ional en i onmen al ag eemen s. In: Ca a o C (ed) In e na ional
en i onmen al nego ia ions: s a egic policy issues. Edwa d Elga , Chel enham, pp 9–25
Ba e S (2013) Clima e ea ies and app oaching ca as ophes. J En i on Econ Manag 66(2):235–250
Bay amoglu B, Finus M, Jacques J-F (2018) Clima e ag eemen s in a mi iga ion-adap a ion game. J
Public Econ 165:101–113
Becke GS (1974) A heo y o social in e ac ions. J Poli Econ 82(6):1063–1093
Becke GS (1981) Al uism in he amily and sel ishness in he ma ke place. Economica 48(189):1–15
Bol on GE, Ocken els A (2000) ERC: a heo y o equi y, ecip oci y, and compe i ion. Am Econ Re
91(1):166–193
Bo eon M, Ca a o C (2001) En i onmen al coali ions wi h he e ogeneous coun ies: Bu den-sha ing
and ca bon leakage. In: Ulph A (ed) En i onmen al Policy, In e na ional Ag eemen s, and
In e na ional T ade. Ox o d Uni e si y P ess, New Yo k
Buchholz W, Haup A, Pe e s W (2005) In e na ional en i onmen al ag eemen s and s a egic o ing.
Scand J Econ 107(1):175–195
Buchholz W, Pe e s W, U e A (2018) In e na ional en i onmen al ag eemen s on clima e p o ec ion: a
bina y choice model wi h he e ogeneous agen s. J Econ Beha O gan. 154:191–205
Ca bone JC, Helm C, Ru he o d TF (2009) The case o in e na ional emission ade in he absence o
coope a i e clima e policy. J En i on Econ Manag 58(3):266–280
Ca a o C, Siniscalco D (1993) S a egies o he in e na ional p o ec ion o he en i onmen . J Public
Econ 52(3):309–328
Cheikbossian G (2021a) E olu iona ily s able in-g oup al uism in in e g oup con lic o e (local) public
goods. Games Econ Beha 127:206–226
Cheikbossian G (2021b) The e olu iona y s abili y o in-g oup al uism in p oduc i e and des uc i e
g oup con es s. J Econ Beha O gan 188:236–252
D’Asp emon C, Jacquemin A, Gabszewicz JJ, Weyma k JA (1983) On he s abili y o collusi e p ice
leade ship. Can J Econ 16(1):17–25
Daube M (2019) Al uism and global en i onmen al axes. En i on Resou ce Econ 73(4):1049–1072
Diaman oudi E, Sa ze akis ES (2006) S able in e na ional en i onmen al ag eemen s: an analy ical
app oach. J Public Econ Theo y 8(2):247–263
Die z T, Fi zge ald A, Shwom R (2005) En i onmen al alues. Annu Re En i on Resou 30:335–372
Ecke H, Nkuiya B (2022) Damage sensi i i y and s abili y in in e na ional en i onmen al ag eemen s.
Ox Econ Pap 74(4):1063–1076
Eichne T, Pe hig R (2022) In e na ional en i onmen al ag eemen s when coun ies beha e mo ally.
CESi o Wo king Pape No. 10090
Engle D, Gu sche G, Simixhiu A, Ziegle A (2022) Social no ms and indi idual clima e p o ec ion
ac i i ies: a amed ield expe imen o Ge many. MAGKS Join Discussion Pape Se ies in
Economics No. 30-2022
Feh E, Schmid KM (1999) A heo y o ai ness, compe i ion, and coope a ion. Q J Econ
114(3):817–868
Finus M (2001) Game heo y and in e na ional en i onmen al coope a ion. Edwa d Elga , Chel enham and
No hamp on
Finus M, Fu ini F, Roh e AV (2021) The e icacy o in e na ional en i onmen al ag eemen s when
adap a ion ma e s: Nash-Cou no s. S ackelbe g leade ship. J En i on Econ Manag 109:102461
Finus M, Fu ini F, Roh e AV (2021b) In e na ional en i onmen al ag eemen s and he pa adox o
coope a ion: e isi ing and gene alizing some p e ious esul s. G az Economics Pape s No. 2021-05
2358
M.Schop
1 3
Finus M, Fu ini F, Roh e AV (2023) The S ackelbe g s. Nash-Cou no olk- heo em in in e na ional
en i onmen al ag eemen s. Econ Le 234:111481
Finus M, McGin y M (2019) The an i-pa adox o coope a ion: di e si y may pay! J Econ Beha O gan
157:541–559
Fuen es-Albe o C, Rubio SJ (2010) Can in e na ional en i onmen al coope a ion be bough ? Eu J Ope Res
202(1):255–264
Goussebaïle A, Bommie A, Goe ge A, Nicolaï J-P (2023) Al uis ic o eign aid and clima e change
mi iga ion. En i on Resou ce Econ 84(1):219–239
G aziosi GR (2009) On he s a egic use o ep esen a i e democ acy in in e na ional ag eemen s. J Public
Econ Theo y 11(2):281–296
G üning C, Pe e s W (2010) Can jus ice and ai ness enla ge in e na ional en i onmen al ag eemen s?
Games 1(2):137–158
Helm C (2003) In e na ional emissions ading wi h endogenous allowance choices. J Public Econ
87(12):2737–2747
Hje pe M, Lö g en Åsa, Linné B, Hennlock M, S e ne T, Jage s SC (2011) Common g ound o e o
sha ing? P e e ed p inciples o dis ibu ing clima e mi iga ion e o s. Uni e si y o Go henbu g
Wo king Pape s in Economics No. 491
Hoel M (1996) Should a ca bon ax be di e en ia ed ac oss sec o s? J Public Econ 59(1):17–32
Hol sma k B, Wei zman ML (2020) On he e ec s o linking cap-and- ade sys ems o CO2 emissions.
En i on Resou ce Econ 75(3):615–630
Hol sma k K, Mid ømme K (2021) The dynamics o linking pe mi ma ke s. J Public Econ 198:104406
IPCC (2021) Clima e change 2021: he physical science basis. Online a : h ps:// www. ipcc. ch/ epo / a 6/
wg1
Ka p L, Simon L (2013) Pa icipa ion games and in e na ional en i onmen al ag eemen s: a non-pa ame ic
model. J En i on Econ Manag 65(2):326–344
Kes e nich M, Löschel A, Ziegle A (2021) Nego ia ing weigh s o bu den sha ing ules in in e na ional
clima e nego ia ions: an empi ical analysis. En i on Econ Policy S ud 23:309–331
Ko chen MJ, Moo e MR (2007) P i a e p o ision o en i onmen al public goods: household pa icipa ion in
g een-elec ici y p og ams. J En i on Econ Manag 53(1):1–16
Lades LK, La an K, Webe TO (2021) Do economic p e e ences p edic p o-en i onmen al beha iou ?
Ecol Econ 183:106977
Lange A (2006) The impac o equi y-p e e ences on he s abili y o in e na ional en i onmen al
ag eemen s. En i on Resou Econ 34(2)
Lange A, Vog C (2003) Coope a ion in in e na ional en i onmen al nego ia ions due o a p e e ence o
equi y. J Public Econ 87(9–10):2049–2067
Lange A, Vog C, Ziegle A (2007) On he impo ance o equi y in in e na ional clima e policy: an
empi ical analysis. Ene gy Econ 29(3):545–562
Lange A, Schwi plies C (2017) (un) ai delega ion: explo ing he s a egic use o equi y ules in
in e na ional clima e nego ia ions. En i on Resou Econ 67:505–533
Lessmann K, Ma schinski R, Finus M, Ko nek U, Edenho e O (2014) Emissions ading wi h non-
signa o ies in a clima e ag eemen -an analysis o coali ion s abili y. Manch Sch 82:82–109
Loepe A (2017) C oss-bo de ex e nali ies and coope a ion among ep esen a i e democ acies. Eu
Econ Re 91:180–208
Ma kusen JR (1975) In e na ional ex e nali ies and op imal ax s uc u es. J In Econ 5(1):15–29
McGin y M (2007) In e na ional en i onmen al ag eemen s among asymme ic na ions. Ox Econ Pap
59(1):45–62
McGin y M (2020) Leade ship and ee- iding: decomposing and explaining he pa adox o coope a ion
in in e na ional en i onmen al ag eemen s. En i on Resou Econ 77:449–474
Meulemann M, Ziegle A (2015) The ole o bu den sha ing ules in in e na ional clima e nego ia ions.
In: Max M (ed) Fai ness and componen s o a chi ec u es in in e na ional clima e nego ia ions.
ETH Zü ich, Zü ich, pp 19–48
Nkuiya B (2020) S abili y o in e na ional en i onmen al ag eemen s unde isoelas ic u ili y. Resou
Ene gy Econ 59:101128
Nkuiya B, Ma ouch W, Bahel E (2015) In e na ional en i onmen al ag eemen s unde endogenous
unce ain y. J Public Econ Theo y 17(5):752–772
Nybo g K (2000) Homo economicus and homo poli icus: in e p e a ion and agg ega ion o
en i onmen al alues. J Econom Beha O gan 42(3):305–322
Nybo g K (2018) Recip ocal clima e nego ia o s. J En i on Econ Manag 92:707–725
Pa lo a Y, De Zeeuw A (2013) Asymme ies in in e na ional en i onmen al ag eemen s. En i on De
Econ 18(1):51–68
2359
Sel ‑En o cing In e na ional En i onmen al Ag eemen s and…
1 3
Pollak RA (1988) Tied ans e s and pa e nalis ic p e e ences. Am Econ Re 78(2):240–244
Rabin M (1993) Inco po a ing ai ness in o game heo y and economics. Am Econ Re 83(5):1281–1302
Ricke K, D oue L, Caldei a K, Ta oni M (2018) Coun y-le el social cos o ca bon. Na Clim Chang
8(10):895–900
Roeme JE (2015) Kan ian op imiza ion: a mic o ounda ion o coope a ion. J Public Econ 127:45–57
Rogna M, Vog CJ (2022) Op imal clima e policies unde ai ness p e e ences. Clim Change
174(25):1–20
Schwalm CR, Glendon S, Du y PB (2020) RCP8.5 acks cumula i e CO
2
emissions. P oc Na l Acad
Sci 117(33):19656–19657
Segendo B (1998) Delega ion and h ea in ba gaining. Games Econom Beha 23(2):266–283
Spyche S, Winkle R (2022) S a egic delega ion in he o ma ion o modes in e na ional en i onmen al
ag eemen s. Eu Econ Re 141:103963
S eg L (2016) Values, no ms, and in insic mo i a ion o ac p oen i onmen ally. Annu Re En i on
Resou 41:277–292
Taj el H, Tu ne JC, Aus in WG, Wo chel S (1979) An in eg a i e heo y o in e g oup con lic . In: Aus in
WG, Wo chel S (eds) The social psychology o in e g oup ela ions. B ooks/Cole, Mon e ey, pp 33–37
The Wo ld Bank (2023) Ca bon p icing dashboa d. Online a : h ps:// ca bo np ic ingda shboa d. wo ld
bank. o g
Ulph A, Ulph D (2023) In e na ional coope a ion and Kan ian mo al beha iou —Complemen s o
subs i u es? Uni e si y o Manches e Economics Wo king Pape No. EDP-2302
UN (2015) Pa is ag eemen . Online a : h ps:// un ccc. in / p oce ss- and- mee i ngs/ he- pa is- ag ee men / he-
pa is- ag ee men
UN (2023) ‘Emissions gap epo ’, Online a : h ps:// www. unep. o g/ esou ces/ emiss ions- gap- epo - 2023
an de Pol T, Weika d H-P, an Ie land E (2012) Can al uism s abilise in e na ional clima e
ag eemen s? Ecol Econ 81:112–120
Vog C (2016) Clima e coali ion o ma ion when playe s a e he e ogeneous and inequali y a e se.
En i on Resou ce Econ 65(1):33–59
Yamagishi T, Kiyona i T (1999) Bounded gene alized ecip oci y: in-g oup boas ing and in- g oup
a o i ism. Ad G oup P ocess 16:161–197
Yu S, Yinhao W (2022) Implica ions o ca bon ade wi h endogenous pe mi s o pos -Pa is clima e
ag eemen s. Clim Change Econ 13(4):2250006
Ziegle A (2020) He e ogeneous p e e ences and he indi idual change o al e na i e elec ici y con ac s.
Ene gy Econ 91:104889
Publishe ’s No e Sp inge Na u e emains neu al wi h ega d o ju isdic ional claims in published maps and
ins i u ional a ilia ions.