New Roads to Internatonal Envronmental Agreements: The Case of Global Warmng * Second draft: February, 24 Johan Eyckmans K.U.Leuven, Centrum voor Economsche Studën, Naamsestraat 69, B-3 Leuven, Belgum Johan.Eyckmans@econ.kuleuven.ac.be Mchael Fnus Department of Economcs, Unversty of Hagen, Proflstr. 8, 5884 Hagen, Germany Mchael.Fnus@fernun-hagen.de Abstract We analyze the formaton of nternatonal envronmental agreements (IEAs) employng the wdely used concept of nternal&external stablty and suggest several modfcatons. Countres objectve functons are derved from from an ntegrated assessement model of clmate change. We relax the assumptons of a sngle agreement and open membershp rule. It turns out that multple agreements are superor to a sngle agreement and exclusve s superor to open membershp n welfare and ecologcal terms. Moreover, we show the mportance of transfers for successful treaty-makng. We relate our results to the desgn of current and past IEAs as well as to other ssues of nternatonal polcy coordnaton. JEL-Classsfcaton: C68, C72, H41, Q25 Keywords: desgn of clmate treaty protocol, coalton formaton, non-cooperatve game theory * The authors acknowledge research assstants by Sebastan Bnsch and Danel Petzold. Both authors have greatly benefted from dscussons wth Carlo Carraro, Alfred Endres and Henry Tulkens. The ttle of ths paper s nspred by Carraro (2).
1. Introducton Accordng to the Intergovernmental Panel on Clmate Change (IPCC 21) the enhanced greenhouse effect, caused by anthropogenc emssons of so-called greenhouse gases (GHGs) lke carbon doxde and methane, wll negatvely affect lvng condtons of current and future generatons n almost all regons of the world. The enhanced greenhouse effect s a typcal example of a global common problem. In every country, a multtude of fossl fuel users (cars, lorres, households, ndustres and farmers) emt GHGs that dsspate nto the atmosphere where they mx unformly. Snce the global atmosphere s an open-access depostory of GHGs, ndvdual polluters have no ncentve to nternalze ther clmate change externaltes. As t s well-known, ths non-cooperatve stuaton s not optmal from the global socety s pont of vew (Arce and Sandler 21, Cornes and Sandler 1996; Endres 1997, Tahvonen 1994 and Eyckmans et al. 1993). In order to reach a globally optmal soluton, some knd of nternatonal coordnaton of clmate polces s needed. However, economsts are skeptcal about the prospects of effectve nternatonal polcy coordnaton due to free-rder ncentves and the lack of a supranatonal enforcement power. The bulk of the envronmental economcs lterature has been usng non-cooperatve game theory 1 to explan the problems of formng coaltons by applyng the concept of nternal and external stablty (e.g., Barrett 1994, Carraro and Snscalco 1993, Hoel 1992 and Rubo and Ulph 21). It s assumed that countres formng an nternatonal envronmental agreement (IEA),.e., a non-trval coalton 2, coordnate ther polces by jontly maxmzng the aggregate welfare to ther coalton. An IEA s sad to be nternally stable f none of ts members wants to leave; t s externally stable f none of the outsders wants to jon. A key result of ths lterature, whch has been called a paradox by Barrett (1994), s that whenever cooperaton (global optmum) would generate large global welfare gans compared to a non-cooperatve stuaton (Nash equlbrum), stable coaltons acheve only lttle. Moreover, t s ponted out that from partcpaton one cannot conclude success of cooperaton: small coaltons may acheve more than large coaltons n terms of global welfare and emsson reducton. 3 Internal&external stablty (I&E-S) makes at least two mplctly assumptons that have been questoned by Carraro (1997) for the frst tme n the context of IEAs. Frstly, I&E-S restrcts coalton formaton to only one (non-trval) coalton. That s, countres have only the opton to jon an agreement or to reman a non-sgnatory (sngleton) but cannot group nto dfferent agreements. Clearly from a theoretcal pont of vew, such a restrcton s not satsfactory. The key questons are whether countres wll form multple agreements nstead of a sngle agreement n equlbrum f ths assumpton s gven up and f so whether multple agreements are superor n welfare or ecologcal terms. 4 From the theoretcally orented lterature (e.g., Carraro 2, Carraro and Marchor 23, Fnus 21 and 1
23b and Fnus and Rundshagen 23a) t appears that, ndeed, n equlbrum multple coaltons wll emerge. However, those results have been derved under the assumpton of symmetrc (dentcal) players and welfare and ecologcal conclusons can only be derved for even more restrctve assumptons (e.g., statc payoff structure and domnant strateges). Thus, t s the frst objectve of ths paper to analyze the effect of sngle versus multple coalton formaton, usng data from an ntegrated assessment model of clmate change. 5 However, ths ssue has also an emprcal dmenson that may seem more controversal. On the one hand, one may argue that all IEAs that have been sgned up to now are sngle agreements. There s only one Montreal Protocol that regulates CFCs (chloro-fluoro-carbons), one Oslo Protocol that ams at reducng sulfur emssons and only one Kyoto Protocol wth the objectve to mtgate global warmng. On the other hand, at least for more recent protocols, t s evdent that members are treated dfferently and that therefore these protocols may be nterpreted n game theoretcal terms as multple coalton agreements. 6 For nstance, the Kyoto Protocol dstngushes between Annex-B- and non-annex B- countres where only the former group has agreed to quantfed emsson celngs. Another example s the Montreal Protocol that makes specal provsons for developng countres, allowng for a longer transton perod for complance wth abatement targets, exemptng them from certan regulatons and provdng the opton to draw on funds that are fnanced by developed countres. Intutvely, we expect that allowng for the possblty to form multple coaltons wll ncrease the success of nternatonal polluton control. Multple agreements allow for more flexblty n coordnatng dfferent nterests. Countres wth smlar nterests wll gather n a coalton. Hence, the free-rdng problem wll be less pronounced because of homogenous coaltons. Some countres that would not jon the global agreement because they fnd abatement efforts too ambtous mght form ther own agreement wth lke-mnded countres, mplementng at least moderate abatement targets. Thus f no large sngle agreement s stable, small regonal agreements may be a pragmatc second best soluton. The second assumpton of I&E-S s that of open membershp, whch follows from the defnton of external stablty. That s, countres can jon an agreement wthout the consent of exstng members. Hence, t s easy for outsders to upset a potentally stable coalton,.e., a coalton that s nternally stable. Consequently from a theoretcal pont of vew, t s evdent that some form of exclusve membershp may help to stablze IEAs (e.g., Carraro and Marchor 23 and Fnus and Rundshagen 23a,c). Less evdent s the queston what more stablty means n terms of welfare and ecologcal varables (emssons and concentraton). Agan, the theoretcal lterature can only provde partal answers snce results have been derved under very restrctve assumptons (e.g., symmetrc countres 2
and statc payoff structure). Thus, t s the second am of ths paper to analyze open versus exclusve membershp usng data from an ntegrated assessment clmate model. From an emprcal pont of vew, t s nterestng to observe that currently all exstng IEAs that deal wth global envronmental problems are of an open membershp nature. For nstance, the Kyoto Protocol does not requre any votng before a new country can accede. However, other nternatonal nsttutons (that do not necessarly deal wth global publc goods or bads) requre the consent of all ther exstng members before a newcomer can jon. For nstance, NATO (North Atlantc Treaty Organzaton) and WTO (Word Trade Organzaton) vote by unanmty on new members. Also the accesson of ten new countres to the EU (European Unon) had to be approved unanmously by the European Councl, though approval n the European Parlament requred only a smple majorty. Thus, our modfcaton of open mem-bershp may be nterpreted as applyng typcal club good rules to the publc good agreement IEA. In ths paper, we focus on two extreme types of exclusve membershp rules. The frst rule assumes that only f 5 percent or more of the coalton members are n favor of accesson, the potental entrant s allowed to jon. We call ths exclusve membershp majorty votng. The second rule assumes that only f all members agree to accesson, an outsder s permtted to jon. We call ths exclusve membershp unanmty votng. Other exclusve membershp rules (e.g., 2/3 qualfed majorty rule) can be consdered as ntermedate cases but are not analyzed n ths paper. Taken together, we beleve our paper extends prevous work n three drectons. Frstly, t s n the tradton of publc choce theory that analyzes the effect of dfferent votng procedures on the provson of publc (or club) goods (see, n general for publc good provson: Mueller, 23; for IEAs n partcular, see: Eyckmans 1999 and Fnus and Rundshagen 1998). However, most of ths work has been focusng on the level of publc good provson, the choce of emsson reducton targets or envronmental polcy nstruments that s assocated wth decsons n the second stage of coalton formaton. In contrast, we focus on dfferent membershp rules (sngle versus multple coaltons and open versus exclusve mem-bershp) that are assocated wth the frst stage of the coalton formaton process n whch countres decde on ther partcpaton (see secton 2 for detals). Secondly, as mentoned above, our paper s nspred by recent developments n non-cooperatve game theory that queston fundamental assumptons of the tradtonal stablty analyss of IEAs (e.g., Carraro 1997 and 2). However, n order to gan further nsghts, we depart from the assumpton of symmetrc players. Because of the dffcultes obtanng analytcal results, we base our analyss on data derved from an ntegrated assessment clmate model. Thrdly, our paper s n the tradton of the lterature that emprcally tests stablty of clmate coaltons (e.g., Bosello et al. 21, Botteon and 3
Carraro 1997, Buchner et al. 22, Fnus et al. 23 and Tol 21). In contrast to the bulk of ths lterature, we pay more attenton to the game theoretc underpnnng of our model, consder modfcaton of standard stablty concepts and use an ntegrated assessment clmate model that captures all mportant dynamc aspects of the greenhouse gas problem. In the followng, we lay out the game theoretcal module n secton 2 and descrbe the emprcal module of our model n secton 3. Stable coalton structures are reported and evaluated n secton 4. Secton 5 summarzes our man fndngs and concludes wth some fnal remarks. 2. The Game Theoretcal Background of Coalton Formaton 2.1 The Two-Stage Game Coalton formaton s modeled as a two-stage game. In the frst stage players (.e., countres or regons) decde on ther membershp n a coalton, n the second stage coalton members choose ther economc strateges. Frst Stage The decson n the frst stage s modeled as a coalton game. Its defnton comprses three elements: 1) the set of players I={1,..., N} wth a partcular player denoted by ndex or j, 2) the set of coalton (or, alternatvely, announcement) strateges Σ =Σ 1 Σ 2 ΣN wth a partcular strategy of player I denoted by σ Σ, and 3) a coalton functon ψ that maps membershp strateges σ= ( σ1,..., σ N) nto coalton structures, ψ : Σ C: σ ψ( σ). A coalton structure a partton of players where a partcular coalton s denoted by c k, k {1,..., M), c k c = I and c C where C s the set of all possble coalton structures. k 1 M c = (c,..., c ) s l c = " kπl, We consder two coalton games n the sprt of Y and Shn s (1995) open membershp game that we call sngle and multple coalton game. The sngle coalton game captures the noton that players can only choose between strategy σ = that means I do not want to sgn the agreement and σ = 1 that means I want to sgn the agreement. More formally, we have: 7 Defnton 1: Sngle Coalton Game (SCG) a) The set of coalton strateges of player ŒI, I={1,, N}, s gven by Σ = {,1} where a partcular strategy σ s an announcement of an address. b) Let c denote the coalton to whch player wll belong. Coalton functon ψ SCG maps strategy vector σ nto coalton structure c as follows: {} f σ = c = {j/ σ j = 1}fσ = 1. 4
In order to capture the possblty that players can form multple agreements, we have to ncrease the number of coalton strateges. Snce the maxmum number of coaltons s N (all players form a sngleton coalton), the strategy set must comprse now N nstead of only two strateges. In terms of the coalton functon, we have to ensure that those players that have made the same announcement wll form one coalton. Thus, we have: Defnton 2: Multple Coalton Game (MCG) a) The set of coalton strateges of player ŒI, I={1,, N}, s gven by Σ = {1,..., N } where a partcular strategy σ s an announcement of an address. b) Let c denote the coalton to whch player wll belong. Coalton functon ψ MCG maps strategy vector σ nto coalton structure c as follows: c = {}» {jô σ = σ j }. From Defnton 1 and 2 t s evdent that the outcome of the coalton game wll be a coalton structure of the form c = (c,..., c ). In the case of the MCG, coaltons c 2,..., c M may be 1 M non-trval coaltons whereas n the SCG they are always sngletons. If M=N (each player s n a sngleton coalton), ths corresponds to the sngleton coalton structure and f M=1 (all players are n one coalton), ths s called the grand coalton. Second Stage The decson n the second stage depends on the rules how players choose ther economc strateges and possble compensaton payments that follow from the defnton of the valuaton functon. The valuaton functon v(c) maps coalton structures nto a vector of ndvdual payoffs. The defnton comprses a) economc strateges s S, s S = S 1... SN, and possble transfers t T, t T= T 1... TN, and b) payoff functons w :S W, s w (s) wth W = W 1... WN R N n case of no transfers and ŵ:s T W, (s,t) w ˆ (s,t) wth ŵ(s,t) = w(s) + t n case of transfers and c) an nstructon ε (ε n case of transfers) how players choose ther economc strateges (and transfers) for a gven coalton structure c, εˆ :C S T, c εˆ (c) wth ε ˆ(c) = ( ε (c),t), ε:c S. That s, the valuaton functon s a composton of two functons v = w ε ( vˆ = wˆ εˆ ) where ε ( ˆε ) s a functon mappng coalton structures nto a vector of economc strateges (and transfers) and u ( û) s a functon mappng contrbutons (and transfers) nto utlty. We follow the manstream of the lterature (Bloch 1997 and Y 1997) and make two assumptons. 1) Members of coalton k c choose ther economc strateges k* s such as to maxmze aggregate utlty of ther coalton. 2) In case there are transfers, they are only pad among coalton members ( t * > mples to receve a transfer and t * < mples to pay a transfer). More formally, we have: 5
Defnton 3: Valuaton Functon 1 M Fx a coalton structure c = ( c,...,c ), let v( c ) = { v(c)} ŒI ={ w( ε(c))} ŒI ={ w(s )} ŒI n the case of no transfers and ˆv( c ) = { ˆv(c)} ŒI ={ ŵ( ˆ ε(c))} ŒI ={ w( ε(c) + t } I = {w(s ) + t } = * * { v ( c ) + t } and assume some transfer rule t = ε( c ) such that t =. For nstructon ε I assume that all agents belongng to a coalton c Œc jontly maxmze aggregate utlty to ther coalton such that equlbrum economc strateges * s k k c = ε( c ) for coalton structure c satsfy: " ŒC, " s Œ S : k k k c * w(s ) k c k k* w(s,s ) where * s s assumed to be a unque equlbrum. Defnton 3 mples that the valuaton of agent, v(c) ( ˆv (c)), s dentfed by the entre coalton structure c and not only by the coalton c to whch agent belongs. Agents behave cooperatvely wthn ther coalton when choosng ther economc strateges (group effcently), but non-cooperatvely aganst agents belongng to other coaltons. Put dfferently, members of a coalton act as one sngle player, playng Nash equlbrum (economc) strateges. Consequently, the sngleton coalton structure (grand coalton) mples an economc strategy vector correspondng to the "classcal" Nash equlbrum (socal optmum). Hence, neffcences must exclusvely stem from the fact that agents do not form the grand coalton. Exstence and unqueness of on * s for each coalton structure cœc (together wth a partcular assumpton * t ) s mportant to ensure that valuatons are unquely defned. For our emprcal model t turns out that both propertes hold (see secton 3). The standard assumpton of jont welfare maxmzaton requres that welfare s transferable and lnear n money. Ths may seem somehow restrctve but eases the game theoretcal analyss. Ths also true for the assumpton that transfers are only pad among coalton members. 2.2 Stablty n the Reduced Stage Game Provded there s a unque valuaton (vector of ndvdual payoffs) that s assocated wth each coalton structure c C (as t s true for our emprcal model), the entre coalton formaton process can be reduced to one sngle stage. Ths reduced stage game looks as follows: each player chooses hs/her coalton strategy, σ, ether accordng to Defnton 1 (SCG) or Defnton 2 (MCG), the strategy vector σ= ( σ1,..., σ N) s mapped nto coalton structure c, leadng to valuaton v = (v 1,...,v N). 8 Hence, we can defne stable coalton structures n terms of v( ψ( σ )), but may wrte only v( σ ) for smplcty. More specfcally, we can defne stablty n terms of equlbrum announcements σ = ( σ,..., σ ) leadng to coalton structure c *, and possble devatons σ σ, leadng to some * * * 1 N * coalton structure c c, whch should not pay for any player n equlbrum. * 6
There are many ways to defne stablty n the context of sngle and multple coaltons, capturng the notons of open and exclusve membershp. We chose defntons that are nspred by Carraro (1997 and 2) whch are closely related to the concept of nternal&external stablty n order to stress smlartes and dfferences. We start by defnng stablty n the sngle coalton game. Sngle Coalton Game Regardless whch membershp rule we consder, t s evdent that no sgnatory should have an ncentve to leave the agreement. Ths corresponds to the noton of nternal stablty. Moreover, an equlbrum coalton structure should also not be upset by a non-sgnatory jonng the agreement. Under open membershp, ths requres that no non-sgnatory has an ncentve to jon the agreement. Ths s the classcal defnton of external stablty (external stablty condton 1). Of course, f no non-sgnatory has an ncentve to jon the agreement, then an agreement s also stable under exclusve membershp. In other words, there s no need to vote on accesson snce no outsder wll submt an applcaton for jonng the agreement anyway. However, suppose a non-sgnatory has an ncentve to jon, then under exclusve membershp the members of the agreement have to decde whether to accept a new member (external stablty condton 2). Due to the assumpton of complete nformaton, all members can evaluate whether they would beneft from the enlarged coalton. Under majorty votng, accesson wll be accepted f a (strct) majorty s n favor of the applcaton (external stablty condton 2.1) and under unanmty votng only f all members are n favor (external stablty condton 2.2). In other words, a coalton structure that s not externally stable under open membershp may be stable under exclusve membershp f a (weak) majorty (majorty votng) or at least one member (unanmty votng) s aganst accesson. More formally, we have: Defnton 4: Stablty n the Sngle Coalton Game (SCG) In the sngle coalton game, denote the set of players that announce σ * = by I NC wth typcal * element and the set of players that announce σ j = 1 by I C wth typcal element j ( I NC «I C = ). Let the set I C comprse /I C / players and let S be a subgroup of /S/ players n I C. Then, coalton structure * c, generated by announcements σ *, s called stable () under open membershp f t satsfes nternal and external stablty 1, () () under exclusve membershp majorty votng f t satsfes nternal stablty and ether external stablty 1 or external stablty 2.1 and under exclusve membershp unanmty votng f t satsfes nternal stablty and ether external stablty 1, external stablty 2.1 or 2.2. nternal stablty: " Œ I C : * * σ = σ v( 1, ) v( σ =, σ * ). NC * * external stablty 1: " jœ I : v( j σ j =, σ j ) v( σ = σ * j j 1, j ). 7
external stablty 2: * * v( j σ j =, σ j )< v( σ = σ * j j 1, j ), and 1) $ Sà I C, /S/ /I C /2/, " ŒS: 2) $ Œ I C : * * v( σ j =, σ j )> v( σ = σ * j 1, j ). * * v( σ j =, σ j )> v( σ = σ * j 1, j ). Thus, taken together, under all membershp rules stablty requres nternal stablty. However, membershp rules dffer n the defnton of external stablty. The degree of exclusvty rses from open to exclusve membershp and s hgher under unanmty than under majorty votng. Hence, t s more dffcult to upset an equlbrum coalton structure under exclusve membershp than under open membershp and under exclusve membershp t s more dffcult to upset an equlbrum under unanmty votng than under majorty votng. Thus, f we abbrevate the set of equlbrum coalton structures n the sngle coalton game under open membershp, exclusve membershp and majorty votng as well as exclusve membershp and unanmty votng by C SCG (OM), C SCG (EM-MV) and C SCG (EM-UV), then C SCG (OM) C SCG (EM-MV) C SCG (EM-UV) must hold by smple theoretcal reasonng. Therefore, as ponted out n the ntroducton, the nterestng queston s: what are the welfare and ecologcal mplcatons of these relatons? We wll answer ths queston n secton 4 wth the help of an emprcal example. We turn now to stablty n the context of the multple coalton game. Multple Coalton Game In a multple coalton structure, any member of a non-trval coalton can leave ts coalton to become a sngleton by announcng an address that has not been announced before. Hence, nternal stablty s, agan, a necessary condton for stablty under all membershp rules. Moreover, sngletons can jon a coalton by announcng the same address as coalton members of some coalton c I. However, sngletons may also jon another sngleton. By the same token, members of a non-trval coalton may jon another non-trval coalton or a sngleton. Thus, n the context of multple coaltons the meanng of external stablty s less obvous than n the sngle coalton game. Hence, we ntroduce a term called ntracoaltonal stablty. 9 Under open membershp, a coalton structure s ntracoaltonal stable f no player, regardless whether he/she s a sngleton or belongs to a non-trval coalton, has an ncentve to jon another coalton, regardless whether ths s a trval or non-trval coalton (ntracoaltonal stablty condton 1). However, n order to capture the noton of voluntary partcpaton n an agreement, t seems necessary to make sure that f a player has an ncentve to jon a sngleton player, ths player has to agree to accesson (ntracoaltonal stablty condton 2). Ths ensures that sngletons cannot be forced nto cooperaton. 1 8
Of course, f ether no player has an ncentve to change membershp or f a player wants to jon a sngleton but ths suggeston s turned down by the sngleton, ths coalton structure s also stable under exclusve membershp. However, under exclusve membershp, we also have to consder the possblty that a player, currently beng a sngleton or belongng to some non-trval coalton, wants to jon (or swtch to) another non-trval coalton, whch may be turned down by majorty votng (ntracoaltonal stablty condton 3.1) or by unanmty (ntracoaltonal stablty condton 3.2). More formally, we have: Defnton 5: Stablty n the Multple Coalton Game (MCG) In the multple coalton game, denote the set of players that belong to a non-trval coalton by I C * * wth typcal element, and j where and j are members of the same coalton c I because σ = σ j ; let coalton c I be of sze /c I / and denote a subset of players n c I by c I(S) wth sze /c I(S) /; let the set of * * k m players that belong to trval coaltons be denote by I NC wth typcal element k and l because σ σ * * and σ l σ n, mœi\{k}, nœi\{l} where m and n denote arbtrary players that may belong ether to IC or I NC *. Then, coalton structure c, generated by announcements σ *, s called stable () () () under open membershp f t satsfes nternal stablty and ether ntracoaltonal stablty 1 or 2 under exclusve membershp and majorty votng f t satsfes nternal stablty and ether ntracoalton stablty 1, 2 or 3.1 and under exclusve membershp and unanmty votng f t satsfes nternal stablty and ether ntracoalton stablty 1, 2, 3.1 or 3.2. nternal stablty: " Œ I C, " σ σ * m, mœi\{}: * * v( σ, σ ) v( σ σ *, ) ntracoaltonal stablty 1: " mœi, " σ = σ * m n, nœi\{m}: * * v m( σm, σ m ) v σ σ * m( m, m ) ntracoaltonal stablty 2: σ = σ * m k, kœi\{m}, wth σ * σ * k l, lœi\{k}: * * v m( σm, σ m )< v σ σ * m( m, m ) and * * v( k σm, σ m )> v( σ σ * k m, m ). * * ntracoaltonal stablty 3: σ m = σ = σ j, m c I,,jŒ c I * * : v m( σm, σ m )< v σ σ * m( m, m ) and 1) $ c I(S) à I c, /c I(S) / /c I /2/, " Œ c I ( S ) * * : v( σm, σ m )> v( σ σ * m, m ) 2) $ Œc I * * : v( σm, σ m )> v( σ σ * m, m ). Summarzng, also n a multple coalton all membershp rules requre nternal stablty. Agan, the dfference s due to other condtons that we call ntracoalton stablty. Under open membershp, t s 9
easer to swtch membershp than under exclusve membershp and under majorty votng t s easer than under unanmty votng. Hence, followng the same reasonng as n the sngle coalton game, t s straghtforward to establsh: C MCG (OM) C MCG (EM-MV) C MCG (EM-UV) where we may recall that MCG stands for multple coalton game, OM, EM-MV and EM-UV denote open membershp and exclusve membershp under majorty and unanmty votng, respectvely, and C denotes the set of equlbra. As ponted out above, we expect that some equlbrum coalton structures comprse multple nontrval coaltons due to a hgher flexblty of fndng sutable partners. However, t s also evdent from the dscusson that the amount of possble devatons n the multple coalton context s substantally hgher than n the sngle coalton context, makng t easer to upset a potental equlbrum coalton structure. For nstance, suppose that coalton structure c*=({1,2},{3},{4},{5}, {6}) s nternally and externally stable under open membershp n the sngle coalton game. Now suppose that player 3 has an ncentve to jon player 4 and vce versa. Then, c* s not stable anymore n the multple coalton game. Thus, t wll be nterestng to observe n secton 4, whch of the two opposed effects s stronger and what ths mples for the success of coalton formaton. 3. The Emprcal Background of Coalton Formaton 3.1. The CLIMNEG World Smulaton Model The CLIMNEG World Smulaton Model (henceforth abbrevated CWSM) s an ntegrated assessment, economy-clmate model that resembles closely the semnal RICE model by Nordhaus and Yang (1996). The man dfference compared to RICE s that welfare s lnear n consumpton whch s necessary to perform game theoretc analyses n a transferable utlty (TU) framework.we gve here only a short and nformal overvew of CWSM, a more detaled descrpton can be found n Eyckmans and Tulkens (23). The key functons and parameters are provded n the Appendx. CWSM ncoporates an endogenous feedback of clmate change damages on producton and consumpton possbltes. The economc part conssts of a longterm dynamc, perfect foresght Ramsey type of optmal growth model wth endogenous nvestment and carbon emsson reducton decsons. The world s dvded nto sx regons: USA, JPN (Japan), EU (European Unon), CHN (Chna), FSU (Former Sovet Unon) and ROW (Rest of the World). In each regon and n every perod t the followng budget equaton descrbes how gross producton, Y,t, can be allocated to consumpton, Z,t, nvestment, I,t, emsson abatement costs, Y,tC ( µ,t), and clmate change damage, Y,tD( T t) : ( ) ( ) Y = Z + I + Y C µ + Y D T (1),t,t,t,t,t,t t 1
Gross producton can be nterpreted as potental GDP, that s, what could be produced n the absence of the clmate change problem. Abatement costs are an ncreasng and convex functon of emsson abatement µ,t [,1]. Abatement measures the relatve emsson reducton compared to the busnessas-usual scenaro (BAU) wthout any abatement polcy. Clmate change damages are an ncreasng and convex functon of temperature change Tt. Abatement costs, C( µ,t), and clmate change damages, D( T), are treated as proportons of potental producton. Hence, total costs and damages are the product of costs and damages wth potental producton Y, respectvely. Every regon s characterzed by a producton functon of the Cobb-Douglas type that maps combnatons of captal stock and labour nput nto output. The captal stock ncreases wth nvestment and decreases wth some deprecaton rate over tme. Labour supply s assumed to be nelastc and hence producton can be vewed as a functon of endogenous captal nput only. Technologcal progress s assumed to ncrease exogenously over tme, shftng the producton fronter outwards. Producton gves rse to emssons of greenhouse gases that are lnked through an emsson-output rato that decreases over tme through technologcal progress. Emssons accumulate n the atmosphere accordng to a standard accumulaton process. Ths takes n consderaton that only a fracton of emssons adds to the stock of greenhouse gases and that the stock decays over tme due to a natural process. Carbon concentraton leads to an ncrease n temperature that causes envronmental damages. We measure welfare of each country as aggregate lfetme dscounted consumpton: w(s) = Z,t Ω,t (2) t t= [ 1+ ρ ] where ρ stands for the dscount rate of regon and Ω denotes the tme horzon. The strategy vector s conssts of a tme path (35 decades, startng n 199) for emsson abatement and nvestment for all sx s = {I, µ } = Ω, and hence s of length 2x35x6=42. regons,,t,t N;t,, 3.2. Computng Valuatons Accordng to Defnton 3, the valuaton functon maps coalton structures payoffs, Coalton * v(c) w((c)) w(s) 1 M c = (c,..., c ) C nto = ε =, va an nstructon how players choose ther economc strateges s. k c chooses an nvestment and emsson abatement strategy vector k s {I,t,,t} k c ;t =,, Ω order to maxmze the aggregate dscounted welfare over all perods for gven strateges = µ n k s of other countres. Gven the publc bad nature of emssons, the economc strateges of countres are nterdependent. Therefore, two frst order condtons have to be smultaneously solved the for each country at each tme t for every coalton structure c. Snce we assume complete nformaton, the equlbrum strategy vectors can be nterpreted as open loop Nash equlbra. In order to compute the valuaton 11
functon numercally, we use a standard teratve algorthm. We never encountered convergence problems and found always a unque equlbrum for each of the 23 possble coalton structures. As ponted out n secton 2, n the case of no transfers valuatons v (c) follow mmedately from equlbrum economc strateges. In the case of transfers, we derve a corrected valuaton ˆv (c) = v(c) + t. Among many possbltes, we adopt the transfer scheme used n Eyckmans and Tulkens (23), whch s a modfcaton of the scheme proposed by Chander and Tulkens (1995 and 1997). The scheme assumes only transfers wthn coaltons where the surplus of a coalton cooperaton s allocated accordng to a proportonal sharng rule: where shares λ are gven by: ( ) ( ) N N t = v (c ) v c v c v (c ) +λ k c k c from (3) λ = Ω t= k c t= Y D ( T ) Ω,t t t [ 1+ρ] Y D ( T ),t t t [ 1+ρ] (4) and v ( ) c denotes the valuaton n some coalton c and 12 N v (c ) the valuaton n the sngleton coalton structure. The frst term n bg brackets n (3) sets every country back to ts welfare level n the sngleton coalton structure, the second term allocates the total surplus of coalton c k compared to the sngleton coalton structure n proporton to ther margnal damages. Hence, the second term n (3) favors countres wth relatvely hgh potental producton and/or margnal damage estmates and low dscount rates snce they are enttled to a larger share of ther coalton s aggregate payoff. However, the frst term ensures that members, whch would lose from cooperaton wthout transfers because they contrbute much to jont abatement but beneft only lttle because of low margnal abatement and damage costs, break at least even provded there s a surplus from cooperaton. Generally, there may be no surplus f leakage effects are strong enough (Bloch 1997). Wth leakage effects we mean the ncrease of emssons by some countres S I \ c f some countres S c reduce emssons (because they form a coalton or because two or more coaltons merge). However, n our settng, t turns out that any merger of sngle countres or coaltons startng from any coalton structure c C leadng to some coalton structure c C mples an ncrease of aggregate welfare of those countres nvolved n a merger. That s, superaddtvty holds and hence the aggregate gan from cooperaton to a coalton s always postve. Moreover, t turns out that any merger by some countres S c ncreases welfare of each country belongng to S I \ c, regardless whether we assume transfer scheme (12) or not. We call ths feature postve externalty property. It has been descrbed n the lt-
erature (e.g., Bloch 1997 and Y 1997) as a typcal feature of publc good problems and s responsble for strong free-rder ncentves. Ths property has three mplcatons. Frstly, every country s better off n any coalton structure dfferent from the sngleton coalton structure wth transfers. Wthout transfers, ths s only generally true for sngletons. Secondly, we do not have to consder proftablty as a separate condton n our defnton of stablty (see, e.g., Carraro and Snscalco 1993) because t s straghtforward to show that nternal stablty s a suffcent condton for proftablty (see Fnus and Rundshagen 23a). Thrdly, together wth superaddtvty t establshes that any merger ncreases global welfare. Consequently, any coalton structure dfferent from the sngleton coalton structure mples hgher global welfare. 3.3. Reference Smulatons In order to hghlght some general features of our emprcal model, we dscuss some benchmark smulaton: busness-as-usual (BAU), mplyng no emsson reducton ( µ,t =, t), Nash equlbrum (NASH), correspondng to the sngleton coalton structure, and socal optmum, SOCIAL, correpondng to the grand coalton. 11 Carbon Emssons and Concentraton World carbon emssons n 199 amount to approxmately 6 ggatons of carbon. BAU-emssons contnuously grow, reachng more than 62 GtC n 22. NASH-emssons grow only at a slghtly slower rate. In contrast, SOCIAL-emssons are substantally lower: they amount to only 21 GtC n 22. Ths s about almost one thrd of NASH-emssons n 22. In contrast, the SOCIAL-emsson path rses only untl 215, levels off at about 26 GtC, and decreases afterwards. A smlar pattern s found for atmospherc carbon concentraton as shown n Fgure 1. In 199, atmospherc carbon concentraton amounts to approxmately 75 GtC. BAU-concentraton rses steadly and reaches about 1718 GtC n 21 and 3443 GtC n 22. Doublng of concentraton wth respect to 199 level takes place between 28 and 29. The NASH-concentraton path follows closely the BAU-path. In contrast, SOCIAL-concentraton grows at a much slower rate and reaches 1368 GtC n 21 and 217 GtC n 22. Doublng of atmospherc carbon concentraton s postponed untl some tme between 211 and 212. The carbon concentraton levels off at about 2 GtC by the year 22. FIGURE 1 about here At the level of ndvdual countres there are substantal dfferences across regons. Takng averages of abatement over tme, we fnd n the Nash equlbrum that CHN abates about 7.7%, followed by EU 13
wth 7.24% and USA wth 6.44%. The lowest abatement effort s undertaken by ROW wth only 1.45%. World average abatement amounts to 3.74%. For ROW low abatement s due to strong freerder ncentves wthn ths heterogeneous regon. 12 For CHN hgh abatement s due to low margnal abatement costs and for EU ths s due to ther hgh clmate change damage valuaton. In the socal optmum world average abatement s 37.14%. CHN and ROW are requred to reduce ther emssons substantally more than other regons (68.13% and 55.5%, respectvely) due to ther low margnal abatement costs. Macroreconomc Magntudes Fgures 2 and 3 show the tme profles of world consumpton, Z, nvestment, I, abatement cost, YC, and damage costs, YD, for NASH- and SOCIAL-scenaro where potental producton, Y, s the sum of these components (see (1)). It s evdent that producton and consumpton profles are qute smlar n both scenaros. Small dfferences stem from the fact that abatement costs and damage costs consttute a small porton of total producton and consumpton. Hence, strong dfferences n the emsson and concentraton path n both scenaros do not alter YC+YD. However, the composton of YC and YD s dfferent n the two scenaros. In the Nash equlbrum abatement costs are very small (they do not show up n Fgure 3) but clmate change damage are hgh. In contrast, n the socal optmum, damages are relatvely small but ths gan requres devotng part of the producton to emsson abatement. FIGURE 2 and FIGURE 3 about here * Ω Table 1 dsplays total dscounted consumpton v(c) [ ] t = w(s) = Z t,t 1+ρ = for each regon n the Nash equlbrum, N S v, and n the socal optmum, v. The last row World reveals the overall magntudes at stake. Though the gan at the world level from full cooperaton s not a small number (1,771 mllon $), n relatve terms t amounts to only.52%. Ths s due three reasons. Frstly, as ponted out above, abatement costs and clmate change damages are small compared to producton or consumpton. Secondly, dfferences between both scenaros n terms of welfare occure manly n the far future but receve less weght due to dscountng. Thrdly, abatement costs are relatvely hgh compared to the benefts from reduced emssons, so that also n the socal optmum only moderate acton s requred. Nevertheless, there are large dfferences between both scenaros n ecologcal terms: emssons are 16 and concentraton s 138 percent hgher n the Nash equlbrum than n the socal optmum (see also Table 2 and 3 n secton 4). TABLE 1 about here 14
In terms of ndvdual wnners and losers, we fnd that CHN and, to a lesser extent, ROW would lose from full cooperaton wthout transfers. 13 Wth transfers, however, proftablty holds for all countres n the socal optmum and as mentoned above for any other coalton structure dfferent from the grand coaltons as well. Hence, wthout transfers the grand coalton can never be an equlbrum. However, proftablty s only a necessary condton for stablty and, as we wll see from secton 4, by no means suffcent to guarantee stablty. 4. Stable Coalton Structures In ths secton, we report on results of our stablty analyss. In subsecton 4.1, we explan the nformaton contaned n Table 2 and 3 and n subsecton 4.2 we provde some ratonale that helps to explan membershp n stable coaltons. In subsecton 4.3, we evaluate stable coalton structures. 4.1 Prelmnares Table 2 and 3 lst stable coalton structures n the no transfer and transfer case, respectvely. The frst column lsts the number of a partcular coalton structure where to each coalton structure a number between 1 and 23 s attached. Coalton structure no. 1 represents the sngleton coalton structure, correspondng to the "conventonal" Nash equlbrum, whereas coalton structure no. 23 s the grand coalton, correspondng to the "conventonal" socal optmum. Moreover, coalton structure no. 196 represents the old Kyoto coalton before the US decded to wthdraw from the Kyoto Protocol and coalton structure no. 87 corresponds to the new Kyoto coalton after the US-wthdrawal. Apart from stable coalton structures, these coalton structures are lsted because they represent nterestng benchmarks. Column 2 lsts coalton structures n partton form where non-trval coaltons are ndcated bold. Column 3, 4 and 5 contan nformaton whether a coalton s stable (n=not stable, y=stable and -=not defned) n the sngle (S) and multple coalton game (M) under open membershp (OM) and under exclusve membershp majorty votng (EM-MV) and unanmty votng (EM-UV). TABLE 2 and 3 about here Column 6 gves total dscounted welfare over all regons and the entre perod (199-233). We take ths feature to sort coalton structures n descendng order. Column 8 gves concentraton at the end of the perod and column 1 ndcates global cumulatve emssons over the entre perod. In order to evaluate coalton structures, we compute a "degree of externalty ndex" (DEX). Ths ndex measures the dfferences between the outcome n some coalton structure c and the socal optmum (grand coalton) n relaton to the socal optmum, expressed as percentage. By defnton, n the socal opt- 15
mum the degree of externalty s. Columns 7, 9 and 11 dsplay ths ndex for welfare, concentraton and emssons, respectvely. All numbers have been rounded to "sensble" dgts. From Tables 2 and 3, t s evdent that the sngleton coalton structure (no. 1) s stable n the sngle but not n the multple coalton game. In the sngle coalton game ths s an artfcal result of the constructon of the game but does not affect the subsequent nterpretatons. If each player announces σ =, then no sngle player can change hs/her membershp by a sngle devaton. In other words, the sngleton coalton structure s stable by defnton. 14 In the multple coalton game, ths s dfferent. Suppose each player announces a dfferent address. Then coalton structure no. 1 s only stable f ether no player has an ncentve to jon another sngleton by announcng the same address (ntracoaltonal stablty 1) or f there s such an ncentve and the second player has no nterest n such a merger (ntracoaltonal stablty 2). However, snce there are four coalton structures of the form ({,j},{k},{l},{m},{n}) n the no transfer case (no. 2, 4, 5 and 6) and fve n the transfer case (no. 2, 3, 4, 5 and 6) that are nternally stable, t s evdent that there are enough regons that have an nterest n a merger wth another regon and hence no. 1 cannot be ntracoaltonal stable. 4.2 Membershp n Stable Coalton Structures From a frst glance at Tables 2 and 3, t seems that ntuton s not confrmed: n many coaltons there are members of whch one would expect that they should show lttle nterest n formng a coalton and/or not wth those regons lsted n Table 2 and 3. For nstance, n the context of no transfers, t may be suspected that the "rest of the world" (ROW) should show lttle nterest n partcpatng n an agreement and that USA and ROW wll hardly be n one coalton because of dfferent nterests. However, a closer nspecton of the underlyng fundamentals resolves ths puzzle. Frstly, clmate change damage parameters n our model are modfed estmates of RICE that may not be n lne wth the presumed percepton of regons damages. For nstance, t has been argued that developng countres wll pay lttle attenton to envronmental damages due to strong preferences for economc growth. Ths would suggest for nstance that the damage costs of ROW should be very low, though n our model they are relatvely hgh, despte we assume hgher dscount rates for ROW and CHN than for the rest of the countres (see the Appendx). Secondly, the conjecture that countres formng a coalton wth other countres are the "good guys" and countres remanng sngletons are the "bad guys" s premature. Ths conjecture presumes that coalton members wll substantally reduce ther emssons compared to the non-cooperatve benchmark and compared to outsders. However, ths may not always be the case. For nstance, suppose two regons that both have hgh margnal abatement costs and low margnal damages costs form a coalton. Then jont welfare maxmzaton calls only for a moderate emsson reducton. Hence, nternal 16
stablty wll not be much of a problem for these regons. In contrast, a sngleton wth low margnal abatement costs and hgh margnal damage costs may already reduce emssons substantally by tself. Thrdly, not only low abatement but also a homogenous ncentve structure among coalton members s mportant for nternal stablty. In the case of no transfer, clearly, homogenous ncentves follow from smlar margnal abatement and damage costs patterns. However, also a regon of type 1 (e.g., ROW) wth relatvely low margnal abatement costs and hgh margnal damages and a regon of type 2 (e.g., JPN) where ths s reversed have a smlar ncentve structure. Type 1 contrbutes much to jont abatement but also benefts much whereas for type 2 ths s reversed. Hence, contrbutons and gans are equally dstrbuted. In such a coalton also a regon of type 3 (e.g., USA and FSU) wth moderate margnal abatement costs and margnal damages may ft n. Ths explans why USA, JPN, FSU and ROW are frequent members of stable coalton structures as lsted n Table 2. In contrast, a regon of type 4 (e.g., EU) wth relatvely hgh margnal abatement and damage costs fnds t dffcult to fnd partners for cooperaton (though t has much nterest n cooperaton). It contrbutes relatvely lttle to jont abatement but benefts more than proportonally. Moreover, t causes that a hgh abatement target s mplemented wthn the coalton due to ts hgh margnal damages. Ths explans why EU s a member of a coalton n only two coalton structures lsted n Table 2. Fnally, a regon of type 5 (e.g., CHN) wth low margnal abatement and margnal damage costs would fnd many cooperatng partners but has no ncentve tself to jon a coalton as long as there s no compensaton. Ths explans why CHN s no coalton member of any stable coalton structure lsted n Table 2. Ths s dfferent n the case of transfers (see Table 3). Now nterests are more balanced. CHN s compensated for her hgh contrbuton and receves a far share of the gans from cooperaton. For other regons, cooperaton wth CHN but also wth ROW s attractve snce ths lowers abatement costs of jont cooperaton. Fourthly, not only the lack of nternal stablty but also of external or ntracoaltonal stablty explans membershp. For nstance, under open membershp and to some extent under exclusve membershp wth majorty votng, coaltons ncludng CHN are not stable because outsders would have an ncentve to jon. 4.3 Evaluatng Stable Coalton Structures General comments The grand coalton s not stable regardless of the membershp rule. In the no transfer case ths follows mmedately from the fact that CHN and ROW are worse off than n the sngleton coalton structure (see Table 1). However, proftablty s only a necessary but not a suffcent condton for nternal stablty. An mportant reason for nstablty s hgh abatement contrbutons of all partcpants as ths s 17
the case n the socal optmum. Hence, t s partcular attractve for a member to leave the grand coalton because ths reduces abatement costs substantally but ncreases damages only moderately. A smlar argument explans why also coaltons of fve or four regons are not stable: the ncentve to leave a coalton ncreases wth the number of coalton members. Therefore, t also not surprsng that we fnd n lne wth other studes (e.g., Barrett 1998, Bosello et al. 21, Eyckmans 21 and Fnus et al. 23) that nether the old nor the new Kyoto coalton s stable. Of course, n our settng abatement targets follow from the assumpton of the valuaton functon and may therefore dffer from those agreed n Kyoto and subsequent COP-meetngs. Also welfare mplcatons may be dfferent because we do not model permt tradng. Nevertheless, our results help to explan the dffcultes n Kyoto and subsequent meetngs to reach a fnal agreement and to gather enough ratfcaton so that the protocol enters nto force. Interestngly, our results also suggest that both Kyoto coaltons (new and old) would not much narrow the gap between socal optmum and Nash equlbrum and that there are many other coalton structures that would perform far better. Gven the caveats mentoned above, ths ndcates that a subgroup of the Kyoto coalton could mprove upon the outcome of the negotatons by lookng for dfferent members. Of course, ths may requre transfers to provde ncentves for others to jon. Our results also confrm two general conclusons from the theoretcal lterature assumng symmetrc countres that have been mentoned n the ntroducton. 1) The number of partcpants s not necessarly a good ndcator for the success of an IEA. For nstance, the old Kyoto coalton (coalton structure no. 196) counts four members, s not stable, and s nferor n welfare and ecologcal terms to many other stable coalton structures wth and wthout transfers. Also coalton structure no. 4 wth only one coalton of two members s superor to coalton structure no. 2 wth one coalton of three members and no. 153 wth two coaltons of two members that are all stable n the multple coalton game under exclusve membershp, unanmty votng and no transfers (see Table 2). 2) Whenever the degree of externalty s low, only small coaltons are stable but they acheve much and f the degree s hgh, the opposte holds. In our context, ths degree s small n welfare terms (.52 percent; though admttedly t s larger n ecologcal terms) snce abatement costs are relatvely hgh compared to the benefts from reduced damages. In our settng, the largest sngle coalton comprses three members and the largest coalton n a coalton structure wth multple coaltons comprses two members. Nevertheless, those small coaltons close the gap between socal optmum and Nash equlbrum substantally. For nstance, n the case of no transfer coalton structure no. 26 (that s stable under EM-UV; see Table 2) reduces the gap by more than a half n welfare and ecologcal terms and n the case of transfers coalton structure no. 31 (that s stable under EM-MV and EM-UV n the mult- 18
ple coalton game; see Table 3) closes ths gap even more. As Barrett (1994) ponted out, ths relaton may be reversed for CFCs, predctng large coaltons but less success for solvng the problem of the depleton of the ozone layer effectvely. Open versus exclusve membershp In the no transfer case (Table 2), t s evdent that no non-trval coalton structure s stable under open membershp, a few are stable under exclusve membershp and majorty votng and relatvely many under exclusve membershp and unanmty votng. Ths apples to the sngle and multple coalton game. More mportant, those addtonal equlbrum coalton structures mply hgher welfare and lower emssons and concentratons. In the case of transfers, the dfference s less pronounced. In the sngle coalton game, the set of equlbrum coaltons for all membershp rules s the same. However, n the multple coalton game, a smlar general concluson as mentoned for no transfers can be drawn. From a theoretcal pont of vew, the results are nterestng snce they suggest that the assumpton of open membershp s crucal for the negatve conclusons derved n the lterature. From an appled pont of vew, the results are nterestng n two respects. Frstly, t suggests that t may be worthwhle to thnk whether to adopt an exclusve membershp rule, whch s typcal for club good agreements, also for publc good agreements, lke those on clmate change n the future. Majorty votng s nferor to unanmty votng but stll mproves on the open membershp rule. Secondly, votng under exclusve membershp requres some degree of consensus among coalton partners. Thus, though t s usually argued that the need for consensus wthn nternatonal organzaton and governments has a negatve mpact on effcency and effectveness, n the present context consensus s conducve to the success of cooperaton. Sngle versus Multple Coaltons Frstly, we observe that f coalton formaton s not restrcted to a sngle coalton multple coaltons emerge n equlbrum. Secondly, we observe that n the case of transfers the four frstly ranked coalton structures n terms of global welfare are coalton structures wth multple coaltons. Thrdly, our prevous conjecture of secton 2 s confrmed that regons that have no ncentve to jon a coalton wll form ther own coalton f ths s possble and ths mples a Pareto-mprovement. For nstance, n the case of no transfers coalton structure no. 2 ({FSU,ROW},{USA},{JPN},{EU},{CHN}) s stable n the sngle coalton game under exclusve membershp. In the multple coalton game, ths coalton structure s not stable anymore because USA and JPN have an ncentve to form a second coalton leadng to coalton structure no. 153 ({USA,JPN},{FSU,ROW},{EU},{CHN}). Because of the postve externalty property, ths mples that not only USA and JPN beneft from ths merger but all other regons as well. A smlar relaton holds for coalton structures lke no. 4 and 155 and n the case of 19