The Stability and Effectiveness of Climate Coalitions

Abstract

We report results from a comparison of numerically calibrated game theoretic integrated assessment models that explore the stability and performance of international coalitions for climate change mitigation. We identify robust results concerning the incentives of different nations to commit themselves to a climate agreement and estimate the extent of greenhouse gas mitigation that can be achieved by stable agreements. We also assess the potential of transfers that redistribute the surplus of cooperation to foster the stability of climate coalitions. In contrast to much of the existing analytical game theoretical literature, we find substantial scope for self-enforcing climate coalitions in most models that close much of the abatement and welfare gap between complete absence of cooperation and full cooperation. This more positive message follows from the use of appropriate transfer schemes that are designed to counteract free riding incentives.

1 Introduction

1.1 Motivation

This paper reports results from a comparison of models that explore international coalitions for climate policy. These models investigate the incentives of different nations to commit themselves to a climate agreement and examine the extent to which climate agreements are stabilized when participation is driven only by the self-interest of its members.

International climate policy suffers from the adverse incentive structure of public good provision, and it is well known that non-cooperative behavior results in under-provision of such goods. How much a climate coalition improves upon this dilemma depends on the costs and benefits of the individual nations. It is particularly dependent on their heterogeneity and whether nations can compensate each other, i.e. the existence of transfer schemes.

In this paper we investigate this for the first time using an ensemble of five numerical models of climate coalition formation. Numerical models give particularly valuable insights beyond those of their analytical counterparts, when the analysis depends on regional heterogeneities in costs and benefits, quantitative estimates (i.e. their order of magnitude), or detailed representations of reaction functions.

The models in this study are diverse both in their modeling approaches and in the data sources used for calibration, representing a range of estimates for the costs and benefits of real-world regions and their dynamics. Consequently, the models do not necessarily agree in their assessment of the stability of specific coalitions.

The aim of this study is to make the differences in the underlying assumptions of costs and benefits, and their implications for key model results, transparent. We quantify these differences using new, model independent metrics, and we subsequently ask what these metrics can contribute to understanding diverging coalition stability results and the effect of transfers across the models.

Early theoretical investigations of coalition stability have often begun with the assumption of identical (symmetric) players. This has resulted in a pessimistic assessment of the scope of self-enforcing agreements to improve cooperation on international environmental issues. In their seminal paper Carraro and Siniscalco (1993) find stable coalitions to be generally small in size. While stable coalitions may be large in the model setup of Barrett (1994), this only holds if the gains from cooperation are small. Much of the ensuing research has investigated this dilemma and ways around it.¹

The theoretical potential for transfer payments to increase participation and environmental performance of a coalition has been long known (Carraro and Siniscalco 1993). Yet when real world heterogeneity is included, transfers that do not consider strategic implications are unlikely to improve an agreement and may even damage its success (Weikard et al. 2006; Nagashima et al. 2009). In contrast, transfers designed specifically to make cooperation more attractive than the free-riding alternative greatly improve the success of coalitions (Carraro et al. 2006; Nagashima et al. 2009; Weikard 2009). Similarly, McGinty (2007) shows the beneficial effect of such transfers within the modeling framework of Barrett (1994).

Regardless of the design of transfers, the asymmetries in the costs and benefits of climate policy are shown to be important for the achievement of cooperation. Barrett (2001) stresses that asymmetry of players complements the effect of transfers; together, asymmetry and transfers may well improve cooperation. Weikard (2009) shows that higher levels of participation under transfers that target the free-riding incentive are spurred by stronger asymmetry among the coalition members, including the possibility of full cooperation. Fuentes-Albero and Rubio (2010) confirm this and show that differences in marginal damages (rather than abatement costs or the level of damages) are key to this result. Recently Karp and Simon (2013) obtained comprehensive results showing how the functional specification of costs and benefits of abatement impacts on the equilibrium coalition size.

While these studies firmly establish a more optimistic prospect for cooperation and highlight the importance of heterogeneity, the degree of asymmetry often remains a conceptual assumption. Notable exceptions are Carraro et al. (2006) and Nagashima et al. (2009), which rely on integrated assessment models to quantify asymmetries.

To improve the understanding of real-world asymmetries, both the mechanics and the calibration of the models are of central importance. However, the uncertainties are large, both within each model (most prominently concerning model parameters) and between models (concerning model structure). Previously, the issue of how uncertainty and the prospect of future learning about climate change impacts affects international cooperation, has been addressed by including uncertainty in the structure of the coalition formation game (Kolstad and Ulph 2008, 2011; Finus and Pintassilgo 2013). In this paper, uncertainty is reflected in the diversity of assumptions of the models compared. The strength is threefold: it makes uncertainty more transparent; it helps identify robust results across modeling assumptions and parameterizations; and it enables us to learn from the differences.

Our contribution is a better understanding of the well-known cooperation failure, particularly in the heterogeneous setting provided by these numerical models. In addition, we identify transfers and assess their magnitude and direction when used as a tool to enhance cooperation.

1.2 International Climate Agreements

Central to this study is the concept of “self-enforcing agreements” or “coalition stability”. A climate coalition is a subset of the world’s regions that agree to cooperate on climate change mitigation policies. More specifically, we assume that within the coalition, climate change is addressed in an efficient manner, i.e. in a manner that maximizes coalitional welfare.² The coalition adopts a joint climate policy and interacts with the remaining regions as a single player. Each player is assumed to act selfishly with respect to the others.

Coalition formation is hence modeled as a game with two stages: a “participation stage game,” where players decide to either become members of the coalition or to remain outside; and an “emission stage game” where players choose economic strategies which (directly or indirectly) determine the emissions and abatement of greenhouse gases. Strategies therefore result from a combination of the membership decision in the first stage and the economic strategies of the players in the second stage of the game.³ This setup is similar to the Partial Agreement Nash Equilibrium (PANE) concept introduced by Chander and Tulkens (1995).

The equilibrium concept in stage 1 is cartel stability (d’Aspremont and Gabszewicz 1986) in all models. A coalition is considered “stable” if it satisfies two conditions. First, it is internally stable, meaning that no member is willing to leave the coalition. Second it is externally stable, meaning that all non-members prefer to remain singletons.⁴ Formally, any given coalition $S$ is stable if for the payoff of player $i$ facing coalition $S$, $\pi _i(S)$, we have:

$$\begin{aligned} \pi _i(S) \ge \pi _i(S\setminus \{i\})\quad \text{ for } \text{ all } i \in S, \quad \pi _j(S) \ge \pi _j(S\cup \{j\})\quad \text{ for } \text{ all } j \notin S \end{aligned}$$

(1)

Cartel stability allows us to analyze the whole range of partial cooperation. Note that the notion of “core stability” was simultaneously developed for this class of models (Chander and Tulkens 1995). Core stability derives directly from classical cooperative game theory. Its specific properties are quite different from those of cartel stability so its analysis is left for future research but the tools that facilitate this model comparison are also applicable to core stability, see Kornek et al. (2014) and footnote 13. We refer the interested reader to Bréchet et al. (2011) who take a comparative look at both concepts.

Thus building solely on cartel stability, we aim to explore the drivers of cooperation. In particular we also examine the effects of transfer schemes on the prospects for cooperation. To investigate transfers, we employ the concept of potential internal stability (PIS, as defined in Carraro et al. 2006). A coalition is said to satisfy the PIS property if a transfer scheme exists that can redistribute payoffs within the coalition such that the coalition is internally stable. Formally, PIS requires the existence of a vector of transfers $\tau _i$ with $\sum _i \tau _i = 0$ such that:

$$\begin{aligned} \pi _i(S) + \tau _i \ge \pi _i(S\setminus \{i\})\quad \text{ for } \text{ all } i \in S \end{aligned}$$

(2)

Note that simple addition of transfers is only appropriate in models with transferable utility. For models that do not assume transferable utility but feature a transferable commodity (e.g. consumption), transfers can be implemented at the commodity level. Here, a transfer scheme consists of a redistribution of the commodity between regions for each time period.⁵

The rest of the paper is structured as follows. An overview of the different integrated assessment models used in this analysis is given in Sect. 2. Section 3 focuses on the role of transfers. Section 4 summarizes results and concludes.

2 Characterization of the Models

In all models in this study, economic strategies are derived with respect to climate change mitigation from a dynamic optimization framework. Each model combines the two level game described above with an integrated climate economy model in the second stage. These models are solved numerically, and thus their parameters need to be calibrated. Reflecting uncertainty in knowledge over climate change economics, calibration varies with the different empirical estimates of costs and benefits of climate change abatement used for the specific models. More detailed information on the models can be found in Appendix; model equations are documented in Online Resource 1.

In the Stability of Coalitions model (STACO) each region’s monetary payoff equals regional benefits (avoided damages) less costs of abatement (Nagashima et al. 2009, 2011). The time dependence of both benefits and costs is calculated through an approximation of a Ramsey type growth model (Ramsey 1928). STACO does not model the consumption/savings decision endogenously. Instead it uses exogenous baseline projections for economic development and carbon emissions.

The other four models determine each region’s payoff through the use of dynamic, long-term, perfect foresight, Ramsey-type optimal growth models which determine savings behavior and abatement endogenously.

The first multi-region economic-climate model following this approach was RICE (Nordhaus and Yang 1996) and we use an updated version in this study (Yang 2008). RICE examines the relationship between economic growth, greenhouse gas emissions and climate change by explicitly modeling the stock of emissions in the atmosphere and the resulting global temperature.

Closely related to this is the ClimNeg World Simulation (CWS) model, a modified version of the RICE model, updated with new data on its cost and damage parameters (Eyckmans and Tulkens 2003; Eyckmans and Finus 2006; Bréchet et al. 2011). As one of its prominent distinctions, the payoff in CWS is in monetary units rather than an abstract utility metric, which facilitates an implementation of transfer payments at the payoff level.

The Model of International Climate Agreements (MICA) follows the same economic framework as RICE but with different assumptions about costs and benefits. Formally, its main distinction is to include the international goods markets (Lessmann et al. 2009; Lessmann and Edenhofer 2011; Kornek et al. 2013).

The aforementioned models rely on stylized abatement cost functions to model emissions reductions. In contrast, WITCH incorporates an explicit representation of mitigation options, particularly in the energy system (Bosetti et al. 2006). With this level of detail comes a trade-off: the higher computational complexity necessitates the use of selected coalitions.

2.1 Non-cooperative and Fully Cooperative Solutions

The modeling assumptions, model structures, and data sources of the five models reflect quite different views of the world economy and its development (see Table 1). A key difference between the models is the way they value the present against the future. For monetary values such as abatement costs or climate change damages, this is determined by each models’ endogenous interest rate. Simple Ramsey models suggest that this interest rate depends on the pure rate of time preference and, if the intertemporal elasticity of substitution is strictly positive, on consumption growth. This follows from the Keynes–Ramsey rule $\dot{c}/c = 1/\eta \; (r-\rho )$ with per capita consumption $c$ and $\dot{c}$ its derivative with respect to time, and two preference parameters: the elasticity of marginal utility $\eta$ and pure rate of time preference $\rho$. At the interest rate $r$ households are indifferent between one unit now or $(1+r)$ units later. Table 1 (top section) shows how models differ in their preference parameters.

Table 1 Modeling assumptions and key numbers of non-cooperative equilibrium and fully cooperative solution

Together with assumed projections of technological progress, these preference parameters determine the growth rates of economic output (Table 1, middle section) which range from 1.2 to 2.1 % per year over the first century. The pure rate of time preference is highest for MICA, WITCH, and RICE at 3 %, which has a direct consequence on the interest rates in these models (around 5 %).⁶ For these models, all costs and benefits occurring in the future will be discounted at this higher rate. For STACO, the pure rate of time preference is lower (at 1.5 %) but the (exogenous) assumption of relatively strong growth in the coming decades leads to a high initial discount rate, especially for emerging economies, which declines over time to values of around 3 %, giving an average of 4.2 %. Finally, in CWS the interest rate, at 1.5 %, is the same as the pure rate of time preference, which is the lowest of all the models.

A non-cooperative equilibrium is one where no coalition forms. In the non-cooperative equilibrium, greenhouse gas emissions are of the same order of magnitude in all models, with moderately lower values in MICA and RICE. As regional damages are internalized in the non-cooperative equilibrium, emissions are lower compared to a hypothetical case without damages. We measure these emission reductions relative to a no damage business-as-usual scenario (BAU) and find that they are of comparable magnitude in 4 out of 5 models (about 10 % of emissions), and 5 % in RICE.

In the cooperative solution for the grand coalition, emissions are substantially lower than those in the non-cooperative equilibrium (Table 1, bottom section). This is again with the exception of RICE, which is probably due to the extent of climate change damages. In the other models, emission reductions bring down climate change damages by several percentage points in 2100. In STACO and WITCH in particular, high damages occurring in the non-cooperative equilibrium are reduced by about 4 % points. In contrast, the formation of the grand coalition in RICE leaves climate change damages almost unchanged. When we derive a metric for damages in the next sections, we will see that damage estimates are indeed relatively low in RICE.

2.2 Cost/Benefit Information

In this section, we introduce two metrics to characterize the severity of climate change damages and abatement costs in the models, both globally and on the regional scale. Perhaps the most intuitive metric would be to compare marginal cost functions and marginal damage functions. Unfortunately this information is not easy to extract from, or make comparable between, the models. Instead we propose alternative metrics based on model output rather than assumptions regarding functional forms and parameter values.

2.2.1 Measuring Marginal Climate Change Damages

Figure 1 compares aggregate discounted damages in the non-cooperative equilibrium across the models. The figure highlights that the damage calibration is low in RICE, also reflected in the relatively low carbon price in the cooperative solution; the average price in 2100 is 208 $/tC compared to a range from 369 to 966 $/tC in the other models (Table 1). ⁷

Fig. 1

Aggregate damages 2015–2100 in the non-cooperative equilibrium in trillion US$, discounted at the model specific discount rates

In order to compare the marginal damages from climate change between regions for each model, we take a slightly different approach to that provided by the total damages shown in Fig. 1. Instead, we say that a region has high marginal damages if the carbon price of the grand coalition is significantly reduced when the region in question leaves. The impact on the coalitional carbon price is a good indicator of how much the region is affected by climate change; this region’s damages are reflected in the carbon price if and only if the region is part of the coalition.

We take the discounted sum of this carbon price difference for each region in the grand coalition compared to the sub-coalition when the one region in question is leaving, and average the differences. Taking the average only matters when coalitions do not establish a uniform carbon price, which is the case for WITCH and RICE. We normalize this metric to the maximal difference over all regions (Fig. 2).

Fig. 2

Climate change damages and abatement potential indicators scaled to $[-1, 1]$. The climate change marginal damage indicator for a particular region was calculated by taking the average of the difference in discounted carbon prices of the grand coalition and the grand coalition minus the particular region at hand. This indicator was normalized relative to the maximum average difference over all regions. Abatement potential was calculated by implementing a common carbon tax trajectory for all regions in every model. The resulting abatement trajectory (measured in tons) was integrated over each model’s time horizon and scaled according to the maximum abatement level. Model regions are specified in Appendix 1

Each model yields a different distribution of marginal damages across regions. In particular there is no agreement between the models about the region incurring highest marginal damages. This reflects the fact that the assumptions made by the models about the regional distribution of damages differ greatly. These differences concerning the marginal damage assumptions are a primary driver of the results of the comparison.

2.2.2 Measuring Regional Marginal Abatement Costs

For our metric of regional abatement costs, we look at the cumulative emissions reduction in each region at a uniform carbon price. Higher emissions reductions at such a global carbon price signal a flatter marginal abatement cost curve up to this point, and hence lower abatement costs for a prescribed abatement target. Since high figures indicate low marginal costs, we talk about this metric as being the region’s “abatement potential”.

Technically, all models implement the common carbon price scenario by imposing the same global emissions tax trajectory under conditions of disabled climate change damages. The cumulative abatement is the absolute emissions reduction, summed over each model’s time horizon.

We find the global abatement potential to be largest in case of MICA, followed by WITCH, STACO, CWS, and RICE in declining order. Only about two thirds of the abatement prescribed by MICA are achieved in RICE. Despite this, we see that the potential and hence abatement costs are of the same order of magnitude in all five models.

Figure 2 shows the abatement potential indicator for each model. The abatement potential indicator is the tax scenario normalized to the maximum abatement level over all regions. The indicator shows that China and India always rank high on abatement potential while for Japan the mitigation costs are perceived to be amongst the highest. We will use the information from this table extensively when discussing the main objectives of this paper: incentives of specific regions to join a climate agreement and the characterization of transfers. In general, one can say that the models seem to be in good agreement over their assumptions on the costs of abatement.

2.3 Incentives of Regions

The incentive to remain in a coalition (or in short: incentive to stay) is defined as the payoff received as a member of a given coalition minus the payoff of being outside the coalition (i.e. as a free-riding non-member). For the following discussion, we want to structure the driving forces that determine the incentive to stay for a given region in the following way:

• 1. First, the benefit of joining the coalition, which is in turn influenced by:

  • (a) the extent of climate change damages in this region. When a region joins the coalition, any damages it incurs are henceforth internalized by all coalition members. Thus, the higher the marginal damages in the joining region, the greater the abatement of the coalition as a whole. Any region benefits from such additional abatement, and this is particularly pronounced for a region with high marginal damage.

  • (b) the response of non-members. For example, the free-riding non-members are likely to raise their emissions in reaction to the reduced emissions of the coalition. Such “leaked” emissions offset the abatement of the coalition and therefore reduce the benefit of joining such a coalition.

• 2. Second, the additional costs incurred by the region upon joining the coalition. We distinguish the abatement costs of a coalition member and other opportunity costs as follows:

  • (a) abatement costs are a result of the distribution of emission reductions which are determined by efficiency in abatement (i.e. the lower the marginal costs, the more a region needs to abate), and the overall ambition of the coalition, which depends on the collective marginal climate change damages of all coalition members.

  • (b) other opportunity costs emerge when regions are coupled through more channels than just the externality. For example, when carbon pricing affects the world demand for fossil resources, price changes in such resources will represent a cost of participating in the coalition for net exporters of such fuels.

The extent of 1a and 2a in the models is covered by the indicators derived above and summarized in Fig. 2. We will see that often these indicators suffice to understand model behavior. Before we take a look at the incentives, we discuss how damages, abatement and leakage vary by considering the OECD coalition. For our purposes, all regions generating at least half their economic output from OECD countries are considered members of this coalition.

2.3.1 Distribution of Damages

The extent to which a region benefits from abatement is measured through the carbon price (see discussion of Fig. 2). Figure 3 reports the percentage decrease in abatement price when a nation leaves the OECD coalition.⁸

Fig. 3

Carbon price in the OECD coalition (as average net present value). Percentages indicate how climate change damages in the member regions contribute to the overall carbon price

The absolute level of the carbon price, given above each bar, shows the ambition in the coalition’s emissions reductions across the models. In the case of the STACO model, the OECD coalition combines regions with high damages. This makes the carbon price of this coalition very high, and free-riding on this coalition’s abatement very attractive. In contrast, the ambition of the OECD coalition and hence the incentive to free-ride is much lower in MICA.

There is reasonable agreement across the models that it is the USA and Europe⁹ which contribute the most to damages: they both score highly in every model. The USA and Europe would therefore gain much from the abatement undertaken by the coalition. Their share of coalitional abatement must, of course, be taken into account to determine the incentive of these regions.

2.3.2 Distribution of Abatement

There are many ways to distribute overall abatement amongst the members of climate coalitions, guided by many criteria, e.g. pragmatic, normative or incentive compatible. The default distribution in coalition models is normative: the maximization of coalition welfare.¹⁰ We follow this approach.

Figure 4 shows that the OECD coalition’s total abatement over the first century is quite different across the models, partly because the composition of the coalition is different between models. However, since differences turn out to be large even when regions are identical, we conclude that much of the variation in abatement allocation is due to different cost and benefit assumptions.

Fig. 4

Allocation of emission reductions in the OECD coalition as percentages of overall emissions reduction, the time horizon is one century

The distribution of abatement for a given country varies substantially across the models. For example, the USA share falls anywhere within the range of 20–60 %, that of Japan between 1 and 18 %, and for Europe within the range 10–30 %. All models agree that the largest share of abatement ought to be achieved in the USA, often followed by Europe.¹¹

2.3.3 Leakage Emissions

Carbon emissions are said to “leak” out of the climate coalition if non-members increase their emissions in response to the coalition’s abatement. The amount of leakage depends on the sensitivity of the reaction functions of nations not in the coalition. These reaction functions depend largely on model features that determine the ways in which non-members are affected by the coalition.

There is zero leakage in STACO. This is a consequence of assuming constant marginal damages, which implies that abatement is chosen independently by each region. In all other models, the regions react to the abatement decisions of the others. MICA, CWS, and RICE show only very moderate leakage: leakage rates per region are less than 1 % of the coalition’s abatement (not shown).

Regions in WITCH show the strongest free-riding behavior in terms of leakage, with total leakage rates of 16 % of the OECD’s coalition abatement (not shown). In WITCH, the coalition affects non-members through an additional channel: energy markets (see Bosetti and De Cian 2013, for details). The coalition’s abatement effort drives down oil prices and free-riders increase their consumption of the carbon-intensive oil grades in particular.

2.3.4 Overall Incentives

The interplay of all the drivers discussed above jointly shapes the incentive to join or leave a given coalition. We consider the OECD coalition and the grand coalition in turn.

Figure 5 shows the incentive to stay inside the OECD coalition for its members. If the incentive to stay was positive for all members, the coalition would be internally stable without transfers. Conversely, the figure shows which regions are responsible when the OECD coalition fails to be internally stable in any of the models. For easy reference, the indicators of abatement potential and climate change damages from Fig. 2 are repeated in Fig. 5.

Fig. 5

Incentive to stay in the OECD coalition, calculated as the difference between inside and outside payoff and scaled to the gap in global aggregated payoff between non-cooperative equilibrium (=0) and cooperative solution for grand coalition (=100). The inset tables list the regional indicators of climate change damages and abatement potential, denoted “D” and “A”, respectively

While the models all agree that the OECD coalition is not internally stable, each model suggests that different regions want to leave the coalition. For example, the USA would support the OECD coalition in MICA and CWS, but would not support it in STACO, WITCH, or RICE.

In general, low abatement potential and high marginal damages have a positive effect on the incentive to stay. Low abatement potential indicates a steep marginal abatement cost function and therefore a low mitigation burden. High marginal damages indicate that a region will benefit much from increased coalitional abatement.

According to this logic, the incentives for Europe appear relatively simple: in all models Europe is a coalition member characterized by relatively high marginal damages and low abatement potential. Such players have much to gain from cooperation, but have low costs as their share of the mitigation burden is small. The models therefore agree that Europe would want to remain in the OECD coalition.

This is not the case for the USA, which has a strong motivation to defect from the OECD coalition. This is because the USA’s estimated abatement potential is high, which means that the USA would carry a large share of the emission reductions in the coalition. In fact three of the models find that the USA would not support the OECD coalition (STACO, WITCH, and RICE). In MICA and CWS however, the costs are more than compensated for by large benefits. In these models the USA incur the highest marginal damages of all coalition members and thus have an incentive to remain in the coalition. It also helps that in these two models the ambition level of the OECD coalition is low, resulting in a low burden for its members as most high marginal damage regions are outside the OECD coalition.

Japan is modeled as a single country region in three of the five models. The models unanimously see little abatement potential in Japan alone, mainly due to the relatively small size of its economy. Thus Japan would carry only a small burden, which makes it better off inside the coalition in MICA and STACO. In CWS, the estimated marginal damages are also very low for Japan. Japan can therefore defect (and save on abatement costs) without substantially lowering the ambition level of the coalition, which turns out to be preferred by Japan. The larger Canada/Japan/New Zealand aggregate region of WITCH incurs substantial abatement costs, tipping the balance towards defection as marginal damages are only average compared to the other OECD players.

Moving to the grand coalition, positive net incentives to stay become rare (not shown). This is a consequence of more ambitious emission reductions in this coalition, which places a larger burden on all members. The few exceptions are either of the high damage/low burden type discussed above (e.g. Japan and Europe in STACO, and Sub Saharan Africa (SSA) in WITCH) or very large players (ROW in CWS and RICE). The latter aggregate much of the world’s damages and abatement potential due to their sheer size.

In WITCH, net revenues from trade in oil are part of the region’s income and an additional driver of incentives. Coalitions that strongly abate emissions consume substantially less oil leading to a drop in prices. In turn, this increases the outsiders’ consumption. Therefore oil-rich regions, while cutting their own oil consumption when joining the coalition, receive large revenues. Interestingly, the model shows that extraction does not change very much and the price differences are only minor. However, the pattern of consumption changes between different grades of oil, leading to increased exports of low carbon intensive grades. The top three regions showing the strongest increase in oil revenues prefer to stay in the grand coalition.¹² This effect is negative for the regions Canada/Japan/New Zealand and South Korea/South Africa/Australia.

3 Transfers

3.1 Stable Coalitions

In this section, we compare two stability concepts without transfers (internal/external stability, IES, and internal stability, IS) with potential internal stability (PIS).¹³ Table 2 shows the number of stable coalitions for each stability concept, along with maximum coalition size, maximum abatement achieved and maximum welfare achieved. For the latter two measures, we use the “closing the gap” indicator to characterize the performance of coalitions. This indicator relates global emission reductions and welfare to the gap between the non-cooperative equilibrium – set to zero – and to the cooperative solution for the grand coalition, set to unity (cf. Eyckmans and Finus 2007).

Table 2 Stable coalitions for internal/external stability and potential internal stability

We find coalitions that are internally/externally stable to be small and achieve little, which is in line with existing literature. CWS is an interesting exception: the best internally/externally stable coalition achieves 77 % of the global welfare gains of the grand coalition. This is due to the very large region ROW which enables a two player coalition to abate a large share of global emissions. The best performing coalition that does not include ROW achieves a closing the gap indicator for welfare of only 21 %.

When we focus on internal stability alone, more coalitions are stable, and their performance improves. We highlight two observations: first, participation remains almost unchanged (with the exception of an increase from 3 to 4 players in one model, MICA); second, the performance improvement when ignoring external stability is substantial for some models, and negligible in others.

Turning to coalitions with PIS, the transfers implicit in this concept have a strong effect: the number of stable coalitions increases by 1–2 orders of magnitude. The corresponding improvement in the closing the gap indicator is also large. The CWS model even finds the grand coalition to have the PIS property. In MICA, STACO, and WITCH, PIS transfers improve the closing the gap indicator from single digit values to values roughly half that of the grand coalition (47, 68, and 38 %, respectively). In STACO, the coalition with PIS generating the highest global welfare is not only internally stable after receiving the implied transfers but is also externally stable.¹⁴

Thus, the model comparison shows that transfers exist that make it possible to stabilize coalitions that substantially close the welfare gap. This is a considerably more optimistic message than the traditional conclusion derived from analytical models so far. With our multi-model approach, we conclude that this claim is robust with respect to modeling approaches and parameterizations.

3.2 Transfers and Stable Coalitions

The PIS transfers in the preceding section are determined by stability considerations. In contrast, transfers based on conventional burden sharing rules (Table 3) are designed to be either equitable or pragmatic. How does this departure from incentive compatibility affect the ability of conventional burden sharing schemes to induce stable coalitions?

Table 3 Permit allocation schemes

To evaluate how burden sharing affects stability of coalitions, we convert permit allocations to monetary transfers using the carbon price of the coalition. The monetary transfers are added either to the consumption streams or payoff (in case of CWS and STACO).¹⁵

In a first look at the implications of the conventional transfer schemes, we analyze how a selection of four schemes from Table 3 affects internal stability. Table 4 shows the number of internally stable coalitions under these transfers and how this number changes in relation to the scenario without transfers.

Table 4 How transfers affect coalition stability

The main conclusion is that transfer schemes that were designed without coalition stability in mind have an almost unanimously adverse effect on stability. This is evident from the decrease in the number of internally stable coalitions (cf. the almost exclusively negative numbers in the column ${\varDelta }$coal). An exception is “grandfathering” in CWS.

In Table 5 we compare two additional statistics of the conventional transfer schemes to the PIS-transfers to investigate the poor performance of conventional transfer schemes. The first column of each model shows the share of members of coalitions with PIS where the direction of transfers coincides with PIS transfers i.e. regions that need a positive transfer are receivers. By definition, PIS transfers reach the perfect score of 100 % and other transfers score lower.

Table 5 Permit transfer schemes compared to PIS-transfer schemes

We find that most conventional transfer schemes stay well below 100 % for this indicator and often around 50 % or lower. Most models find that specific transfer schemes do better; however, the models disagree on which transfer scheme performs best.

The second column displays the average flow of money between the regions across the ensemble. Models agree that the stability-enhancing PIS-transfers need relatively small flows of money. Of the other schemes, transfers for “quota BAU” and “grandfathering” are roughly in the same order of magnitude. These two schemes often also score high on the direction indicator. In the other transfers schemes, more money is transferred than is necessary for internal stability.

Thus, we have identified two problems of the conventional transfer schemes with respect to their negative effect on stability, namely the direction of the induced transfers and their magnitude.

To investigate how PIS transfers depend on the properties of coalition members, we relate properties of coalition members to the frequency with which they receive a positive transfer. The results are found in Table 6.

Table 6 Characterization of PIS transfers with properties of players

We find significant agreement between the models regarding the relationship between damages and transfers. The more damages a region incurs from climate change, the more likely it is that this region has a surplus to share with other members, i.e. PIS transfers will be negative. We find no significant correlation between transfers and either abatement potential or abatement per unit damage, although the results do indicate that in most cases the direction of the relationship is the same.

4 Summary and Conclusions

We have compared five different models to explore the stability and performance of international coalitions for climate change mitigation in a setting where regional heterogeneity reflects real-world asymmetries of regions. To facilitate comparison of the impact of modeling assumptions on the costs and benefits of mitigation we developed two indicators measuring, first, the regional abatement potential and, second, regional exposure to climate change damages. While the models’ estimates for abatement potentials are in agreement for key world regions, we find substantial differences in the climate change damage estimates that the models produce for certain regions. To a large extent, the differences reflect the variations in the literature sources upon which the model parameterizations are based, and therefore they reflect the uncertainty over costs and benefits of climate change mitigation in the literature (cf. Metz et al. 2007).

It is therefore not surprising that the models differ in their assessment of whether certain coalitions are stable, and whether certain world regions or nations have an incentive to be members of a given coalition. A notable exception is the assessment of the EU, for which all the models unanimously attest an incentive to support a coalition of OECD countries. However, when we turn from the identity of the players to their cost-benefit characteristics in terms of the two indicators suggested in this study, the models are remarkably consistent in their predictions. We find that the indicators of a region’s abatement potential and its exposure to climate change damages substantially reflect its incentives and allow us to understand its preference for or against membership in a coalition. When regional abatement potential is low (implying a steep marginal abatement cost function) or regional marginal climate change damages are high, there is a greater chance for a positive incentive to stay in a coalition.

In the absence of transfers, all models agree that stable coalitions tend to be small and achieve little, due to a lack of internal stability of larger, more ambitious coalitions. This is in accordance with the theoretical literature and therefore not surprising.

Transfers designed to minimize free-riding incentives as far as possible achieve much more: the models find that coalitions with PIS are substantially larger than internally stable coalitions and achieve about half or more of what full cooperation would achieve both in welfare and in terms of greenhouse gas abatement.

In contrast, conventional transfer schemes do not improve cooperation; they often even undermine existing stable coalitions. The reason is, of course, that conventional transfers do not reflect incentives; among other things they are frequently too large in magnitude and transfer wealth in the wrong direction, i.e. regions that need transfers to be convinced to stay in a coalition are effectively paying regions that have no incentive to defect from the coalition. Conversely, we conclude that when transfers are designed to take incentives into account, the financial flows need to be small compared to the cases, for example, of an allocation based on historic emissions.

Finally, we examine how the properties of coalition members affect the PIS transfers necessary to stabilize the coalition. We find that players with high damages tend to benefit enough from cooperation to allow them to share some of the gains, and thus compensate those players with high abatement potential that provide the necessary mitigation.

For future research, there are several possible extensions of this analysis. First, our stability analysis focused on one particular non-cooperative concept (internal/external stability) but could be extended to alternative game theoretic stability concepts.

Second, we found that on many issues, the different models were remarkably unanimous. However, where results were substantially different it could be argued that this is caused by differences in assumptions. In this paper we preferred to represent a broad range of possible future economic dynamics. More insights into the modeling details, or the parameters causing models to diverge in their assessment could, however, be gained by a close harmonizing of baseline assumptions of the models.

Third, our analysis has stressed that assumptions on climate change damages are very influential but at the same time highly uncertain. This concerns both the data and the modeling. Additional empirical studies on the economic impact of climate change are badly needed, and the modeling of climate change damages could be improved beyond the standard assumption found in the participating models.

Appendix: Model Factsheets

Model: MICA (Model of International Climate Agreements), PIK, Germany
Model description: Kornek et al. (2013)
Model concept	Solution method
Multi-region optimal growth model with climate externality and international trade	Competitive equilibrium, full internalization of climate change damage within the coalition; implemented as non-linear optimization problem solved with a modified Negishi algorithm
Welfare concept	Parametric specification
Discounted utilitarianism in each region, joint welfare maximization with constant Negishi weights for the coalition	Pure rate of time preference $\rho = 3$%, elasticity of marginal utility $\eta = 1$
Markets and Trade	Model anticipation
Consumption good	Perfect foresight
Number of region: 11
AFR     Sub-Saharan Africa without South Africa
CHN    China
EUR     EU-27
IND     India
JPN     Japan
LAM    All American countries except Canada and the United States
MEA    North Africa, Middle Eastern and Arab Gulf countries, resource exporting countries within the former Soviet Union, and Pakistan
OAS     South East Asia, North Korea, South Korea, Mongolia, Nepal, Afghanistan
ROW    Australia, Canada, New Zealand, South Africa and non-EU27 European states except Russia
RUS     Russia
USA     United States of America
Base year	Time horizon and step
2005	2005–2195, 10 years
Climate	Climate change
Greenhouse Gases: CO$_2$	Temperature response model
	Carbon dioxide concentration (ppm)
	Temperature change ($^{\circ }\hbox {C}$)
Mitigation options	Climate impacts
Abatement cost function for CO$_2$ based on mitigation cost information from the REMIND model (Luderer et al. 2013)	Region-specific quadratic damage function in temperature increase
	Damage as [%] of GDP based on Fankhauser (1995) following Finus et al. (2006)
Land use	Resources considered
—	—

Model: STACO-3 (Stability of Coalitions), Wageningen University, The Netherlands
Model description: Nagashima et al. (2011), Dellink et al. (2015)
Model concept	Solution method
Combined game-theoretic and integrated assessment model with regional benefits (avoided damages) and abatement costs of greenhouse gas emissions	Partial agreement Nash equilibrium between signatories and singletons
Welfare concept: Discounted net present value of regional payoff in each region, joint payoff maximization within coalitions; no full welfare evaluation but the Keynes–Ramsey rule used for discounting payoffs is consistent with a logarithmic utility function.	Parametric specification: Pure rate of time preference $\rho =1.5$%; implicitly $\eta =1$
Markets and Trade	Model anticipation
Carbon Trade is modelled as transfers between coalition members	Perfect foresight
Number of region: 12
BRA    Brazil
CHN China
EUR EU and EFTA (EU-27, Iceland, Liechtenstein, Norway, Switzerland)
HIA     High-income Asia (Indonesia, Malaysia, Philippines, Singapore, South Korea, Taiwan, and Thailand)
IND     India
JPN Japan
MES    Middle Eastern countries
OHI     Other high income countries (including for example, Australia, Canada and New Zealand)
ROE     Rest of Europe
ROW    Rest of the world
RUS     Russia
USA     United States of America
Base year	Time horizon and step
2011	2011–2106, 5 years
Climate	Climate change
Greenhouse Gases: CO$_2$, CH$_4$, N$_2$O, PFCs, HFCs, SF$_6$, based on EPPA-5 model to calibrate the regional GHGs BAU emission paths	CO$_2$-e concentration (ppm) Radiative Forcing (W/m$^2$)Temperature change (${^{\circ }\hbox {C}}$)
Mitigation options: Regional abatement cost functions for GHGs are based on regional cost parameters from the EPPA model (Morris et al. 2008)
Climate impacts: Benefits are calculated as the net present value of the stream of future avoided damages from a unit of abatement in the current period, taking regional GDP growth and inertia in the climate system into account (Nagashima et al. 2011). This function is calibrated to a simple climate module, based on the DICE model (Nordhaus 2008), but calibrated on the EPPA-5 model (Paltsev et al. 2005; Paltsev 2010). The linear global benefit function is based on estimates of climate damage by Tol (2009). Benefits are allocated across regions with a share for each region (Finus et al. 2006).
Land use	Resources considered
—	—

1. Notes: Exogenous technological change (annual efficiency improvement in abatement costs) is considered to be $0.5 - 2 \%$ per year (regionally differentiated)

Model: CWS (ClimNeg World Simulation model, Version 2.0), KU Leuven, Belgium
Model description: Bréchet et al. (2011)
Model concept	Solution method
Multi-region optimal growth model with climate externality, maximization of coalition welfare, internalization of climate externality for coalition members	Nash equilibrium of carbon emission game solved by tatonnement algorithm between coalition and non-members
Welfare concept	Parametric specification
Discounted utilitarianism in each region, coalition’s welfare maximization with equal welfare weights for all members	$\rho = 1.5$% (constant), $\eta = 0$ (linear in consumption)
Markets and Trade	Model anticipation
no trade in goods, trade in carbon emission permits (optional)	Perfect foresight
Number of region: 6
USA:    United States of America
JAP:     Japan
EU:     South East Asia
China:   China
FSU:    Former Soviet Union
ROW:    Rest of the World
Base year	Time horizon and step
2000	2000–2310, 10 years
Climate	Climate change
Greenhouse Gases: CO$_2$	3-box model of carbon cycle (atmosphere, lower and upper ocean)
	CO$_{2}$-e concentration (ppm)
	Radiative Forcing (W/m$^2$ )
	Atmospheric and ocean temperature change ($^{\circ }\hbox {C}$)
Mitigation options	Climate impacts
Exogenous emission efficiency improvement over time plus region-specific abatement cost functions (power functions, exponent 2.887)	Region-specific damage function, power function of atmospheric temperature change (exponent 3.0), damage as [%] of GDP
Land use	Resources considered
–	–

Model: WITCH (World Induced Technical Change Hybrid model, version 2012), FEEM, Italy
Model description: Bosetti et al. (2014)
Model concept	Solution method
Hybrid Optimal growth model, including a bottom-up energy sector and a simple climate model, embedded in a game theoretic setup	Regional growth models solved by non-linear optimization and game theoretic setup solved by tatonnement algorithm between coalitions and non-members (Nash equilibrium)
Welfare concept	Parametric specification
Discounted Utilitarianism, coalition’s welfare maximization with equal welfare weights for all members	$\rho = 3$% decreasing, $\eta = 1$ (log of consumption)
Markets and Trade	Model anticipation
Oil	Perfect foresight
Number of region: 13
CAJAZ:     Canada, Japan, New Zeland
CHINA:     China, including Taiwan
EASIA:     South East Asia
INDIA:     India
KOSAU:     South Korea, South Africa, Australia
LACA:     Latin America, Mexico and Caribbean
MENA:     Middle East and North Africa
NEWEURO:   EU new countries, CHE, NOR oldeuro: EU old countries (EU-15)
SASIA:     South Asia
SSA:     Sub Saharan Africa
TE:     Non-EU Eastern Europe, including Russia
USA:     United States of America
Base year	Time horizon and step
2005	2005–2150, 5 years
Climate	Climate change
Greenhouse Gases:	3-box model of carbon cycle
CO$_2$, CH$_4$, N$_2$O, HFCs, CFCs, SFs	CO$_2$-e concentration (ppm)
Aerosols considered: yes	Radiative Forcing (W/m$^2$ )
	Temperature change ($^{\circ }\hbox {C}$)
Mitigation options	Climate impacts
Abatement cost functions for non-CO2 GHGs	Region-specific damage function with linear and power function term with exponent 2.2 in the temperature increase Damage as [%] of GDP
Land use
Decarbonization options in the Energy system (Renewables, Nuclear, Biomass, CCS)
Land use	Resources considered
Emissions from land use change are considered	Coal, Oil, Gas, Uranium, Biomass

Model: RICE Regional Integrated model of Climate and the Economy, SUNY Binghampton, USA
Model description Yang (2008)
Model concept	Solution method
Multi-region Ramsey-type growth model with joint production of GHG emission that causes climate externality	the non-cooperative Nash equilibrium; cooperative solutions under various assumptions of incentive compatibilities; coalition solutions (called “hybrid” Nash equilibria in Yang (2008))
Welfare concept	Parametric specification
Discounted sum of regional utility functions.	Pure rate of time preference $\rho =3$%, elasticity of marginal utility $\eta =1$
Markets and Trade	Model anticipation
-	Perfect foresight
Number of region: 6
CHN    China
EEC     Eastern European countries and the former Soviet Union
EU     European Union
OHI     Other high-income countries
ROW    Rest of the world
USA     United States of America
Base year	Time horizon and step
2000	2000–2245 (5 years)
Climate	Climate change
CO$_2$ emissions and other exogenously set GHG emissions	the Schneider box model
Mitigation options	Climate impacts
Mitigation cost functions based on Nordhaus and Yang (1996) and updated with Yang (2008) which contains updates provided by Nordhaus	Climate damage functions based on Nordhaus and Yang (1996) and updated with Yang (2008) which contains updates provided by Nordhaus
Land use	Resources considered
exogenously set	Availability of fossil fuel resources at global level has been checked implicitly