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1 D S E Dpartmento Scenze Economche Workng Paper Department of Economcs Ca Foscar Unversty of Vence Carlo Carraro Johan Eyckmans Mchael Fnus ISSN: 1827/336X No. 44/WP/2006 Revsed Verson July 2006 Optmal Transfers and Partcpaton Decsons n Internatonal Envronmental Agreements

2 Workng Papers Department of Economcs Ca Foscar Unversty of Vence No. 44/WP/2006 ISSN X Optmal Transfers and Partcpaton Decsons n Internatonal Envronmental Agreements Carlo Carraro Correspondng author. Unversty of Vence and Fondazone En Enrco Matte FEEM Johan Eyckmans European Unversty College Brussels EHSAL and Center for Economc Studes, Katholeke Unverstet Leuven Mchael Fnus Department of Economcs, Unversty of Hagen and Natonal Unversty of Sngapore Revsed Verson July 2006 Abstract The lterature on nternatonal envronmental agreements has recognzed the role transfers play n encouragng partcpaton n nternatonal envronmental agreements. However, the results acheved so far are overly specfc. Therefore, we develop a more general framework that enables us to study the role of transfers n a systematc way. We propose transfers usng both nternal and external fnancal resources for makng welfare optmal agreements self-enforcng. To llustrate the relevance of our transfer scheme, we use a stylzed ntegrated assessment smulaton model of clmate change to show how approprate transfers may nduce almost all countres nto sgnng a selfenforcng clmate treaty Keywords Self-enforcng Internatonal Envronmental Agreements, Clmate Polcy, Transfers JEL Codes C72, H23, Q25, Q28 Address for correspondence: Carlo Carraro Department of Economcs Ca Foscar Unversty of Vence Cannarego 873, Fondamenta S.Gobbe Veneza - Italy Phone: (++39) Fax: (++39) e-mal:ccarraro@unve.t Ths Workng Paper s publshed under the auspces of the Department of Economcs of the Ca Foscar Unversty of Vence. Opnons expressed heren are those of the authors and not those of the Department. The Workng Paper seres s desgned to dvulge prelmnary or ncomplete work, crculated to favour dscusson and comments. Ctaton of ths paper should consder ts provsonal character. The Workng Paper Seres s avalble only on lne ( For edtoral correspondence, please contact: wp.dse@unve.t Department of Economcs Ca Foscar Unversty of Vence Cannarego 873, Fondamenta San Gobbe Vence Italy Fax:

3 1. Introducton Transfers play a promnent role n the analyss of self-enforcng nternatonal envronmental agreements (IEAs) (e.g., Carraro and Snscalco 1998 and Fnus 2001 and 2003a). There are two reasons why ths s not surprsng. Frst, large asymmetres n the cost and beneft structure between countres may lead to a hghly asymmetrc dstrbuton of the gans from cooperaton that may hamper successful treaty-makng. Second, IEAs provde a publc good and therefore face strong free-rder ncentves. Both of these sources of potental nstablty of IEAs mght be mtgated through the use of approprate transfers. The majorty of recent contrbutons to the lterature on IEAs uses the tools of noncooperatve coalton theory (see Bloch 2003 for an overvew). The analyss s based on the valuaton functon that assgns an ndvdual payoff to every coalton member takng nto account the entre coalton structure,.e. the partton of players nsde and outsde a coalton. The man focus s on explanng free-rdng behavor n the context of externaltes, dentfyng the man economc factors that determne the relatve success of partal cooperaton and suggestng nstruments for dscouragng free-rdng. In the context of the non-cooperatve approach, transfers have been analyzed n ther ex-ante and ex-post forms (see Fnus 2003a for an overvew). Ex-ante means that countres commt to a certan transfer rule before they decde upon ther partcpaton n an IEA. Ex-post means that after an agreement has formed, transfers are used to broaden an exstng coalton. The frst putatve paper on transfers goes back to Carraro and Snscalco (1993). They analyze varous forms of commtment that enables coaltons to expand va ex-post transfers and they suggest two types of transfers that may mprove upon the status quo: 1) nsders (coalton members) brbng outsders (non-coalton members) to jon ther coalton and 2) outsders brbng other outsders to jon the coalton. 2

4 The dea of varous forms of commtment and ex-post transfers was also pursued n later papers by Botteon and Carraro (1997), Jeppesen and Andersen (1998) and Petraks and Xepapadeas (1996), though commtment s certanly not an assumpton n lne wth the noton of self-nterested players. Therefore, t was mportant to llustrate that expansons of coaltons va ex-post transfers may also be possble wthout commtment as ths has been done by Botteon and Carraro (1997) n a smple emprcal model wth fve heterogeneous countres. Later papers have looked at the effect of varous ex-ante and ex-post transfers rules on the success of coalton formaton and on the possblty of expandng stable coaltons (e.g., Altamrano-Cabrera and Fnus 2006, Bosello et al. 2003, 2004, Carraro and Snscalco 2001, Eyckmans and Fnus 2003, 2004a, Fnus et al and Wekard et al. 2006). Most of these papers used a more elaborate emprcal model, looked not only at stylzed transfer schemes derved from cooperatve game theory, but also consdered schemes that are based on varous moral motves for far sharng, consdered transfers va permt tradng and allowed for the possblty of multple coaltons. Roughly speakng, all papers bascally confrm earler studes n concludng that transfers can be conducve to the success of self-enforcng agreements, but that outcomes crucally depend on the partcular transfer rule, the detals of the model and the data set. The mxed evdence and the specfc nature of results motvate us to look for a more general approach to study the role of transfers n the context of non-cooperatve coalton theory. In partcular, we want to determne the full potental of transfers. To ths end, we go back to the roots of the analyss of IEAs, removng n ths paper any unnecessary complcaton as a frst step. That s, we assume a smple cartel formaton game and apply the concept of nternal and external stablty. We employ a noton of optmal transfer schemes meanng transfers desgned to maxmze global welfare under the constrant that the underlyng IEA s selfenforcng. 3

5 The mportance of ths research ssue for polcy makng s evdent when consderng for nstance the crucal role fnancal or technology transfers are playng n recent dscussons on possble post-kyoto clmate polces n the framework of the Unted Natons Framework Conventon on Clmate Change (UNFCCC). Frst, multlateral fnancal transfers take place under the so-called Global Envronment Faclty (GEF) program. Though not large n absolut terms, GEF allocates and dsburses currently about 250 mllon dollars per year n projects for mprovng energy effcency, fosterng renewable energy use, and pushng for sustanable transportaton. Second, the flexble mechansms (.e. Emssons Tradng ET, Jont Implementaton JI and Clean Development Mechansm CDM) foreseen n the Kyoto Protocol are expected to generate mportant flows of fnancal resources among the Protocol member states and even between sgnatores and non-sgnatores n the case of CDM projects. These fnancal and flexblty mechansms can be nterpreted as multlateral transfer schemes. Therefore, t s mportant to get new nsghts on how transfer schemes should be desgned n order to acheve maxmum success of future, voluntary nternatonal clmate polcy agreements. In what follows, we present our model n secton 2. Ths comprses not only a theoretcal but also an emprcal part. The emprcal part s based on a modfed verson of RICE (Nordhaus and Yang 1996) - a well-known ntegrated assessment model of clmate change polcy whch s used to llustrate our concepts. In secton 3, we analyze the mpact of dfferent transfer desgns on the formaton of stable coaltons. Secton 4 concludes. 2. Model 2.1 Theoretcal Background Coalton formaton s modeled as a two-stage game. There are n players and N = {1,...,n} denotes the set of countres or regons whch we smplfy refer to as countres n the sequel. In 4

6 the frst stage, countres choose ther membershp: a country can ether jon coalton S N and become a sgnatory or reman a sngleton and non-sgnatory. These decsons lead to coalton structure C = {S,{ l },...,{n}},.e., a partton of players, wth s sgnatores (s denotes the cardnalty of S) and n-s non-sgnatores. Gven the smple structure of the frst stage, a coalton structure C s fully characterzed by coalton S. 1 In the second stage, countres choose ther economc strateges. Economc strateges nclude for nstance polcy varables lke emsson abatement and captal nvestment as descrbed n subsecton 2.2. At ths stage, t suffces to denote the vector of economc strateges by ω (S) = ( ω1(s),..., ω n(s)) wth assocated ndvdual payoffs π ( ω (S)), gven that a coalton S has formed n the frst stage. We compute the subgame-perfect equlbra of ths two-stage game by backward nducton. 2 To do ths, t s suffcent for strateges to consttute a Nash equlbrum at every stage. For the second stage, ths entals that economc strateges form a Nash equlbrum between coalton S and the n-s non-sgnatores. Ths mples that non-sgnatores S choose ther economc strateges so as to maxmze ther ndvdual payoff π ( ω ), whereas all sgnatores S jontly maxmze the aggregate payoff of ther coalton, π S ( ω ). Strategcally, ths means that the behavor of non-sgnatores towards all other countres s selfsh and non-cooperatve; sgnatores behave cooperatvely towards ther fellow members, but non-cooperatvely towards outsders. Economcally, ths means strateges are effcent wthn coalton S (but not globally). Hence, the equlbrum economc strategy vector ω * (S) corresponds to the socal optmum f coalton S comprses all countres (S=N),.e. the grand coalton forms, and 1 2 The assumpton of a sngle coalton seems to be the most obvous and realstc n the context of IEAs. Therefore, t has been frequently adopted n the lterature. Exceptons are consdered n Bosello et al. (2003, 2004), Carraro (2000), Eyckmans and Fnus (2006) and Fnus (2003b). Our assumpton s n lne wth the manstream of the lterature on coalton theory. For an overvew see Bloch (2003) and Y (2003). 5

7 corresponds to the Nash equlbrum f coalton S comprses only one member (S={}). Hence, any neffcency,.e., global welfare loss compared to the global Pareto optmum, stems from the fact that S s not the grand coalton. Gven that the second stage of the game has been solved, we defne v (S) =π( ω (S)) as the * valuaton of country f coalton S forms. Ths defnton summarzes all nformaton relevant to the second stage. For the frst stage, we defne a Nash equlbrum n terms of partcpaton: 3 nternal stablty: v(s) v(s\{}) S. (1) external stablty: v(s) v(s {}) S. (2) That s, n equlbrum, no sgnatory belongng to coalton S has an ncentve to leave ts coalton n order to become a non-sgnatory, gven the partcpaton decsons of all other countres. By the same token, no non-sgnatory has an ncentve to jon coalton S, gven the decsons of all other countres. Note that by defnton coalton S={} s nternally stable and coalton S=N externally stable by defnton. Regardless of whether we consder ex-ante or ex-post transfers, we assume that optmal economc strateges are not affected by transfers. 4 Valuatons wth transfers ˆv (S) are related to those wthout transfers v (S) smply through the relaton ˆv (S) = v(s) + t where t > 0 means recevng and t < 0 means payng a transfer. We make the standard assumpton that 3 4 Ths defnton s due to d Aspremont et al. (1983) and has been frequently appled n the lterature on IEAs as for nstance by Barrett (1994), Carraro and Snscalco (1993), Hoel (1992) and by many scholars afterwards. That s, we follow the standard assumpton of a transferable utlty (TU) framework n the lterature on coaltons for smplcty. Ths means to neglect ncome effects nduced by transfers. For our smulaton model ths seems a reasonable assumpton, gven the relatve small sze of transfers compared to total GDP. 6

8 transfers balance,.e., and hence ˆv (S) = v(s) t N 0 = (e.g., Carraro and N N Snscalco 1993). 2.2 Smulaton Model In order to llustrate the mportance of transfers for the success of coalton formaton, we derve valuatons from the CLIMNEG World Smulaton Model (hereafter abbrevated as CWSM). CWSM s an ntegrated assessment, economy-clmate model that captures the endogenous feedback of clmate change damages on producton and consumpton. 5 The strategc polcy varables n the CWSM are nvestment and carbon emsson reducton. In the CWSM, 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 every regon, and at every tme t, the followng budget equaton descrbes how potental GDP, Y,t, can be allocated to consumpton, Z,t, nvestment, I,t, emsson abatement costs, Y,tC ( μ,t), and clmate change damages, Y,tD ( Δ T) t : ( ) ( ) Y = Z + I + Y C μ + Y D Δ T (3),t,t,t,t,t,t t Output Y,t s produced wth captal and labor. Captal s bult up through nvestment whch s the frst strategc polcy varable n the model. Labour supply s assumed to be nelastc. Abatement costs Y,t C ( μ,t ) are expressed as loss of potental GDP : C s the share of potental GDP devoted to abatement, whch s a functon of μ,t [ 0,1], a varable that measures the relatve emsson reducton compared to the busness-as-usual scenaro wthout any abatement polcy. Damages Y D ( T ),t t Δ are also expressed as loss of potental GDP : 5 Almost all parameter values are taken from the RICE model of Nordhaus and Yang (1996). A complete overvew of the equatons and parameter values of the CWS model can be found n Eyckmans and Tulkens (2003). The CWS model code and and GAMS program to check coalton stablty s avalable at 7

9 D s the share of potental GDP destroyed by clmate change damages, whch s a functon of temperature change ΔT t. Temperature change depends on the stock of greenhouse gases, whch n turn depends on emssons that accumulate n the atmosphere. Fnally, emssons are proportonal to producton, but can be reduced by the abatement rate μ,t whch consttutes the second strategc choce varable n the model. Both choce varables (nvestment and abatement) affect output, abatement costs, damage costs and therefore also consumpton, not only domestcally but also abroad. Ths s mmedately evdent wth regard to abatement because remanng emssons (after abatement) ncreases the stock of greenhouse gases, whch affects envronmental damages n every country. However, t s also true for nvestment, snce captal s an nput n the producton process and emssons are proportonal to producton. For every of the 58 possble coaltons S, we compute the Nash equlbrum ω * (S) between S and N\S n order to derve valuatons * v(s) =π( ω (S)). That s, we determne nvestment and abatement strateges that maxmze welfare (.e. lfetme dscounted consumpton) of coalton S and of sngletons n N\S for gven nvestment and abatement strateges of the other players as descrbed n subsecton Basc Incentve Structure In ths secton, we brefly dscuss the basc ncentve structure mpled by the calbraton of CWSM. Frst, USA, JPN and EU face steep abatement cost curves, whle CHN, FSU and ROW face flat ones. The regonal dfferences n abatement costs manly reflect dfferences n energy effcency. Energy effcent regons face hgher margnal costs when cuttng back 6 Ths mplctely assumes that some harmonzed carbon tax or a tradable permt system s mplemented wthn coalton S such that every pollutng frm n S s confronted wth the coaltonal damage costs of ts emsson behavour. Thus, the polcy nstruments coordnates prvate nvestment and emsson reducton decsons wthn coalton S. 8

10 emssons than regons characterzed by low energy effcency because they have already exploted the cheapest energy savng technques. Second, damage functons are partcularly steep n EU and ROW, less steep n USA and JPN and relatvely flat n FSU and CHN. The hgh damage estmate (as a percentage of potental GDP ) for ROW s due to the fact that clmate change s beleved to affect developng countres strongly because ther economes tend to depend on clmate related producton processes lke agrculture, fshery and forestry (IPCC (2001)). 7 The hgh damage of EU s due to a hgh potental GDP; the low damage estmate for FSU s due to some expected benefts from moderate temperature ncrease, lke the ncreased avalablty of arable land. Thrd, n a gven coalton S, the steeper the margnal damage cost curves and the flatter the margnal abatement cost curves of the members of S are, the hgher the optmal abatement of coalton members wll be, whch follows from the frst-order condtons of jont welfare maxmzaton of coalton S. In every perod, coalton members should abate up to the pont where ther margnal abatement costs are equal to the dscounted sum of all coalton members avoded future margnal clmate change damages. Fourth, coalton members wth a flatter margnal abatement cost curve have to contrbute more than those wth a steeper curve, all else beng equal, whch also follows from the frst order condtons, mplyng cost-effectveness wthn coalton S Propertes of Valuatons To conclude ths secton, we dscuss two general propertes whch determne the ncentve structure n the coalton formaton game. Both propertes hold for the valuatons derved from our smulaton model CWSM. The frst property s called superaddtvty and means that the aggregate valuaton of country j and coalton S ncreases f country j jons coalton S. 7 Because ROW comprses many heterogenous countres, the clmate change damage parameters have been revsed downward n all coalton structures n whch ROW acts as a sngleton followng Nordhaus and Yang (1996). Wthout ths modfcaton, non-cooperatve emsson control rates by ROW would be unrealstcally hgh. 9

11 Defnton 1: Superaddtvty A coalton game s superaddtve f and only f for all S { j} S j S N and j S : v(s {j}) > v(s) + v (S). That s, there s coaltonal gan from cooperaton and hence cooperaton s group ratonal or coaltonally ratonal. Ths makes cooperaton attractve for those countres partcpatng n an IEA. Ths property means that startng from any coalton S and ncreasng the degree of cooperaton by movng to S {j} or even larger coaltons, t s generally possble to allocate the coalton gan such that t consttutes a Pareto-mprovement to all regons nvolved n cooperaton. The second property s called postve spllovers, meanng that f country j jons coalton S, all countres that do not belong to S {j} are better off. Defnton 2: Postve Spllovers A coalton game exhbts postve spllovers f and only f for all S N, j S and all l S { j} : v(s {j}) > v(s) l l. Consequently, there s an external gan or a postve spllover from cooperaton, makng free-rdng (.e. not jonng S) attractve. From a non-sgnatory s pont of vew, the most favorable condton s the one n whch all other countres partcpate n the agreement. 8 It s then clear that a regon s decson to jon a coalton as well as the stablty of an IEA depends on the magntude of both propertes. On the one hand, the ntensty of the superaddtvty effect whch, together wth the sharng rule of the coaltonal gan, determnes the payoff of cooperaton. On the other hand, the ntensty of the postve externalty effect whch determnes the free rdng payoff. We wll study these effects n more detal n 8 The mportance of postve (and negatve) spllovers has been stressed n the recent lterature on coalton theory (Bloch 2003, Y 2003 and Maskn 2003). 10

12 secton 3, but note here that superaddtvty and postve externalty together mply that global welfare ncreases through cooperaton. That s, gven a coalton S, whenever a sngle or several countres jon coalton S, global welfare s rased because both the coalton members (through superaddtvty) and the outsders (through postve spllovers) beneft. Table 1 llustrates the magntudes at stake for the CWSM model. It dsplays for a selecton of coaltons global welfare and two envronmental varables (carbon concentraton and global emssons) n absolute and relatve terms. The relatve magntudes can be nterpreted as a closng the gap ndex, measurng how close a coalton comes to the global optmum where the performance n the global optmum s 100 percent and the performance wth no cooperaton s 0 percent by normalzaton. Apart from stressng that both full and partal cooperaton can make a large dfference n welfare and ecologcal terms compared to no cooperaton, Table 1 llustrates that not only the sze of a coalton matters for the global success of cooperaton as suggested by Barrett (1994). In the context of our model wth heterogenous players, the dentty of members s more mportant. For nstance, coalton no. 32 ncludng fve members (USA, JPN, EU, CHN, FSU) ranks lower than many coalton structures comprsng coaltons of only three or four members and even lower than coalton no. 31 wth only two members (JPN and ROW). From Table 1 t s also clear that, as a general tendency, the mportance for global welfare of partcpaton of partcular countres decreases wth the followng sequence: ROW, CHN, EU, USA, FSU and JPN. ROW s and CHN s mportant role stems from the fact that they are characterzed by a relatvely flat emsson abatement cost curve; hence they can provde cheap abatement. However, apart from emsson abatement costs, also envronmental damages matter. If a gven coalton maxmzes ts jont welfare, the hgher the margnal damages of coalton members are, the hgher jont abatement efforts wll be (and the hgher a postve spllovers), all else beng equal. Ths explans the global mportance of EU for cooperaton. 11

13 Summarzng, cooperaton between countres wth low margnal abatement costs (.e. cheap supplers of abatement effort) and countres wth hgh margnal wllngness to avod clmate change (.e. hgh demand for abatement effort), proves mportant to acheve substantal emsson reductons n an IEA Stable Coaltons In ths secton, we analyze coalton formaton both under the assumpton of no transfers and varous forms of transfers. Results and arguments are llustrated wth the CWSM model. In subsecton 3.1, we start wth no transfers. Subsecton 3.2 deals wth ex-ante transfers and shows the advantage of optmal transfers, as defned n Eyckmans and Fnus (2004b), compared to smple transfer schemes, as assumed n most papers up to now. Subsecton 3.3 analyzes the expanson of coaltons va ex-post transfers. 3.1 No Transfers In the case of no transfers, there s no coalton that s both nternally and externally stable at the same tme, see Table 2. In the absence of transfers, although cooperaton may be coaltonally and globally ratonal, t may not be ndvdually ratonal to all coalton members. The reason s that an effcent allocaton of abatement burdens wthn a coalton S would result n a hghly asymmetrc allocaton of the net gans from cooperaton among coalton members that face a markedly heterogeneous beneft and cost structure. For nstance, regons facng a flat margnal abatement cost and damage cost curve are typcally losers from cooperaton wthout transfers. These regons are requred to contrbute substantal abatement efforts but they do not value strongly the ensung mprovement n envronmental qualty. Thus, wthout transfers, Chna faces the strongest free-rder ncentves among all sx regons n CWSM. 9 Smlar conclusons can also be found n Buchner et al. (2002). 12

14 3.2 Ex-Ante Transfer Schemes In the lght of the above negatve concluson, we now turn to ex-ante transfer schemes. That s, the membershp decson n the frst stage of the game s based on the assumpton that coalton S wll not only choose ts optmal economc strateges n the second stage, but wll also allocate the coalton gan from cooperaton among ts members accordng to a partcular transfer scheme. We start by consderng three transfer schemes that have played an mportant role n prevous analyses of self-enforcng IEAs (see the lterature cted n the Introducton). We call these schemes smple n order to dstngush them from our optmal transfer schemes that we ntroduce subsequently. Through the llustraton of smple and optmal transfer schemes, the full potental of an optmal desgn of transfers wll become apparent Smple Transfer Schemes All three smple transfer schemes that we consder orgnate from cooperatve coalton theory. It requres only a slght modfcaton of ther orgnal defntons to account for the fact that coalton S may not only be the grand coalton but any subcoalton of N (Aumann and Drèze 1974). The followng formulas descrbe valuatons of player beng a member of a gven coalton S N. The frst transfer scheme s the Shapley Value and mples valuatons of the followng form: t!(s t 1)! ˆv = v (T {}) v (T) S (4) SV k k T S s! k T {} k T T wth coalton SÍ N, T S a subgroup of S and t and s the sze of group S and T. Roughly speakng, the Shapley Value gves every country a valuaton accordng to ts average margnal contrbuton over every possble subcoalton T of S (term between square brackets n (4)), weghted by the probablty that ths subpartton forms (frst factor n (4)). 13

15 The second smple transfer scheme s the Nash Barganng soluton (wth equal weghts): NB 1 ˆv = v ({}) + v j(s) v j({}) S s js js (5) Every member n S receves ts valuaton under no cooperaton (frst term) plus an equal share of the coaltonal surplus compared to no cooperaton (second term). Thus, no cooperaton serves as the threat pont. The thrd smple transfer scheme s the Chander and Tulkens transfer scheme (Chander and Tulkens 1997) n the verson as appled n Eyckmans and Tulkens (2003): D ˆv = v ({}) + v (S) v ({}) S CT j j D j js js js (6) wth D dscounted margnal damages of member. It s evdent that ths scheme s a verson of the Nash barganng rule wth unequal weghts. Ths rule gves a hgher share of the gans from cooperaton to those that are most affected by clmate change. It s straghtforward to show that all three smple transfer schemes are all coaltonally ratonal,.e. S N: ˆv j(s) v(s) j, and ndvdually ratonal,.e., S js js : ˆv (S) v({}) snce superaddtvty holds (and hence the term n square brackets s postve). The results of our smulatons, as summarzed n Table 2, confrm our ntuton and also many prevous studes on transfers: smple transfers mprove upon the outcome wthout transfers. However, t s mportant to realze that ths result s by no means general. Frst, we cannot generally conclude that smple transfer schemes would always enhance stablty. Second, we cannot conclude that the Nash barganng soluton performs better than the other transfer schemes. Though n our example, stable coalton no. 16 generates hgher global welfare than n any other stable coalton under the other two transfer schemes, other parameter values or 14

16 other models could yeld dfferent conclusons. Fnally, and most mportantly, we have no nformaton about whether we could do any better than the smple transfer schemes consdered here and f so what the best transfer scheme would be. Ths queston wll be addressed n the followng secton Optmal Transfer Schemes In order to address the ssues rased above n a systematc way, we frst focus on nternal stablty. For ths purpose, we ntroduce the concept of a Potentally Internally Stable Coalton (PISC) whch we defne as follows (see Eyckmans and Fnus 2004b and Botteon and Carraro (1997) for a smlar concept): Defnton 3: Potentally Internally Stable Coalton (PISC) A coalton S s sad to be potentally nternally stable (PIS) f and only f v(s) v(s\{}). S S Thus, f a coalton S s PIS, ths means that t has suffcent resources to guarantee each of ts members at least ts free rdng payoff. Hence, f S s PIS there does always exst a transfer scheme that can ensure nternal stablty to all members of S. All what s requred to construct such a transfer scheme s to gve every member of S at least hs free-rder payoff or outsde opton v (S \{}). The remanng surplus can then be shared n a proportonal way: Defnton 4: Optmal Transfer Schemes (OPTS) A transfer scheme s called optmal f t satsfes OP S N, S : ˆv (S) = v(s\{}) + λ (S) j Sv j(s) j Sv j(s\{}) s 1 s wth λ(s) Δ = { λ + j Sλj = 1}. 15

17 By the constructon of OPTS, t s easy to see that any transfer scheme that belongs to the class of OPTS wll make any PISC nternally stable. The desgn of OPTS suggests that we have much leeway n choosng weghts λ (S). As long as the surplus of cooperaton over the free-rdng valuatons, as well as all weghts λ (S), are postve, the resultng allocaton wll be nternally stable regardless of the choce of weghts. Ths means that the set of nternally stable coaltons does not depend on the choce of weghts. Interestng, though less evdent, ths robustness result also carres over to the set of externally stable coaltons. Intutvely, through OPTS a lnk between nternal and external stablty s establshed. If S s PIS, OPTS makes t nternally stable and hence all coaltons S wthout a member are externally unstable. If S not PIS, S wll not be nternally stable and S wthout s externally stable. Result 1: Invarance of stablty for surplus sharng weghts Any famly of weghts λ (S) of an OPTS wll lead to the same set of nternally and externally stable coaltons after transfers. A second result s that the coalton wth the hghest global welfare among all PISC, say coalton hence stable. * S, s not only nternally stable (because t s PISC) but also externally stable and Result 2: Welfare optmalty and stablty Under OPTS, the coalton wth the hghest global welfare among all PISC s stable. Intutvely, f * S were not externally stable, then there would exst a larger PISC wth hgher global welfare (because of superaddtvty and postve spllovers), volatng the ntal assumpton that * S generates the hghest global welfare. 16

18 Result 1 and 2 are proved n Eyckmans and Fnus (2004b). They are llustrated n Table 2 wth our smulatons. Frst, the three smple transfer schemes lead to a dfferent set of stable coaltons. In partcular, despte the Nash Barganng soluton and the Chander and Tulkens s transfer scheme only dffer n weghts, they produce very dfferent results. In contrast, any set of weghts for OPTS leads to the same set of stable coaltons as dsplayed n Table 2. Second, OPTS explots the full potental of self-enforcng cooperaton. In our example, OPTS acheves 94.5 percent of total maxmum welfare for coalton no. 5 {USA, EU, CHN, ROW} whereas for the smple transfer schemes the maxmum s acheved under the Nash Barganng soluton wth only 68.7 percent. 3.3 Ex-Post Transfer Schemes In ths subsecton, we consder ex-post transfers. Ths means that after a coalton S has formed, transfers are used to modfy the status quo. The status quo s a stable coalton that has emerged from the coalton formaton process wthout transfers or wth some ex-ante transfer scheme. In our example, these are the coaltons lsted n Table 2. Followng Carraro and Snscalco (1993), we cte two cases. In the frst case, a coalton S uses transfers to expand ts agreement by brbng outsders to jon the coalton (subsecton 3.3.1); n the second case, an outsder j S uses transfers to brbe another outsder k S to jon coalton S (subsecton 3.3.2) Expanson of Coaltons through Internal Means The standard procedure to analyze the expanson of coaltons through nternal means s to pck a stable coalton S as startng pont and to check whether expanson of ths coalton s possble when current coalton members pay some outsder j for jonng them (Botteon and Carraro 1997). It s natural to requre that expanson of coalton S s feasble f and only f 17

19 1) the expanson consttutes a Pareto-mprovement to all members of S and for the newcomer j, and 2) the enlarged coalton S {j} s nternally stable. The frst requrement of a Pareto mprovement follows from the presumpton that current members of S wll only brbe an outsder to jon f they are better off after the expanson. Lkewse, regon j wll only accept the deal f t can mprove tself. The second requrement smply follows from the defnton of stablty. Now, t turns out that the frst requrement s the condton of superaddtvty, whch holds n our global emsson game (as n many other models), and hence t s non-bndng. For the second requrement t can be shown that a necessary condton s that the enlarged coalton S {j} s potentally nternally stable. Snce coalton * S wth the hghest global welfare among all PISC s stable under (ex ante) OPTS, ths means that no expanson va nternal means s possble from ths coalton to form * S {j}. Result 3: OPTS exhausts all possbltes for expanson by nternal means Coalton * S whch acheves the hghest global welfare among all PISC cannot be mproved upon by expansons usng nternal means. Result 3 s proved n the Appendx. It mples that coalton S * can be regarded as the best possble outcome that can be acheved by means of expanson usng nternal means. Ths can also be nterpreted that f an optmal ex ante transfer scheme s employed, the analyss of ex post transfers to enlarge a coalton wth nternal means s redundant. In our example, ths means that we cannot do better than coalton no. 5,.e. {USA, EU, CHN, ROW} Expanson of Coaltons by External Means We now turn to the queston of whether the expanson of a coalton S s possble through external means. Ths means that an outsder k S brbes another outsder j S to jon 18

20 coalton S. Stable coaltons for whch expansons va nternal means are not possble are the obvous, although not exclusvely, potental canddates for expansons va external means. 10 Agan, two condtons must be satsfed that expansons s successful. Frst, expanson must consttute a Pareto-mprovement to all nvolved players, whch we know s not bndng f superaddtvty holds. Second, the enlarged coalton S {j} must be nternally stable. Snce by assumpton enlargement starts from S whch s nternally and externally stable, under OPTS, S {j} s not PIS. Consequently, expanson s only possble f and only f the enlarged coalton receves suffcent transfers to compensate for the lack of PIS and, n addton, the external player s better off despte provdng these resources. That s, v (S {j}) + t v (S {j}\{}) (7.a) S {j} S {j} S {j} v k(s {j}) + tk v k(s) (7.b) must hold where typcally t 0 and t k 0 and due to budget neutralty t S {j} {k}. That s, the postve spllover effect accrung to regon k v k(s {j}) v k(s) 0 must be larger when coalton than the free-rdng effect v(s {j}\{}) v(s {j}) > 0 S {j} S {j} S s expanded to coalton S {j}. In general, we cannot derve conclusve theoretcal results usng general propertes lke superaddtvty or postve spllovers for expansons usng external means. Therefore, condtons (7.a) and (7.b) have to be checked for all possble expansons startng from a PIS coalton. Result 4: Possblty of expanson usng external means Startng at a stable coalton S, expanson usng external means of S s possble only f the postve spllover to the external player k N\S that pays another outsder j N\S to jon 10 As long as expanson va nternal means s possble, t s very unlkly that expanson va external means are conducted. Ths s because outsders beneft from expanson va nternal means through postve spllovers wthout any contrbuton, knowng that ths expanson s n the nterest of all current members of coalton S. 19

21 S, s greater than the ncrease n the free-rder effect of the members of the expanded coalton S { j}. Fgure 1 shows all possbltes of expanson from coaltons wth four members that are stable n our example. Fgure 1 llustrates that from coalton no. 5, whch s the coalton wth the hghest global welfare usng nternal means, no expanson va external means s possble. However, from some other coaltons wth four members, expanson that rases global welfare s possble. It s nterestng to note that only the US and the EU are potental canddates that have suffcent resources to pursue a unlateral polcy of brbng other countres to partcpate n a clmate agreement. Gven that coalton no. 5 can already be acheved wthout external means, t s only JPN, FSU and the US that should pursue such a polcy n the nterest of the global good, though among ths group only the US has the means and the ncentve to do so. The maxmum degree of optmalty whch can be acheved by means of a clever transfer strategy s 95.6 percent (coalton no. 4 comprsng all countres except USA). Of course, full partcpaton cannot be acheved snce expanson va external means requres that at least one country remans an outsder. More generally, our results stress that n the context of ncentves to free-rde countres can play an mportant role, even f they do not actvely partcpate n an IEA. By subsdzng emsson abatement projects abroad, those outsders mght help other outsders to become a formal member of an IEA and to comply wth ts requrements. Ths result may be partcularly useful for the desgn of future IEAs lke for nstance post-kyoto negotatons. 4. Summary and Conclusons The non-cooperatve game theoretc lterature on nternatonal envronmental agreements has largely neglected the role of transfers as a tool to enhance partcpaton n nternatonal 20

22 treates. The few exstng results on transfers and nternatonal envronmental agreements (IEAs) are very specfc and do not explot the full potental of transfers for successful treatymakng. In ths paper, we have proposed a transfer mechansm that s capable of maxmzng global welfare gven that an IEA has to be nternally and externally stable. Ths result can be acheved by usng ether ex-ante or ex-post transfers where n the latter case we dstngushed between nternal and external transfers. We have shown that ex-post nternal transfers are redundant f ex-ante transfers are optmally desgned. By contrast, ex-post external transfers can help to acheve a welfare mprovng, self-enforcng IEA (compared to a stuaton wthout ex-post transfers). All results depend only on very general propertes of the underlyng valuaton functons, n partcular, only on the propertes superaddtvty and postve spllovers, whch hold for most publc good models, not only those that deal wth envronmental ssues. To show the relevance of the theoretcal results, we used a stylzed ntegrated assessment model of clmate change polcy. Our smulaton results hghlghted the dffculty of reachng an effectve agreement on clmate polcy because of the large asymmetres across countres and ncentves to free-rde on the provson of the publc good clmate change control. We showed that the stuaton can be largely mproved by adoptng an approprate transfer scheme. In the case of transfer usng nternal resources, our optmal transfer scheme leads to far better results than the smple transfer schemes well-known n exstng lterature. In the case of transfers usng external resources, we demonstrated that t s possble to reach a selfenforcng agreement nvolvng all but one country but where ths outsder contrbutes fnancally, n ts self nterest, to stablze a successful agreement. 21

23 Both results have mportant mplcatons for post-kyoto clmate polcy negotatons. On the one hand, they stress how mportant s to devote suffcent tme to the desgn of transfer schemes so that partcpaton can be rased n the future. On the other hand, they hghlght the mportant role that current outsders lke the USA and Australa can play. Although they dd not ratfy the Kyoto Protocol and may not even jon ths agreement at a later stage, they mght nevertheless be nvolved n future protocols va new fnancal mechansms through whch they could sponsor developng countres to promote energy effcency and, eventually perhaps to assume quanttatve emsson celngs and to become a full member of the Kyoto Protocol. These transfers may well be n the nterest of the outsders f the resultng ncrease n global greenhouse gas emsson control and ensung reducton of clmate change damages outweghs the cost of the transfers and the cost of takng domestc emsson control measures. The analyss of ths paper could be extended n several drectons. For nstance, t would be nterestng to analyze the role of transfers when multple coaltons can form or when coaltons nstead of sngle players could devate from an exstng coalton. Moreover, the relatonshp between the optmal transfer scheme proposed n ths paper and the transfer scheme mplct n the mplementaton of an emsson tradng market s certanly also a research topc for future research (see Bosello et al for some prelmnary numercal results). 22

24 References Altamrano-Cabrera, J.-C. and Fnus, M. (2006). Permt tradng and stablty of nternatonal clmate agreements. Journal of Appled Economcs, 9 (1): Aumann, R.J. and Drèze J.H. (1974). Cooperatve games wth coalton structures. Interna tonal Journal of Game Theory 3 (4): Barrett, S. (1994). Self-enforcng nternatonal envronmental agreements. Oxford Economc Papers 46 (October): Bloch, F. (2003). Non-cooperatve models of coalton formaton n games wth spllovers. In C. Carraro (Ed), Endogenous Formaton of Economc Coaltons, Cheltenham, UK: Edward Elgar. Bosello, F., Buchner, B. and Carraro, C. (2003). Equty, development, and clmate change control. Journal of the European Economc Assocaton 1 (2-3): Bosello, F., Buchner, B., Carraro, C. and Ragg, D. (2004). Can equty enhance effcency? Some lessons from clmate negotatons. In C. Carraro and V. Fragnell (Eds.), Game practce and the envronment, Cheltenham, UK: Edward Elgar. Botteon, M. and Carraro, C. (1997). Burden-sharng and coalton stablty n envronmental negotatons wth asymmetrc countres. In C. Carraro (Ed), Internatonal envronmental negotatons: strategc polcy ssues, Cheltenham, UK: Edward Elgar. Buchner, B, Carraro, C. and Cersosmo, I. (2002). Economc consequences of the US wthdrawal from the Kyoto Protocol. Clmate Polcy 76 (2): Carraro, C. (2000). Roads towards nternatonal envronmental agreements. In H. Sebert (Ed), The economcs of nternatonal envronmental problems, Tübngen: Mohr Sebeck. Carraro, C. and Snscalco, D. (1993). Strateges for the nternatonal protecton of the envronment. Journal of Publc Economcs 52 (3): Carraro, C. and Snscalco, D. (1998). Internatonal envronmental agreements: ncentves and poltcal economy. European Economc Revew 42 (3-5): Carraro, C. and Snscalco, D. (2001). Transfers, commtments and ssue lnkage n nternatonal envronmental negotatons. In A. Ulph (Ed), Envronmental polcy, nternatonal agreements and nternatonal trade, Oxford: Oxford Unversty Press. Chander, P. and Tulkens, H. (1997). The core of an economy wth multlateral envronmental externaltes. Internatonal Journal of Game Theory 26 (3): d Aspremont, C., Jacquemn, A., Gabszewcz J. J. and Weymark, J. A. (1983). On the stablty of collusve prce leadershp. Canadan Journal of Economcs 16 (1): Eyckmans, J. and Fnus, M. (2004a). Measures to enhance the success of global clmate treates. Forthcomng n Internatonal Envronmental Agreements: Poltcs, Law and Economcs. 23

25 Eyckmans, J. and Fnus, M. (2004b). An almost deal sharng scheme for coalton games wth externaltes. CLIMNEG Workng Paper Nr. 62, Leuven, Belgum: Katholeke Unverstet Leuven. Eyckmans, J., and Fnus, M. (2006). Coalton formaton n a global warmng game: how the desgn of protocols affects the success of envronmental treaty-makng. Natural Resource Modelng 19 (3): Eyckmans, J. and Tulkens, H. (2003). Smulatng coaltonally stable burden sharng agreements for the clmate change problem. Resource and Energy Economcs 25 (4): Fnus, M. (2001). Game theory and nternatonal envronmental cooperaton. Cheltenham, UK: Edward Elgar. Fnus, M. (2003a). Stablty and desgn of nternatonal envronmental agreements: the case of transboundary polluton. In H. Folmer and T. Tetenberg (Eds.), Internatonal yearbook of envronmental and resource economcs, 2003/4, Cheltenham, UK: Edward Elgar. Fnus, M. (2003b). New developments n coalton theory: an applcaton to the case of global polluton. In L. Marslan, M. Rauscher and C. Wthagen (Eds.), Envronmental polcy n an nternatonal perspectve, Dordrecht, The Netherlands: Kluwer. Fnus, M., Sáz, E. and Hendrx, E.M.T. (2004). An emprcal test of new developments n coalton theory for the desgn of nternatonal envronmental agreements. Mansholt Workng Paper Seres, Nr. 14, Wagenngen, The Netherlands: Unversty of Wagenngen. Hoel, M. (1992). Internatonal envronment conventons: the case of unform reductons of emssons. Envronmental and Resource Economcs 2 (2): IPCC (2001). Clmate change 2001: mtgaton. Contrbuton of workng group III to the thrd assessment report of the ntergovernmental panel on clmate change, Cambrdge, UK: Cambrdge Unversty Press. Jeppesen, T. and Andersen, P. (1998). Commtment and farness n envronmental games. In N. Hanley and H. Folmer (Eds.), Game theory and the envronment, Cheltenham, UK: Edward Elgar. Maskn, E. (2003). Barganng, coaltons, and externaltes. Mmeo. Paper presented at the EEA-ESEM Meetng n Stockholm, August. Nordhaus, W.D. and Yang, Z. (1996). A regonal dynamc general-equlbrum model of alternatve clmate-change strateges. Amercan Economc Revew 86 (September): Petraks, E. and Xepapadeas, A. (1996). Envronmental conscousness and moral hazard n nternatonal agreements to protect the envronment. Journal of Publc Economcs 60 (1): Wekart, H.-P., Fnus, M. and Altamrano-Cabrera, J.-C. (2006). The mpact of surplus sharng on the stablty of nternatonal clmate coaltons. Oxford Economc Papers, 58 (2):

26 Y, S.-S. (2003). Endogenous formaton of economc coaltons: a survey of the partton functon approach. In C. Carraro (Ed), Endogenous formaton of economc coaltons, Cheltenham, UK: Edward Elgar. Appendx The frst requrement of Pareto-mprovement means that S: v(s {j}) + t v(s) (A1.a) v(s j {j}) + tj v(s) j (A1.b) must hold where typcally t 0 and t j 0. By addng (A1.a) and (A1.b), summng over all regons S {j} nvolved n the expanson and notng that transfers should balance (.e. ), we obtan: v(s {j}) v(s) t S {j} 0 = whch mples that superaddtvty S {j} S {j} should hold n the move from coalton S to S {j}. The second requrement of nternal stablty of the expanded coalton means: S: v (S {j}) + t v (S {j}\{}) (A2.a) v(s j {j}) + tj v(s) j (A2.b) A smlar manpulaton as above reveals that a necessary condton (2.a) and (2.b) to hold s v(s {j}) v(s {j}\{}) whch s the condton of potental nternal stablty S {j} S {j} (PIS). 25

27 Table 1: Welfare and Envronmental Implcatons of Dfferent Coaltons* Coalton Welfare Concentraton Cumulatve Emssons N Sze Membershp 1 6 Grand Coalton (Full Cooperaton) USA, EU, CHN, FSU, ROW USA, JPN, EU, CHN, ROW JPN, EU, CHN, FSU, ROW USA, EU, CHN, ROW USA, JPN, CHN, FSU, ROW EU, CHN, FSU, ROW JPN, EU, CHN, ROW USA, CHN, FSU, ROW USA, JPN, CHN, ROW EU, CHN, ROW USA, CHN, ROW JPN, CHN, FSU, ROW USA, JPN, EU, FSU, ROW USA, EU, FSU, ROW JPN, ROW USA, JPN, EU, CHN, FSU USA, EU, CHN, FSU JPN, EU Only Sngleton Coaltons (No Cooperaton) * N : coalton number accordng to welfare rankng. Sze: number of coalton members. Membershp: composton of coalton. Welfare: global welfare expressed n relatve terms: N N ( P N ) ( F N = 1(w (c ) w (c )) / = 1(w (c ) w (c ))) where welfare s dscounted lfetme consumpton ntegrated over , global welfare wth full cooperaton s w(c) = 1 N F =339,831 bll US$ 1990 (bllon N N US dollars expressed n 1990 levels), global welfare wth no cooperaton s w(c ) = 1 =338,060 bll N P US$ 1990 and global welfare wth partal cooperaton s denoted by w(c ) = 1. Concentraton: atmospherc N P N F carbon concentraton M at tme t=2300 expressed n relatve terms: (M(c ) M(c )) /(M(c ) M(c )) F where concentraton wth full cooperaton s M(c ) = GtC (gga tons carbon), concentraton wth N P no cooperaton s M(c ) = GtC and concentraton wth partal cooperaton s denoted by M(c ). Cumulatve Emssons: cumulatve emssons of carbon over tme nterval expressed n relatve N P N F terms: (CE(c ) CE(c )) /(CE(c ) CE(c )) where cumulatve emssons wth full cooperaton are F N CE(c ) = GtC, cumulatve emssons wth no cooperaton are CE(c ) = GtC and P cumulatve emssons wth partal cooperaton are denoted by CE(c ). 26

28 Table 2: Stable Coalton Structures Under Dfferent Transfer Schemes* N Membershp Sze Welfare Concentraton Cumulatve Emssons 1 Grand Coalton (Full Cooperaton) No Transfers Shapley 27 CHN,ROW Nash Barganng 16 CHN,FSU,ROW EU,ROW Chander- Tulkens OPTS 27 CHN,ROW USA,ROW FSU,ROW JPN,ROW USA,EU,CHN,ROW EU,CHN,FSU,ROW JPN,EU,CHN,ROW USA,CHN,FSU,ROW USA,JPN,CHN,ROW JPN,CHN,FSU,ROW USA,EU,FSU,ROW USA,JPN,EU,ROW JPN,EU,FSU,ROW USA,JPN,FSU,ROW Only Sngleton Coaltons (No Cooperaton) * The same legend as wth Table 1 apples. 27

29 Fgure 1: Enlargng Partcpaton through External Means Legend: Bold numbers refer to the rankng of coaltons n terms of global welfare; descrpton of coalton at level 5 means a coalton of 5 members,.e., full partcpaton wthout regon j; descrpton of coalton at level 4, the descrpton ncludes the 4 coalton members that are lsted; arrow means enlargement through brbng s possble from coalton at level 4 to coalton at level 5; regon attached to an arrow s the regon that can be brbed to jon coalton at level 4 to form coalton at level 5 through regon j lsted under coalton structure at level 5 (.e., wthout j ).