Can altruism stabilise international climate agreements?

Ecological Economics 81 (2012) 112–120

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Ecological Economics journal homepage: www.elsevier.com/locate/ecolecon

Analysis

Can altruism stabilise international climate agreements? Thomas van der Pol, Hans-Peter Weikard ⁎, Ekko van Ierland Wageningen University, Environmental Economics and Natural Resources Group, Hollandseweg 1, 6706 KN Wageningen, Netherlands

a r t i c l e

i n f o

Article history: Received 14 March 2011 Received in revised form 6 June 2012 Accepted 9 June 2012 Available online 3 July 2012 JEL classification: D64 F51 H41 Keywords: Stability of international climate agreements STACO model Altruism

a b s t r a c t We study the impact of altruism on the stability of international climate agreements. We consider the standard two-stage game for the analysis of international environmental agreements where countries announce their participation at the first stage and abatement levels are chosen at the second stage. We modify the game to consider altruism in the participation decision, i.e. countries consider, to a certain extent, the net benefits for other countries in their decisions. We study two types of altruism: impartial altruism, where countries show a concern for all other countries, and community altruism, where the concern extends only to coalition partners. We use the stability of coalitions model (STACO) to illustrate the impacts of both types of altruism on the stability of a climate agreement. We find that a limited degree of altruism is sufficient to stabilise the Grand Coalition such that a globally efficient climate policy can emerge while in the absence of altruism only a fraction of countries would join a climate agreement and the benefits of cooperation would largely remain unexploited. Our results indicate how moving beyond national interests can support the success of international climate agreements. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Climate change will continue to be a major challenge for international politics. While environmental legislation falls essentially into the domain of individual sovereign nation states, the efficient reduction of greenhouse gas emissions requires international cooperation. The political process from the Rio Earth Summit (1992) to Kyoto (1997), Copenhagen (2009), Cancún (2010) and Durban (2011) indicates how difficult it is to achieve effective cooperation. Greenhouse gas abatement is a global public good and its provision suffers from severe free-rider incentives. Recent literature has explored the incentives of individual nation states to sign and ratify an international climate agreement (e.g. Asheim et al., 2006; Barrett, 1994 and 2001; Carraro and Siniscalco, 1993 and 1997; Hoel, 1992; Nagashima et al., 2009; Weikard et al., 2006). Results from this literature show that an international climate agreement (ICA) will have only few signatories if reduction targets are ambitious and gains from cooperation are high. Only less ambitious ICAs will show widespread participation (cf. Altamirano-Cabrera et al., 2008). The inefficient outcomes that these modelling approaches suggest are largely driven by the assumption that individual countries adopt strategies that maximise their own welfare disregarding the effects of externalities. This assumption leads to results that contradict high degrees of cooperation that are frequently observed in public goods games

⁎ Corresponding author. Tel.: + 31 317482494; fax: + 31 317484933. E-mail address: [email protected] (H-P. Weikard). 0921-8009/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolecon.2012.06.011

(e.g. Isaac et al., 1984; Willinger and Ziegelmeyer, 2001). There are various approaches to explain cooperation and pro-social behaviour ranging from evolutionary biology (e.g. Hamilton, 1964) to economic psychology (e.g. Bolton et al., 1998; Kahneman and Knetsch, 1992; Rabin, 1993) and to Fehr and Schmidt's (1999) theory of fairness, competition and cooperation that maintains the assumption of selfcentred rationality but introduces inequality aversion. The aim of our paper is to explore the effects of altruistic, otherregarding preferences on cooperation. We do not explore the drivers of cooperative behaviour but rather we investigate how altruism may help to overcome the free-rider incentives in international climate policies such that countries prefer to become signatories of an ICA. For that purpose we study the two-stage game that has served as a ‘work-horse’ model for the analysis of international environmental agreements in theoretical (e.g. Barrett, 1994) and applied works (e.g. Carraro et al., 2006; Finus et al., 2005). In this game the participation decision is announced at the first stage. At the second stage signatories, acting jointly, play a public goods game with non-signatories where abatement of greenhouse gases is the public good. The outcome is a partial agreement Nash equilibrium (Chander and Tulkens, 1995) that determines individual abatement levels. The associated abatement costs and the benefits of avoided damages from climate change constitute the payoffs of the game. We adjust this standard game to study two types of altruism: impartial altruism, where countries show a concern for all other countries, and community altruism, where the concern extends only to coalition partners (signatories) but not to other countries (non-signatories or free-riders). The latter implies a relative disadvantage to free-riders and is in line with, for

T. van der Pol et al. / Ecological Economics 81 (2012) 112–120

instance, the findings of Fehr and Gächter (2000) who observe a willingness to punish free-riders. We model altruism by giving a positive weight to others' net benefits from climate policies in the payoff function. We provide theoretical results and we use the stability of coalitions model (STACO) (cf. Dellink et al., 2009) to provide a numerical appraisal of the strengths of the impacts of both types of altruism on the stability of a climate agreement. We find that a limited degree of community altruism is sufficient to establish full participation in an ICA such that a globally efficient climate policy can emerge. Full participation can also be obtained under impartial altruism, but only for higher weights attached to others' net benefits. In addition we find that with a well-designed transfer rule the degree of altruism required to stabilise the Grand Coalition is even lower. 1 By contrast, in the absence of altruism full cooperation cannot be obtained, even if transfers are used to ‘buy international cooperation’ (Fuentes-Albero and Rubio, 2010). Without altruism only a fraction of countries would join the climate agreement and the benefits of cooperation would largely remain unexploited. The outline of our paper is as follows. We start with a brief review of the concepts of altruism. Section 3 describes our game and we introduce the main lines of the STACO model. Section 4 offers results for a baseline scenario (no altruism) and four different scenarios: impartial and community altruism with and without transfers. Section 5 offers discussion and conclusions. 2. Concepts of Altruism The term “altruism” is used for a variety of related concepts. The role of this section is not to review the philosophical, psychological and economic literature on altruism but rather to introduce four conceptual distinctions in order to locate our analysis in the ‘landscape’ of altruism. A comprehensive review is provided by Kolm (2006). The first distinction concerns the motives for altruism. These can be hedonistic or normative (Kolm, 2006). Hedonistic motivations are affection, sympathy, empathy, compassion and pity. Normative motives may be due to moral convictions or social norms. The former cause guilt, the latter shame upon the violation of a rule or norm. Secondly, we can distinguish pure and impure altruism. Pure altruism is the concern for others' well-being, no matter how it is assessed. By contrast, impure altruism refers for instance to the ‘warm glow of giving’ (Andreoni, 1989). The impure altruist attaches value to the act of giving rather than to others' well-being. A typical formal representation of pure altruism is ui = ui(uj, xi), where individual i's utility ui is derived from others' utility uj and a vector of characteristics of i's own situation (including consumption) xi. Impure altruism may be represented as ui = ui(tij, xi) where individual i's utility depends on a transfer tij to individual j instead of j's utility. Impure altruism may explain diverse observed phenomena, for example why private charitable giving is not completely crowded out by, for example, publicly provided social security. Thirdly, pure altruism can be described as non-paternalistic or paternalistic (Bergstrom, 1982; Hori, 2001). Non-paternalistic altruism is a concern for others' well-being in their own assessment. Paternalistic (or vicarious) altruism is the concern for others' wellbeing in one's own assessment. A typical formal specification of non-paternalistic altruism is again ui = ui(uj, xi), while paternalistic altruism is of the form ui = ui(xj, xi), cf. Becker (1974). Finally, altruism can be impartial or not. With impartial altruism the degree of concern for others is the same regardless of who the others are. Impartial altruism as a moral idea is supported by the notion of justice as impartiality. Its most prominent specification is Bentham's utilitarianism where each individual's well-being gets 1 Experimental evidence for the effectiveness of such transfers is provided by McGinty et al. (2012).

113

equal weight. This view is contrasted with the idea of family or community altruism. For example, Rachlin and Jones (2008) have demonstrated in experiments that people are more altruistic to close relatives and to those who are socially close compared to those who are perceived as far-away in terms of genetic or social distance. Brewer and Kramer (1986) provide evidence that social group identity helps to overcome social dilemma situations. With increasing group size, however, these altruistic effects get weaker. This is compatible with the well-known ‘bystander effect’ that the chance to be rescued in an emergency is smaller with a larger number of bystanders. In the remainder of this paper we examine the effects of two types of altruism on the willingness to sign an international climate agreement. The motives of altruism will not be discussed further. We will concentrate on pure altruism and disregard ‘warm glow effects’. We will consider non-paternalistic altruism only, but in two variants: ‘impartial altruism’ and ‘community altruism’. These choices will be further motivated below.

3. The Formation of International Climate Agreements — a Two-stage Game In this section we first introduce the standard game of coalition formation employed in the literature on international environmental agreements. Then we will motivate and explain the refinements that we introduce to capture the effects of altruistic behaviour and derive some general theoretical results. Finally, we briefly introduce the calibrated numerical simulation model STACO that we use to obtain insights into the strength of the effects predicted by our theoretical analysis.

3.1. The Standard Model The standard model of the formation of international environmental agreements is a cartel formation game adapted from the industrial organisations literature; cf. d'Aspremont et al. (1983). There is a set N of n countries and there are two stages of the game, the participation stage and the abatement stage. At the participation stage each country decides whether to sign a unique agreement or not. The signatories form a coalition S p N and act as a single player at the second stage of the game. Hence, the second-stage game has |N| − |S| + 1 players. These players, the coalition and the remaining non-signatories, play a transboundary pollution game (Folmer and von Mouche, 2000; Mäler, 1989). In the context of climate coalitions transboundary pollution comprises greenhouse gases. We assume that greenhouse gas abatement is a global public good. We investigate the partial-agreement Nash equilibria (Chander and Tulkens, 1995) of this game, that is, each of the non-signatories and the coalition (acting as a single player) adopt abatement paths q = (q1,…, qn) that are mutually best responses. Details of the transboundary pollution game are discussed below in Section 3.4. Here we assume that the equilibrium is unique and therefore associated to a unique payoff vector for all players under every coalition S p N. Hence, more formally, the equilibrium of the abatement game generates a partition function V that assigns payoffs to the coalition, denoted by VS(S) and the non-signatories, Vj(S) for all j ∈ N \ S. We assume that the coalition payoff is distributed to the individual members by a sharing rule r = (ri)i ∈ S with ∑ i ∈ Sri = 1 that determines the shares of the coalition payoff that accrue to individual members such that the coalition payoff equals the sum of all members' payoffs. Formally, we have Vi = ri VS for all i ∈ S and ∑i∈S V i ¼ V S . This establishes a valuation function. 2 2

Another name is ‘per-member partition function’.

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Equipped with individual payoffs we can establish the equilibria of the coalition formation game. Here we employ the standard Nash equilibrium solution concept where no player has an incentive to deviate from an equilibrium strategy. Hence we require that each signatory is better off as a signatory and each non-signatory is better off as a non-signatory, given all others' membership choices. 3 The conditions for a Nash equilibrium of a participation game have been named ‘internal’ and ‘external’ stability (e.g. d'Aspremont et al., 1983). 4 A formal definition follows: A coalition S is internally stable if and only if V i ðSÞ≥V i ðS figÞfor all i∈S:

ð1Þ

A coalition S is externally stable if and only if V i ðSÞ ≥ V i ðS∪figÞ for all i ∈ N n S:

U i ðSÞ ¼ V i ðSÞ þ α ∑ V j ðSÞ þ β ∑ V k ðSÞ for all i∈S;

r

ð3Þ

i∈S

This completes the description of the basic structure of the standard game of cartel formation as it is employed for the analysis of international environmental agreements (e.g. Barrett, 1994, 2001; Carraro and Siniscalco, 1993; Hoel, 1992) and specifically for climate agreements (e.g. Finus et al., 2005; Nagashima et al., 2009). 3.2. Altruistic Preferences in the Participation Decision In the following we are employing a specific notion of altruism. We start with noting that players in our climate policy game are sovereign countries, not individual people. Our earlier discussion of concepts of altruism can, however, be extended to this case. As we focus on the formation and stability of ICAs, we will consider the incentives of altruistic governments. That is, we will assume that each government, when it decides to participate in an ICA or not, exhibits a concern for other countries. We assume that altruism only extends to the participation decision, but does not (directly) affect the abatement decision. This setting is chosen to explore the potential of altruism to increase cooperation while previous work has explored how altruism increases emission reductions (cf. Kemfert and Tol, 2002). Moreover, our setting reflects findings that agents may hold different preferences when acting in different social situations, for example as consumers or as citizens (cf. Howley et al., 2010). This line of reasoning is also supported by Nyborg's (2000) distinction between ‘homo politicus’ and ‘homo economicus’. The main idea here is that different realms of decision-making can be separated. One is an ‘economic’ decision about the technology employed and the domestic regulations adopted at the abatement stage. The chosen technology and regulations are supposed to maximise a country's welfare position

3

j∈Snfig

ð2Þ

A coalition S is stable if and only if it is internally stable and externally stable. For the individual payoffs of coalition members we will focus on sharing rules that guarantee internal stability whenever this is possible, that is whenever the coalition payoff is at least as large as the sum of the outside option payoffs of all coalition members. Such sharing rules are called ‘optimal sharing’ (cf. Carraro et al., 2006; FuentesAlbero and Rubio, 2010; McGinty, 2007; Weikard, 2009). Formally we require of an optimal sharing rule r* that if V S ðSÞ ≥ ∑ V i ðS n figÞ; then V i ðSÞ ≥ V i ðS n figÞ for all i∈S:

under the constraints set by international agreements. The concern for others in this realm does not extend over and above the willingness to ‘stick to the rules’ (Kolm, 2006). The second realm is a ‘political’ decision whether or not to participate in an ICA. Here we will assume that the decision is impacted by altruistic concerns. More specifically, we will consider pure altruism where governments attach a positive weight to other countries' welfare gains from climate policy. This type of altruism can be classified as ‘non-paternalistic’ since the impacts of climate policies are assessed from each individual country's perspective. Note, however, that our conception of altruism is ‘local’ because it is not others' welfare as such – whether a country is rich or poor – that is considered but rather the net gains due to global abatement decisions.5 Hence we adopt the following specification:

Hence, we consider only single deviations and the equilibria we find may not be coalition-proof (cf. Bernheim et al., 1987). 4 Note that Caparrós et al. (2011) introduced a refinement of external stability such that external instability requires internal stability of an enlarged coalition.

ð4Þ

k∈NnS

where Ui(S) is the utility function of country i∈S that reflects this country's altruistic political preferences. The parameters α≥0 and β≥0 reflect the strength of altruism towards own group members and outsiders, respectively. Hence, typically we have α≥β. Eq. (4) describes community altruism if α>β, and impartial altruism if α=β. The non-signatories do not belong to any community and the equivalent of (impartially) altruistic political preference is given by U i ðSÞ ¼ V i ðSÞ þ β ∑ V k ðSÞ for all i∈N n S: k∈Nnfig

ð5Þ

Community altruism is a convincing feature if we can assume that a climate coalition constitutes a distinct group such that the social distance between group members is lower compared to the distances between members and non-members (Rachlin and Jones, 2008); or group members have a shared opinion, like ‘mitigation of greenhouse gases is important’. People are known to be more altruistic towards people who share their opinion (e.g. Fowler and Kam, 2007; Rotemberg, 2009; Tucker et al., 1977). Moreover, belonging to a group “relates to dispositions as to favor in-group and to be hostile to out-groups” (Zeggelink et al., 2000). Altogether, these notions support the hypothesis of community altruism among the signatories of an ICA. Non-members are presumed to be dispersed since they are not connected through a climate treaty. Consequently, non-members are presumed to treat all other countries similarly. They are impartially altruistic. Here we do not consider the case of strong reciprocity where members of the group that contribute to a public good are willing to punish the free-riders (Bowles and Gintis, 2004). However this case is compatible with our model if we allow β b 0 for group members. With α = β Eq. (4) is similar to the specification adopted by Kemfert and Tol (2002). There are two differences, however. We assume local altruism, i.e. regions are assumed to care about others' climate policy related net benefits, not their overall utilities as assumed by Kemfert and Tol. Furthermore, altruism is restricted to the participation decision which distinguishes our model from Kemfert and Tol (2002) and also from Lange (2006) who studies the impact of inequality aversion on coalition stability. In the formal analysis equilibria of the stage-two abatement game are the partial-agreement Nash equilibria of a standard game. The payoffs generated at the second stage are subject to altruistic concerns at the first stage where we identify stable coalitions as Nash equilibria of the participation game. 3.3. Some General Results Altruistic concerns affect the participation decision. The relevant valuation functions are now Ui(S) which are derived from the initial 5

This meaning of the word ‘local’ is borrowed from Elster (1992).

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Vi(S) by our specification of altruism in Eqs. (4) and (5). For ease of reference we will refer to Ui(S) as utilities (or altruistic payoffs) and to Vi(S) as standard (or non-altruistic) money payoffs. Clearly, for α = β = 0 we obtain the standard model as a special case of the altruistic model. In order to obtain some general insights on how altruism affects stability we focus our attention on partition functions that are superadditive and exhibit positive spillovers. Superadditivity means that entry of a member to a coalition increases the coalition payoff sufficiently such that it is at least as much as the entrant's and the members' initial payoffs. Positive spillovers imply that non-members would not lose but might gain from some country's entry to a coalition. Both conditions are natural requirements in a public goods game. The first is warranted under a limited leakage, i.e. when additional provision of the public good (abatement) by coalition members is not overcompensated by a reduction of provision by free-riders. The second is a direct consequence of the positive externality of the public good. Applying the definition of internal stability (1) to the altruistic valuation functions we obtain

Now suppose we use transfers that guarantee that every coalition member gains when another player joins, i.e. ∑j∈Snfig V j ðSÞ≥ ∑j∈Snfig V j ðS n figÞ, and with 1 ≥ α ≥ β ≥ 0 Eq. (7b) is always positive. Then, from Eq. (7) we can also draw conclusions regarding the impact of community altruism compared with impartial altruism. For a given level of concern for outsiders β an increase of community altruism α will strengthen stability; see Eq. (7b). The effect of β on stability is, however, ambiguous. A lower β implies a stronger relative concern for community members which strengthens internal stability; see Eq. (7b). But a lower β reduces the impacts of positive spillovers, i.e. player i's incentive to join the coalition because this would benefit outsiders. Below we will examine the impact of a change of β using the STACO model. Finally, consider the Grand Coalition of all players N. When is N internally stable such that no country wants to leave? Using Eqs. (1), (4) and (5) we obtain

V i ðSÞ þ α ∑ V j ðSÞ þ β ∑ V k ðSÞ ≥ V i ðS n figÞ

It is easy to see that, for any given strength β of (impartial) altruism of a non-signatory, condition (8) can be satisfied if community altruism is sufficiently strong, i.e. if α is sufficiently high. It is also clear from Eq. (8) that the minimum level of α such that Eq. (8) is satisfied and the Grand Coalition is internally stable increases with β. Hence, in the particular case of the Grand Coalition the effect of β is no longer ambiguous. In this case the lowest level of community altruism α necessary to have an internally stable Grand Coalition is obtained for β=0. Generally we denote the minimum level of community altruism necessary to internally stabilise coalition S by αS(β).

j∈Snfig

k∈NnS

þ β ∑ V k ðS n figÞ for all i∈S:

ð6Þ

k∈Nnfig

To see how altruism affects internal stability we have to compare Eq. (6) with Eq. (1). Splitting the sum on the right hand side of Eq. (6) and rearranging gives V i ðSÞ−V i ðS n figÞ þ α ∑ V j ðSÞ−β ∑ V j ðS n figÞ j∈Snfig

j∈Snfig

þ β ∑ V k ðSÞ−β ∑ V k ðS n figÞ≥0 for all i∈S: k∈NnS

ð7Þ

k∈NnS

Condition (7) is organised as the sum of three differences capturing the effects on payoffs when i joins S \ {i}: (i) the effect on i, (ii) the effect on other coalition members S \ {i}, and (iii) the effect on freeriders N \ S. From Eq. (7) we can see that altruism strengthens internal stability, i.e. the incentive to join an ICA. Looking at the first difference we have V i ðSÞ−V i ðS n figÞ≥0 for all i∈S

ð7aÞ

if S is stable under the non-altruistic valuation function. The second difference α ∑ V j ðSÞ− β ∑ V j ðS n figÞ for all i∈S j∈Snfig

j∈Snfig

ð7bÞ

is ambiguous, however. When members other than i lose when i joins S \ {i}, then Eq. (7b) is negative and works against internal stability. Looking at the third difference we have β ∑ V k ðSÞ−β ∑ V k ðS n figÞ ≥ 0 for all i∈S k∈NnS

ð7cÞ

k∈NnS

because a larger coalition provides more abatement which is always to the benefit of the non-signatories (positive spillovers). Although Eq. (7b) is ambiguous we can establish that altruism strengthens internal stability even without transfers. This result follows from the superadditivity of V and a (mild) requirement on the strength of altruism: 1≥α≥β≥0. This just means that one's concern for others is not stronger than the concern for oneself. The proof of our result is relegated to Appendix A. If we allow for transfers, the result that altruism strengthens internal stability follows directly from superadditivity and positive spillovers. In this case, because of superadditivity, payoffs to coalition members can always be arranged such that the difference in Eq. (7b) is positive and no coalition member loses when an additional player joins the coalition.

V i ðNÞ þ α ∑ V j ðNÞ ≥ V i ðN n figÞ j∈Nnfig

ð8Þ

þβ ∑ V k ðN n figÞ for all i∈N: k∈Nnfig

3.4. The STACO Model With this general model structure we now turn to the numerical analysis in order to obtain further results. We are particularly interested in how the altruism parameters α and β affect ICA participation and whether a Grand Coalition will become stable if governments have altruistic policy preferences with a “reasonable” degree of altruism. For that purpose we use an abatement game that has been specified as a module of the STACO (stability of coalitions) model, which was first introduced by Finus et al. (2006) and further developed by Nagashima et al. (2009). The STACO abatement game is a calibrated public goods game. The public good is carbon emission reduction. The players are 12 world regions: USA (USA), Japan (JPN), European Union-15 (EU15), other OECD countries (OOE), Eastern European countries (EET), former Soviet Union (FSU), energy exporting countries (EEX), China (CHN), India (IND), dynamic Asian economies (DAE), Brazil (BRA) and the rest of the world (ROW). Their strategies are abatements qi ∈[0, ēi] with baseline emissions ēi. Global abatement is the sum of regional abatements q≡∑i∈N qi . Regional payoffs are obtained from the benefits Bi(q) of global abatement (the public good), individual abatement costs Ci(qi) and transfers between coalition members Ti(r) that are specified through a sharing rule r. A full specification of the model is provided by Dellink et al. (2009) and by Nagashima et al. (2009). We assume that non-signatories maximise their own benefit by equating marginal benefits and marginal costs of abatement: ∂Bj ∂qj

¼

∂C j ∂qj

for all j∈N n S:

ð9aÞ

Coalition members are assumed to maximise their joint benefit. By Samuelson's rule they equate individual marginal costs with the sum of the marginal benefits of coalition members:

∑ j∈S

∂Bj ∂qi

¼

∂C i for all i∈S: ∂qi

ð9bÞ

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In the STACO specification (version 2.1) marginal benefits are assumed to be constant. Hence, all regions have dominant strategies. The largest marginal benefits accrue to USA, EU15 and JPN. Marginal costs are quadratic with CHN, USA and IND offering the cheapest abatement options. For details of the model calibration we refer the reader to Dellink et al. (2009). A standard partition function can then be calculated from Eqs. (9a) and (9b). Denote by qiS the partial-agreement Nash equilibrium abatement under coalition S. Then standard (non-altruistic) payoffs are specified as follows:

payoff requirements
of all players are satisfied. This sum of all transfers is  r given by ∑i∈S min V imin ðSÞ−V i 0 ðSÞ; 0 .7 Note that the transfer payments are not directly motivated by altruistic behaviour. Rather, these payments are part of the agreement to establish cooperation. To obtain our results we study the effect of altruistic preferences by varying parameter values α and β. As just explained we apply two sharing rules, one that does not involve any transfers and the one that implements optimal sharing with minimum necessary transfers.



 S S V j ðSÞ ¼ Bj q −C j qj for all j∈N n S:

4. Results ð10Þ




 S S for all S⊆N: V S ¼ ∑ Bi q −C i qi

ð11Þ

We will first consider impartial altruism and then turn to community altruism.

i∈S

4.1. Impartial Altruism The partition function we obtain is superadditive and exhibits positive spillovers. Individual payoffs can be determined by applying a sharing rule. We consider two particular sharing rules. The first is a sharing rule r0 that involves no transfers such that an individual coalition member's standard payoff is

 r S S V i 0 ðSÞ ¼ Bi q −C i qi for all i∈S:

ð12Þ

The altruistic payoff can easily be derived from Eq. (12) using Eq. (4). The second is a sharing rule r* from the class of optimal transfer rules that guarantee internal stability whenever this is possible, that is, whenever the coalition payoff is at least as large as the sum of the outside option payoffs of all coalition members. Hence we require: r

if U S ðSÞ≥ ∑ U i ðS n figÞ; then U i ðSÞ≥U i ðS n figÞ for all i∈S:

ð13Þ

i∈S

We will work with one particular sharing rule that satisfies Eq. (13). We will use the rule that minimises transfer payments for stabilising a given coalition. 6 From the internal stability condition (6) we can calculate the money payoff for any member i ∈ S that corresponds to its outside option utility. Notice that redistribution of payoffs within coalition S does not change the total coalition utility. Solving the condition for internal stability (Eq. 6) for Vi(S) we obtain as a minimum payoff requirement for any member of a stable coalition ! 1 min V i ðSÞ≥ V i ðS−i Þ þ β ∑ V k ðS−i Þ−β ∑ V k ðSÞ− αV S ðSÞ : ð1−αÞ k∈Nnfig k∈NnS ð14Þ The right hand side of Eq. (14) contains only items that are provided directly by the partition function given by Eqs. (10) and (11). We consider the payoff Vir0(S) a benchmark situation. Now, for any coalition that can be internally stable we know that the coalition payoff must exceed the sum of the minimum payoff requirements of the members, i.e. ∑i∈S V ri 0 ðSÞ≥∑i∈S V imin ðSÞ. The sharing rule (for money payoffs) that minimises money transfers is then implicitly given by ( r V i ðSÞ

¼

r

min

min if V i 0 ðSÞ≤V i ðSÞ V i ðSÞ r V i 0 ðSÞ−T i ðSÞ if V ri 0 ðSÞ > V imin ðSÞ;

ð15Þ

where Ti(S) with 0b Ti(S)b Vir0(S)−Vimin(S) is determined such that it minimises the largest payment made by any country while the minimum 6 We thank an anonymous reviewer for this suggestion. Simple alternatives that can easily be implemented are sharing proportional to outside options and to each the outside option payoff and equal split of the remaining surplus. As shown by McGinty (2011) the latter rule satisfies a risk-dominance property.

We consider impartial altruism (α = β) and examine the effects of the strength of altruistic concerns α on coalition stability. For increasing α we find a decrease of external stability and an increase of internal stability. When altruism is stronger, it is more attractive to be in any coalition and similarly, it is less favourable to be a non-signatory. Hence, larger coalitions become stable with increasing altruism. Table 1 lists the stable coalitions with the highest payoff for different values of α for coalition formation without transfers. The base case (no altruism) is represented by α = 0. The table also reports global payoffs and global utilities. Without altruistic preferences, only Japan and EU-15 would sign a climate agreement. At α = 0.127 the coalition comprising BRA, JPN and EU-15 becomes internally stable and is still externally stable. At α ≥ 0.143 a coalition with {USA, JPN, EU-15} becomes the best stable coalition (in terms of global payoff) while the coalition with {BRA, JPN, EU-15} remains stable as well. Generally we find not more than one or two stable coalitions at any level of strengths of altruism. Furthermore, we observe that stronger altruism does not always result in coalitions with higher global payoffs. The reason is that both internal and external stability conditions must hold. When we compare for example α = 0.39 with α = 0.40 we find {USA, JPN, EU15, OOE, EET, FSU, EEX, CHN, IND, BRA, ROW} and {USA, JPN, EU15, OOE, EET, FSU, EEX, IND, DAE, BRA, ROW}, as stable coalitions respectively. Going from α = 0.39 to α = 0.40 makes China (CHN) leave the coalition while the Dynamic Asian Economies would join. The coalition with China is, however, more favourable in terms of global payoff. Furthermore we can identify the threshold level of impartial altruism αN beyond which the Grand Coalition will be stable. In the case without transfers we find that for any level α ≥ αN all coalitions are internally stable and all are externally unstable except the Grand Coalition. Hence the Grand Coalition is the unique stable coalition. This threshold level is αN = 0.401. The effect of altruism on internal and external coalition stability is stronger under an optimal transfer scheme. The altruistic strength needed to stabilise a given coalition is generally lower under optimal transfers. The Grand Coalition is stable for any strength of altruism equal or larger than αN = 0.308. Table 2 displays the coalitions with highest global payoffs for different strengths of altruism with optimal transfers. With optimal transfers we generally find a large number of stable coalitions for any level of strength of altruism. For example even for α = 0 we find 463 stable coalitions. We observe that levels of altruism as low as α = 0.001 trigger the stability of coalitions with higher global payoffs. We find that the coalition of industrialized countries {USA, JPN, EU15, OOE, EET, FSU} will be stable at α = 0.13 (not reported in the table). In Eq. (4) we have introduced the strength of altruism α as a weight an individual region attaches to the monetary payoffs that accrue to other regions. Regions' utilities Ui(S) can therefore be 7 The algorithm to calculate minimum necessary transfers and the data files are available from the authors on request.

T. van der Pol et al. / Ecological Economics 81 (2012) 112–120 Table 1 Stable coalitions with highest global payoff for different levels of impartial altruism: the case without transfers. Source: Results are obtained from STACO 2.1 as documented by Dellink et al. (2009).

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Table 4 Stable coalitions with highest global payoff for community altruism for different values of β (α = 0.06): the case without transfers. Source: Results are obtained from STACO 2.1 as documented by Dellink et al. (2009).

α

Coalition

Global payoff (billion $)a

Global utility (billion $)a

β

Stable coalition with highest payoff

Global payoff (billion $)a

Global utility (billion $)a

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

{JPN, EU15} {JPN, EU15} {JPN, EU15} {USA, JPN, EU15} {USA, JPN, EU15, BRA} {USA, JPN, EU15, OOE, BRA} {USA, JPN, EU15, OOE, FSU, BRA, ROW} {USA, JPN, EU15, OOE, EET, FSU, EEX, DAE, BRA, ROW} {USA, JPN, EU15, OOE, EET, FSU, EEX, IND, DAE, BRA, ROW} Grand Coalition

5486 5486 5486 6347 6404 6860 8414 10,157

5486 8503 11,520 16,818 20,492 25,725 36,182 49,259

0

{USA, JPN, EU15, OOE, EET, FSU, EEX, IND, DAE, BRA, ROW} {USA, JPN, EU15, OOE, EET, FSU, EEX, DAE, BRA, ROW} {USA, JPN, EU15, OOE, EET, BRA} {JPN, EU15, OOE, BRA} {JPN, EU15, BRA} {JPN, EU15}

11,126

17,233

10,157

15,226

7367 5919 5531 5486

10,164 8452 8507 9106

11,126

60,083

15,211

82,307

0.4 0.401 a

0.012 0.024 0.036 0.048 0.06 a

Table 5 Stable coalitions with highest global payoff for community altruism for different values of β (α = 0.06): the case with transfers. Source: Results are obtained from STACO 2.1 as documented by Dellink et al. (2009).

Discounted sum of net present values from abatement from 2011 to 2110.

Table 2 Stable coalitions with highest global payoff for different levels of impartial altruism: the case with transfers. Source: Results are obtained from STACO 2.1 as documented by Dellink et al. (2009). α

Stable coalition with highest payoff

Global payoff (billion $)a

Global utility (billion $)a

0 0.002 0.02 0.06 0.1

{USA, EET, CHN, IND, DAE} {USA, EET, EEX, CHN, IND} {USA, EET, EEX, CHN, IND, DAE} {USA, EET, EEX, CHN, IND, DAE, ROW} {USA, EET, FSU, EEX, CHN, IND, DAE, BRA, ROW} {USA, OOE, EET, FSU, EEX, CHN, IND, DAE, BRA, ROW} {USA, JPN, OOE, EET, FSU, EEX, CHN, IND, DAE, ROW} {USA, EU15, OOE, EET, FSU, EEX, CHN, IND, DAE, BRA, ROW} {USA, EU15, OOE, EET, FSU, EEX, CHN, IND, DAE, BRA, ROW} {USA, JPN, EU15, OOE, EET, FSU, EEX, CHN, IND, DAE, ROW} Grand Coalition

9830 9947 10,567 11,695 12,927

9830 10,166 12,892 19,414 27,146

13,542

34,397

14,386

42,870

14,873

50,866

14,873

57,411

15,169

65,227

15,211

66,746

0.14 0.18 0.22 0.26 0.3 0.308 a

Discounted sum of net present values from abatement from 2011 to 2110.

β

Stable coalition with highest payoff

Global payoff (billion $)a

Global utility (billion $)a

0 0.012 0.024 0.036

Grand Coalition Grand Coalition Grand Coalition {USA, EU15, OOE, EET, FSU, EEX, CHN, IND, DAE, BRA, ROW} {USA, EET, FSU, EEX, CHN, IND, DAE, ROW} {USA, EET, EEX, CHN, IND, DAE, ROW}

15,211 15,211 15,211 14,873

25,250 25,250 25,250 23,457

12,787 11,695

20,009 19,414

0.048 0.06 a

Discounted sum of net present values from abatement from 2011 to 2110.

payoff is smaller. For the East European Transition countries (EET), for example, the money value of concern for others is about 50% higher than for EU15. Notice that this bias is less severe under the optimal transfer scheme. Table 3 also reports the money value of each region's concern for others as a percentage of regional GDP. In this perspective the mentioned bias looks even more severe. While for USA the concern for others required to stabilise the Grand Coalition is 0.2% (0.2%) of GDP, this figure is 6.4% (8.3%) for EET for the case with (and without) transfers.

Discounted sum of net present values from abatement from 2011 to 2110.

interpreted as the sum of region i's own monetary payoff and a monetary value for its appreciation of others' payoffs. Table 3 reports the money value of the concern for others, α∑j∈N=fig V j for region i (given as a net present value from abatement over the century 2011–2110), for all regions in the Grand Coalition. Clearly, this value is lower for the main beneficiaries of abatement as others'

Table 3 Required concern for othersa to stabilise the Grand Coalition under impartial altruism. Source: Results are obtained from STACO 2.1 as documented by Dellink et al. (2009). Region

USA

JPN

EU15

OOE

EET

FSU

Concern for others, no transfersb (as percentage of regional GDP)c Concern for others with transfersb (as percentage of regional GDP)c

4432 (0.2) 3545 (0.2)

4524 (0.6) 3608 (0.5)

4070 (0.3) 3359 (0.2)

5892 (1.7) 4507 (1.3)

6100 (8.3) 4664 (6.4)

5686 (3.6) 4339 (2.8)

Region

EEX

CHN

IND

DAE

BRA

ROW

Concern for others, no transfersb (as percentage of regional GDP)c Concern for others with transfersb (as percentage of regional GDP)c

6000 (1.8) 4568 (1.3)

6812 (1.5) 4953 (1.1)

5906 (3.5) 4486 (2.7)

6016 (2.1) 4587 (1.6)

5966 (2.8) 4580 (2.2)

5691 (1.5) 4340 (1.1)

a b c

α ∑ j ∈ N/{i}Vj for region i with α = 0.401 for no transfers and α = 0.308 with transfers. Discounted sum of net present values from abatement from 2011 to 2110, billion $. Discounted net present values over the century 2010–2110, billion $.

Fig. 1. NPV (bln $) of global payoffs of the best stable coalitions for different values of α under community altruism (for β = 0) and impartial altruism (α = β) without transfers (left panel) and with transfers (right panel).

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T. van der Pol et al. / Ecological Economics 81 (2012) 112–120

Table 6 Required levels of community altruisma to stabilise the Grand Coalition. Source: Results are obtained from STACO 2.1 as documented by Dellink et al. (2009). Region

USA

JPN

EU15

OOE

EET

FSU

Concern for others, no transfersb (as percentage of regional GDP)c Concern for others with transfersb (as percentage of regional GDP)c

1780 (0.10) 340 (0.02)

1816 (0.25) 357 (0.05)

1634 (0.11) 323 (0.02)

2366 (0.67) 446 (0.13)

2449 (3.35) 461 (0.63)

2283 (1.46) 425 (0.27)

Region

EEX

CHN

IND

DAE

BRA

ROW

Concern for others, no transfersb (as percentage of regional GDP)c Concern for others with transfersb (as percentage of regional GDP)c

2409 (0.71) 450 (0.13)

2735 (0.59) 441 (0.09)

2371 (1.41) 437 (0.26)

2415 (0.84) 453 (0.16)

2395 (1.14) 459 (0.22)

2285 (0.59) 425 (0.11)

a b c

α ∑ j ∈ N/{i}Vj for region i with α= 0.161 for no transfers and α= 0.03 with transfers. Discounted sum of net present values from abatement from 2011 to 2110, billion $. Discounted net present values over the century 2010–2110, billion $.

To summarise, impartial altruism can stabilise coalitions that are unstable in the base case (α = 0). Coalitions found to be stable are only stable for a range of values of α. Without transfers most coalitions can never be stable regardless of the strength of altruism. When regions are altruistic and an optimal transfer scheme is in place, the levels of altruism needed to stabilise any given coalition are generally lower as compared to the case without transfers. 4.2. Community Altruism Turning to community altruism now, we know from the theoretical analysis in Section 3.3 that a differentiation of the strength of altruism can help to stabilise the Grand Coalition. Hence we now investigate coalition stability assuming that α > β. We use β as the altruism parameter for signatories towards non-signatories and for non-signatories towards all others. We will say that signatories form a community. We find that when signatories show a stronger altruism towards members of their community (other signatories) than towards others, the incentive to join the coalition increases compared to impartial altruism. We also find that the number of internally stable coalitions grows quicker and the number of externally stable coalitions decreases faster with the increase of α compared to impartial altruism. This effect is stronger if β is lower. Table 4 illustrates this for community altruism of strength α = 0.06. The results stress the importance of the appropriate specification of altruism. The general

pattern is that coalition size and the global payoff fall as β increases. We also observe that global utility is not monotonic in β. As β falls from β = 0.06 to β = 0.036, we observe an increasing global payoff but decreasing global utility. This is due to a scaling effect. A lower β implies that the payoffs of non-members receive a lower weight. This scaling effect is, however, smaller for larger coalitions, since there are fewer free-riders. Table 5 provides results for α = 0.06 and different values of β for community altruism when it is combined with optimal transfers. We observe a pattern similar to the case with transfers. The Grand Coalition is, however, stable for weaker altruistic preferences. Note that as long as the Grand Coalition can be formed, global utility is only dependent on α, and a change of β does not affect global utility. Next we turn to numerical results for β = 0, the case that is most favourable for the stability of larger coalitions. Fig. 1 shows the global payoff that can be obtained by the best stable coalition under community altruism (black line) and under impartial altruism (grey line) for different values of α. The upper panel, Fig. 1 (a), shows the case without transfers. The lower panel, Fig. 1 (b), shows the case with optimal transfers. We find that the Grand Coalition is stable for α ≥ αN = 0.161 if transfers are not considered and β = 0. The impact of the use of transfers is considerable. In this case the threshold value is αN = 0.030. Table 6 displays the money value of minimum concern for others required to stabilise the Grand Coalition. As in Table 3 in Section 4.1 we also express each region's required concern for others also relative to regional GDP. In the most favourable case of community altruism with no concern for non-signatories (β = 0) and optimal transfers the concern for other signatories does not exceed 0.6% of GDP for any region; for several regions it is around 0.1% or below. Finally, Table 7 presents an overview of the transfers necessary to stabilise a Grand Coalition and, for comparison, provides payoffs for the Grand Coalition and for the non-cooperative Nash equilibrium. Table 7 also provides the respective abatements in percentages of baseline emissions for the non-cooperative Nash equilibrium (column 2) and the Grand Coalition (column 4). Transfers are reported for the lowest level of impartial altruism (α = β = 0.308, column 6) and community altruism (α = 0.03, β = 0, column 7) at which the Grand Coalition is stable. A negative sign indicates that a region receives a transfer such that it obtains its outside option payoff. In the case of impartial altruism three regions (USA, Japan, EU15) pay transfers. These regions are also the

Table 7 Abatement, money payoffs and size of transfer payments. Source: Results are obtained from STACO 2.1 as documented by Dellink et al. (2009). (1)

(2)

(3)

All-singletons

USA JPN EU15 OOE EET FSU EEX CHN IND DAE BRA ROW Global a b

(4)

(5)

Grand Coalition

(6)

(7)

Impartial altruisma

Community altruisma

(α = β = 0.308)

(α = 0.03, β = 0)

Abatement in 2011 % baseline emissions

Payoff (NPV) billion $

Abatement in 2011 % baseline emissions

Payoff (NPV) billion $, before transfers

Transfers (NPV) billion $ (% of gain)

Transfers (NPV) billion $ (% of gain)

9.9 2.5 7.6 5.6 4.4 6.7 1.9 14.8 10.5 1.9 0.1 6.3 8.0

1117 943 1240 188 71 362 164 298 268 136 84 365 5238

22.8 11.7 18.3 29.9 47.6 26.2 28.4 89.3 65.8 34.7 6.2 30.7 36.6

4158 3930 5062 518 −1 1031 248 − 1777 482 209 333 1019 15211

458 432 757 − 62 − 68 − 93 − 132 − 909 − 163 − 110 −9 − 101 1647

288 (9.5) 626 (20.9) 626 (16.4) 186 (56.3) 164 (n.a.)b 2 (0.3) 29 (35.1) − 2286 (n.a.)b − 151 (70.6) 101 (139.3) 432 (173.9) − 17 (2.6) 2454 (24.6)

Lowest altruistic levels at which the Grand Coalition is stable. EET and China would lose from cooperation without transfers.

(15.1) (14.5) (19.8) (18.7) (n.a.)b (13.9) (156.9) (n.a.)b (76.3) (152.4) (3.4) (15.5) (16.8)

T. van der Pol et al. / Ecological Economics 81 (2012) 112–120

main beneficiaries of the climate policy adopted by the Grand Coalition. Under minimum necessary transfers the payoff position of all countries except EU15 is reduced to their outside option position (see Eq. 15). Notice that in this case China's position is special. Their participation in the Grand Coalition contributes significantly to the coalition payoff. Hence, given the level of altruism, China is willing to join the Grand Coalition largely for the sake of the others and receives only partial compensation for its abatement efforts. With community altruism transfer payments are higher (except for USA and EU15) and only three regions receive transfers (CHN, IND and ROW). Since we arrange transfers to minimise individual regions' contributions, we find that the largest contributors, EU15 and Japan, are contributing equally. USA contributes less and their payoff is reduced to their outside option payoff. Generally larger transfers are needed for the case of community altruism compared to impartial altruism since altruistic preferences are weaker in the latter case. In columns (6) and (7) we also present transfer payments as percentages of the gains from coalition formation before transfers (column (5) minus column (3)). 5. Discussion and Conclusion Our analysis and results show that altruistic preferences can have significant impacts on coalition formation in particular when coupled with an optimal transfer scheme. As we discuss in the Introduction and in Section 2, altruism can be conceptualised in different ways and it can take different forms. We study local non-paternalistic altruism where individual countries or regions care about others' benefits from greenhouse gas abatement. This form of altruism does not consider the overall position of a beneficiary of the policy — whether it is a rich or a poor country. We analyse both impartial and community altruism and we compare them. A first intuition that with impartial altruism a public goods problem would be easier to overcome than with community altruism is not supported by our analysis. Surprisingly, community altruism, (i.e. the exclusion of non-signatories from the concerns of the signatories) can be quite effective to generate incentives to participate. We can interpret community altruism as impartial altruism coupled with a ‘punishment’ of non-signatories. The punishment consists of a withdrawal of concern. It is worthwhile to note that an important feature of our model specification is that we consider altruism to prevail only in the realm of policy-making, i.e. when the rules for climate policies are set. Once an ICA has been signed, each region's concern is about its own payoff and the role of altruism is confined to respecting the agreed rules. In this respect our approach differs from Kemfert and Tol (2002) who focus on altruism in the emission control decision. Our approach is motivated by the fact that decision-makers behave differently in different environments (cf. e.g. Blamey et al., 1995; Ovaskainen and Kniivilä, 2005). Buchanan and Tullock's (1962) important distinction between the choice of rules and the choice within rules matters for behaviour. We conclude by summarising our main findings. When countries have altruistic preferences, larger coalitions tend to arise. With sufficiently strong altruistic preferences, the Grand Coalition can be stabilised such that no country or region would like to leave. Community altruism, when a signatory restricts concern for others to signatories, will increase cooperation. Threshold values for the strength of altruism needed to stabilise a given coalition are generally lower for community altruism than for impartial altruism and a higher global payoff can be obtained. We find the lowest degree of community altruism needed to stabilise the Grand Coalition if there is no concern for non-signatories at all (β = 0) and if an optimal transfer scheme is in place. In this case, a weight of 3.0% attached to other signatories' payoffs as compared to a region's own payoff is sufficient to establish the Grand Coalition. Expressed as a ratio of (NPV of) regional GDP, this level of concern is 0.3% or below for most regions; only

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for Eastern European Transition countries a level of 0.6% of regional GDP is required. In a public goods game a Grand Coalition would implement an efficient policy. Hence, with well-designed institutions (transfer schemes) and with a moderate degree of political altruism directed at those who share the concerns about climate change, the mitigation problem can be effectively tackled. Acknowledgments We thank Matthew McGinty and two anonymous reviewers for their valuable comments and we are indebted to our collaborators in the STACO project and in particular to Rob Dellink for supporting this research. Appendix A We prove that for a superadditive valuation function V with positive spillovers altruism strengthens internal stability in a setting without transfers and with limited altruism, 1 ≥ α ≥ β ≥ 0. Consider an internally stable coalition S in the standard game such that Eq. (7a) holds. From Eq. (7c) we observe directly that positive spillovers foster internal stability whenever β > 0. Hence when Eq. (7b) is positive all three differences (Eqs. 7a, 7b, 7c) are positive and S is also internally stable under altruism. The critical case is when Eq. (7b) is negative. In that case, for internal stability to hold under altruism the loss to other coalition members must be overcompensated by i's gain. This follows from superadditivity. Superadditivity requires V S ðSÞ≥V i ðS n figÞ þ ∑ V j ðS n figÞ: j∈Snfig

Splitting the coalition payoff on the left hand side gives V i ðSÞ þ ∑j∈Snfig V j ðSÞ≥V i ðS n figÞ þ ∑j∈Snfig V j ðS n figÞ⇔V i ðSÞ −V i ðS n figÞ≥ ∑j∈Snfig V j ðS n figÞ− ∑j∈Snfig V j ðSÞ≥β ∑j∈Snfig V j ðS n figÞ −α ∑j∈Snfig V j ðSÞ;

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