Economic assessment of the development of CO2 direct reduction technologies in long-term climate strategies of the Gulf countries

This paper proposes an assessment of long-term climate strategies for oil- and gas-producing countries—in particular, the Gulf Cooperation Council (GCC) member states—as regards the Paris Agreement goal of limiting the increase of surface air temperature to 2°C by the end of the twenty-first century. The study evaluates the possible role of carbon dioxide removal (CDR) technologies under an international emissions trading market as a way to mitigate welfare losses. To model the strategic context, one assumes that a global cumulative emissions budget will have been allocated among different coalitions of countries—the GCC being one of them—and the existence of an international emissions trading market. A meta-game model is proposed in which deployment of CDR technologies as well as supply of emission rights are strategic variables and the payoffs are obtained from simulations of a general equilibrium model. The results of the simulations indicate that oil and gas producing countries and especially the GCC countries face a significant welfare loss risk, due to “unburnable oil” if a worldwide climate regime as recommended by the Paris Agreement is put in place. The development of CDR technologies, in particular direct air capture (DAC) alleviates somewhat this risk and offers these countries a new opportunity for exploiting their gas reserves and the carbon storage capacity offered by depleted oil and gas reservoirs.

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Victor Court

Introduction
This paper provides an assessment of the possible mitigation of the macroeconomic cost for the Gulf Cooperation Council (GCC) countries incurred if the Paris agreement goals are to be reached. In particular, we consider the possible contribution of Carbon Dioxide Removal (CDR) technologies in the definition of long-term strategies of the GCC countries to reach these goals. The CDR technologies considered include in particular Biomass Energy with CCS (BECCS 1 ) and Direct Air Capture (DAC 2 ) with carbon sequestration. The GCC countries 3 economies, largely based on oil and gas revenues, could be strongly affected in a worldwide drive toward a net-zero emissions regime, as implied by the Paris agreement. This objective could be reached by 2070, or even as early as 2050, as discussed in COPs 22-24. The contribution of this paper is mainly methodological and prospective. We do not discuss the negotiations leading to a new international agreement; rather we propose an original macroeconomic framework for assessing the role that CDR technologies could play in reaching a worldwide transition to net-zero emissions and their possible impacts on oil and gas exporting economies. 1 For a recent presentation and discussion of BECCS potential see [5] and [11]. 2 For a recent presentation and discussion of DAC see [22]. 3 Bahrain, Kuwait, Oman, Qatar, Saudi Arabia, and the United Arab Emirates.

2
The current stance of the GCC countries is to resist the international drive toward more rapid global abatement because it exposes them to a very high risk for stranded assets. Indeed, a recent IPCC report [37] presents several emission trajectories proposed by different integrated assessment models for abiding by Paris-agreement objectives. All these trajectories impose a very stringent abatement trajectory reaching net-zero emissions before the end of the century. Of particular interest to oil and gas producing countries, the Sky scenario -developed by Shell Corporation [40] -indicates also that the Paris agreement implies reaching net-zero emissions in 2050 (or 2070, at the latest), followed by a period where net-negative emissions occur with declining atmospheric CO 2 concentration. To reach this net-zero and then net-negative emissions, the Sky scenario proposes a profound transformation of energy systems. By 2070, solar will account for 32% of primary energy sources, and wind for 13%. Oil, natural gas and coal will account for 22% and will be associated with Carbon Capture and Storage (CCS). Additionally, and also associated with CCS, bioenergy will account for 14%. BECCS, which consists in a biomass-based combustion power plant with CO 2 capture, is the technology of choice for negative emissions in the Sky scenario. In this process, biomass absorbs CO 2 while growing, and then the power plant captures the CO 2 , therefore resulting in negative emissions. A drawback of choosing BECCS as the main negative emission technology is the logistics of production and transportation of biomass fuels, which will compete with food production and afforestation/reforestation [44]. This imposes stringent limits on any massive BECCS deployment. Another option -much costlier, but likely of strategic importance to oil and gas producing countries, and especially the GCC if a high carbon price is set worldwide -comes in the form of DAC. Developing DAC technologies as a standard industrial process, however, requires investment and is constrained by access to clean energy sources and CO 2 storage capacities.
Among several recently proposed scenarios for global, long-term strategies that comply with the Paris agreement, the DAC appears as a promising technology for attaining a net-zero emissions regime [31]. For example, [29], uses the MERGE-ETL model [27,26] to show that a DAC technology can play an important role in realizing deep decarbonization goals and in reducing regional and global mitigation costs. Indeed, under the 2°C and 1.5°C scenarios analyzed a DAC technology will capture 21 and 40 GtCO 2 , yearly by 2100, respectively; will attain a net-zero emissions regime by 2075 and 2040, respectively; and will be responsible for very large negative emissions at the end of the planning horizon. In these scenarios, the gas and oil producing countries of the Middle East are expected to have a compet-itive advantage in developing DAC because of their access to large carbon sequestration storage capacities. In this regard, a recently published paper [22] gives a complete feasibility and techno-economic assessment of a DAC technology, that uses natural gas for providing needed power and heat. As described, this represents another comparative advantage for the development of DAC technologies in gas producing regions: by transforming their natural gas endowment and sequestration capacity in depleted oil and gas reservoirs into negative emissions, the GCC countries and other oil and gas exporting countries could, if the price of carbon incentivizes it, have access to a new, high economic value resource -emission rights.
Inspired by the insights provided in [31,29], this paper focuses on GCC countries by building upon the results of a more encompassing macroeconomic model. We use a dynamic game formulation of the strategic competition among different groups of countries in reaching the Paris agreement objectives. Briefly, to assess the future price of carbon, we use a general equilibrium model, which evaluates the macroeconomic costs of long-term climate strategies for 10 groups of countries (the GCC being one of them). These groups of countries are defined as natural coalitions in climate negotiations that will almost certainly take place in implementing the Paris agreement. To represent possible competition among these groups of countries, we use a non-cooperative game model that describes the strategic supply of emissions rights in an international carbon market. Strategies for each group of countries include abatement decisions and developments in CDR technologies. The model assumes a transition toward a net-zero emissions climate regime with a limited cumulative emissions budget over the 2020-2100 period, compatible with 2°C warming by 2100. International cooperation is represented by sharing agreements for the remaining cumulative emissions budget 4 , where the supposed financial transfer mechanism to be implemented in the Paris agreement is represented by trading permits in an international emission rights market. With the associated abatement path and development of CDR activities, optimal exploitation of coalitions shares of emissions budgets is given by a Nash equilibrium in a dynamic game model. This meta-modeling approach -where a dynamic open-loop game is calibrated using statistical emulation of a large sample of simulations, performed with a world general equilibrium model -was first proposed in [16] and has subsequently been used in several analyses of climate policies [3,4]. The new contribution of this work lies in the explicit consideration of the GCC economies and the introduction of CDR activities as a strategic choice for coalitions.
Under this framework, we provide an assessment of the contribution of CDR technologies in lowering global mitigation costs, and demonstrate some comparative advantages to oil and gas exporting countries in future longterm climate regimes. Additionally, although a GCC coalition may currently seem unlikely, we show in this study that the GCC countries share common economic risks and opportunities, justifying a much broader cooperation over the next few decades. The results obtained in this study complement previous works [41,29,36] in several ways: (i) they provide an assessment of GDP and welfare losses based on a General Equilibrium Model; (ii) they estimate the impact of CDR technology on an International Environmental Agreement, represented by a shared safety cumulative emissions budget; (iii) and they propose a possible solution that would limit welfare loss to 2.8% of discounted cumulative GDP for every coalition.
The paper is organized as follows. In section 2, we present challenges facing the GCC countries in attempting to define a long-term climate strategy. In section 3, we develop the macroeconomic framework that we use for our assessment. In section 4, as part of a global worldwide effort to reach a net-zero emissions regime, we present the simulation results obtained under this modeling framework and focus particularly on GCC countries and the potential impact of developing DAC technologies. Finally, in section 5, we discuss policy implications and conclude.

Challenges for the GCC countries
The long-term goal established by the UNFCCC in Paris -and reaffirmed in the subsequent COPs -implies reaching a global net-zero emissions regime before the end of the century. This is indicated in the latest IPCC reports, as well as in several integrated assessment models (e.g. [35]). In this context, climate negotiations seek to drastically reduce fossil fuel consumption, which would thus seriously impact energy exporting countries economies [30]. Notably, the GCC countries are part of the Paris agreement, operating within the Arab Group 5 as their primary negotiating bloc. Here, although Bahrain, Kuwait, Oman, Qatar, Saudi Arabia, and the United Arab Emi-rates (UAE) are all members of the Cooperation Council for the Arab States of the Gulf, there are some fundamental differences among those countries which have resulted in diverse policies and strategies. For example, financial resilience differs widely: while Kuwait and Saudi Arabia possess large financial reserves and debt capabilities, Qatar, UAI and Oman show less financial strength to support shocks on oil demand and prices [21]. As such, it is not currently possible to consider the GCC a unified entity, nor ignore these differences among its member states 6 . Indeed, such differences could impact their respective positions toward climate change issues or their ability to act as a unified block and defend their common interests in global negotiations. Nevertheless, all signatory countries must find a way to cooperate on the global challenge posed by the climate change issue and in reaching a net-zero emission regime by the end of the century; and indeed, do so while negotiating to obtain, over the long-term, fair terms of burden sharing. To be sure, the GCC countries share similar exposure to climate change damages, similar exposure to stranded asset risks, and similar access to CO 2 sequestration in depleted oil reservoirs. For these reasons, notwithstanding the differences discussed, our modeling approach considers that the GCC countries form a natural coalition to balance the relative negotiating power of different groups of countries around the world.
Several approaches have attempted to define a road map for reaching the goals of the agreement, e.g., in the IEA Sustainable Development scenario [21] or the Shell Sky scenario [40]. Discussions of the most efficient means to coordinate international efforts have explored uniform carbon taxes and an international carbon market based on a cap and trade mechanisms (see [15]). The basic premise of this paper is thus based on the assumption that there will be negotiations leading to an international emissions trading scheme with a burden-sharing approach to emissions reductions. Even though such a development may appear highly unlikely, the situation described in this study serves as a benchmark, and is certainly more efficient than the one which will emerge from the COP negotiations. This hypothetical assumption of an efficient world is required for drawing economic assessment conclusions concerning long-term strategies for the GCC countries, and assuming a trading scheme is useful for comparing different political solutions toward 6 As is the case between many member states of other regional organizations, the GCC member states hold different positions in relation to different regional and international issues. There is a lack of consensus for example with regard to determining common interests and defining security threats. There are also some major differences among the GCC countries regarding their foreign policies and their positions concerning the Arab spring.
implementing COP agreements and in quantifying possible economic outcomes.

A global macroeconomic framework
Expanding upon previous studies dealing with the assessment of economic impacts of the Paris agreement ( [3,4]), we introduce a macroeconomic framework that combines a computable general equilibrium (CGE) model, namely GEMINI-E3, with a dynamic game model. The resulting "metagame" model -under simplifying, but reasonable assumptions -is used to provide a first insight into possible welfare losses in GCC countries, if they were to implement a long-term mitigation strategy with CDR technologies. The full mathematical description of this model is given in the Appendix. Briefly, the model describes 10 coalitions of countries (including a grouping of GCC countries) competing for the supply of emissions permits in an international cap and trade system as designed to satisfy a global safety cumulative emissions budget (evaluated at 1170 GT of CO 2 over the 2020-2100 period). A net-zero emission regime is reached at the end of this period. To summarize climate negotiations on the burden sharing issue, we consider different possible allocations of a global safety cumulative emissions budget among different coalitions. Once the share of the emissions budget that goes to each coalition is decided, the coalitions are assumed to play a noncooperative game for the supply of emissions permits in the international carbon market. Depending on their respective abatement policies, the coalitions can be net buyers or net sellers of permits. This generates payment transfers that converge toward fair burden sharing. Furthermore, our modeling approach encapsulates several key elements of the design of an international climate regime consistent with Paris agreement goals. The payoffs for the game-theoretic model are obtained from statistical emulation of the GEMINI-E3 CGE model presented below.

Evaluation of welfare losses with the GEMINI-E3 model
is a CGE model specifically designed to assess the impact of climate change mitigation policies in different regions of the world. It has recently been used to assess the COP21 pledges and a fair 2°C pathway compatible with the Paris agreement objectives [4]. For this study, the model has been extended to permit a more detailed representation of the GCC countries and their risk exposure to stranded assets. The model is built on the GTAP 9 database [1], with reference year 2011. In this version, we detail 10 groupings (regions or coalitions) of countries, the GCC countries being one of them; they are: European Union (28 countries), United States of America, China, India, the GCC, Russia, Other Asian countries, Other energy exporting countries, Latin America, and the Rest of the World 7 . Extraction of fossil fuel energy is modeled by carbon content in order to evaluate the "unburnable-oil" effect of climate change mitigation policies. Three fossil fuel sectors/products are represented: coal, crude oil and natural gas. In the model, the impact of deep decarbonization pathways on stranded fossil fuel assets occurs via two main channels: (i) Fossil fuel resources localized in energy exporting countries lose their value, energy rents associated with these resource decrease (i.e., inground reserves become stranded assets), and welfare is directly negatively impacted in countries that own these resources; (ii) Capital invested in energy sectors (coal mining, refineries, pipeline infrastructure) and energy intensive industrial sectors is further depreciated, which in turn negatively impacts households that own these assets. In GEMINI-E3, like most CGE models, households own capital and other resources, e.g., land, fossil fuels resources. While we do not consider National Oil Companies, nevertheless where NOCs are owned by the Government our result are not affected. Indeed, our scenarios assume that the government budget is unchanged with respect to the reference scenario. In this sense, a decline in oil revenue allocated to the government budget requires an increase in household taxation (e.g., direct tax) and a decrease in household income equivalent to our current closure rule.
Since GEMINI-E3 was designed to run on the 2011-2050 period, we take a versatile approach to extend it to 2100 based on steady-state growth through the end of the century. We first, selected a demographic scenario, then used a production function approach to indicate the relationship between GDP per capita and the total factor productivity (TFP). We assume that regional TFPs converge to an exogenously defined common value at the end of our century, represented by the US figure. Finally, we also assume that CO 2 emissions per unit of GDP decrease at an annual rate and 7 The GTAP database is a well established economic database, used by the majority of CGE models and international economic institutions (OECD, European Commission, IFPRI, etc). The GTAP consortium and the collaborators have continuously improved the quality of the database. Although, some developing countries lack accurate Input-Output tables -and so their data are probably less reliable -this is not the case for GCC countries. Data on these countries have undergone extensive improvements over recent years. The authors would like to specifically mention the efforts of David Green, who has built the input-output tables embedded in GTPA8 for Saudi Arabia, Qatar, Kuwait, Oman, Bahrain and the UAE. More recently, Input-Output Tables for Saudi Arabia have been reported in the OECD Input-Output Tables 2018 Edition. converge also to a single common value for each region. This allows us to simulate a BaU scenario through 2100 by setting a value for the three parameters defined above: demographic scenario, TFP, and a carbon intensity per GDP. In this paper, we assume that the TFP and carbon intensity per GDP converge to 1% and -1%, respectively at the end of our century 8 .
This macroeconomic model reproduces historical emissions (2011 to 2018) and its medium term forecast is based on the WEO outlook 2016 [20]. The economic impact of mitigation policies is measured by the gains (or losses) in terms of trade (GTT) and the domestic abatement costs 9 . For energy exporting countries, like the GCC countries, the GTT component represents decreases in energy exporting revenues. CDR technologies are not modelled in GEMINI-E3 since they are new technologies with strategic importance in their development for oil and gas exporting countries. In addressing this, our game model includes explicit decision variables for the investment and use of these technologies.

Meta-Game model and linkage with GEMINI-E3
First proposed in [16], the meta-game model presents coalition payoffs as a function of the macroeconomic costs of abatement policies, the cost of developing CDR technologies, the gains in the terms of trade (GTT) due to global impacts on world energy prices, and the financial gains or losses from trading permits. Statistical emulation of the macroeconomic model are used to calibrate marginal abatement costs and GTT functions.
Regression analysis is used to estimate the payoff functions of the game, where strategic variables are the quotas supplied by the different coalitions, at different times, under an emissions trading scheme. Statistical analysis is based on a sample of 100 numerical simulations of different possible climate policy scenarios performed with GEMINI-E3, as detailed in Appendix A.3.

Brief review of CDR technologies
CDR aims to remove carbon dioxide directly from the atmosphere through different processes that either increase natural carbon sinks -such as oceans and lands -or use chemical engineering to suppress carbon dioxide. Of potential geo-engineering approach [18], CDR technologies are considered less environmentally impactful than stratospheric aerosol injection (SAI), marine cloud brightening, or space reflectors. Within CDR, several approaches have already been tested and implemented, including ocean iron fertilization 10 , biochar 11 , enhanced weathering 12 , large-scale afforestation 13 , BECCS, and DAC. Our analysis focuses on only the last two technologies, which are the most likely backstop technology candidates [40,10].

Techno-economic analysis of CDR technologies
Assessments of DAC technologies are discussed in [24,23]; and more recently, in [19,22]. Their potential role in climate stabilization has been explored in [34], and then in [10], under the WITCH model [9], which predicts comparative advantages in deploying DAC for the Middle East and energy exporting countries. This same comparative advantage was also observed in [29], which used the MERGE-ETL model [26] to explore the potential of the DAC technology. Under these models, the total quantity of CO 2 captured by the DAC and other carbon capture technologies is constrained by the potential for CO 2 storage across regions. As derived in [29], estimates of storage potentials -including deep saline aquifers, hydrocarbon fields, and coal beds -are given in Table 1. Due to potential technical, accessibility and social acceptance issues -among others -, we assume that only a fraction (between 25% and 50%) of these potentials can be used for the DAC and BECCS operations by 2100. We also assume that the DAC technologies will be mature enough for massive deployment by 2040 with a linear deployment trend afterwards. 10 Ocean fertilization refers to the intentional addition of iron into the ocean to stimulate phytoplankton growth. 11 Biochar refers to a "green coal" obtained by pyrolysis of biomass, such as crop or forestry residues, for the latter use in agriculture enhancement, leading to carbon sequestration. 12 Enhanced weathering uses the physicochemical properties of certain rocks capable of extracting carbon dioxide (CO2) from the atmosphere that fixes it in solid form. 13 generally classified in the category of Land-use management [33].
Cost of DAC has been discussed in recent publications. For instance, [22], describes and economically assesses a process fully powered by natural gas, computing a levelized cost of 232 $/t-CO 2 captured; an American Physical Society study [42] proposed a levelized cost of 550 $/t-CO 2 ; [19] determined the cost for powering a DAC plant using a natural gas-fired plant with CCS at 396 $/t-CO 2 avoided; and the extra energy cost of DAC was estimated around 232 $/t-CO 2 captured by [28] and [13,14]. Storage costs were evaluated in [39] to be in the range of 6 to 13 $/t-CO 2 stored. The total levelized cost is thus here set at $300/t-CO 2 captured and stored, for all regions except the USA and EUR. These latter are priced at $350/t-CO 2 captured and stored, assuming higher logistic costs. As for BECCS, the technology standard consists of producing electricity from biomass while capturing and injecting CO 2 into geological formations. We use a unique levelized cost of 60$/t-CO 2 for the whole world, consistent with the IEA estimates [25]. BECCS potentials are estimated from the global and regional assessments [25], which take biomass supply chains and processing into account, and also include deployment issues in terms of policy and regulatory barriers. Using the IEA estimates, we have derived a global bound on GHG captured through BECCS equal to 10.2 Gt CO 2 , based on technical potentials by 2050. Finally, BECCS penetration is related to electricity generation levels and composition by year 2050; we adopt what could be considered rather conservative potential estimates for the end of the century.

Evaluation of fair compensations among GCC countries
To assess the economic consequences of a proposed climate agreement, we assume optimal use -or at least, a second best solution -of the global emissions budget, which will correspond to a Nash equilibrium among the parties. In this sense, we assume a global safety cumulative emissions budget (SCEB) of 1170 Gt of CO 2 over the time horizon 2018-2100. Climate negotiations, in one form or another, will bear how this global safety cumulative emission budget is shared among coalitions, regrouping countries with similar macroeconomic structure. We also assume an international emissions trading system. Here, the coalitions supply permits to the market, strategically crafting abatement policies for their share of the safety cumulative emissions budget. In this sense, the development of CDR activities like BECCS and DAC, will allow coalitions to replenish or increase their own emission budget. We compute a Nash equilibrium around this dynamic game. Briefly, when a coalition reaches capability for a levelized cost of a CDR technology -be it BECCS or DAC -lower than the price of permit, it can then invest to increase the permit allowances and gain advantages in the equilibrium solution. We consider a fair burden sharing is obtained when the share of the remaining safety cumulative emissions budget that is given to each coalition is such that the relative losses of welfare are equal among all coalitions. For the GCC countries, the financial transfers from selling permits through the market will generate compensations for unburnable oil.

The reference scenario
Using GEMINI-E3, we build a BaU scenario -calibrated on the "New Policies" scenario from the World Energy Outlook 2016 [20] -for the period 2017-2050. We extend this BaU scenario to the 2050-2100 period, following [2]. Demographic assumptions are based on the United Nations "median variant" scenario [43]. World population increases by 50% from 2016 to 2100, and reaches 11.2 billion inhabitants in 2100. During the same period, the BaU scenario assumes that global GDP multiplies sevenfold -representing a 2.4% annual growth rate -and that global CO 2 emissions reach a maximum of 48.3 billion tons of CO 2 in 2050, and then decrease down to 46.8 billion tons of CO 2 at the end of the century. This decline in emissions is expected from rarefaction of fossil energies over the second half of the 21 st century. According to this scenario, more than 4.11 trillion tons of CO 2 are emitted during the 21 st century. Such an emissions budget would lead to an increase of surface air temperature over 3.5°C with regards to 1850-1900 period, with probability 66% (see [37]).

Impact of CDR activity in global mitigation scenarios
In contrast to the BaU scenario, we consider an SCEB of 1170 Gt of CO 2 for 2018-2100, under two scenarios with and without CDR technologies. This budget is consistent with the recent IPCC report [37] on the pathway to 2°C. We also assume that very stringent climate policies can be implemented only after 2030. Figure 1 shows the global trajectory of CO 2 net emissions with and without DAC/BECCS. Net emissions are equal to CO 2 emissions minus DAC/BECCS sequestered emissions. The dual variable of the SCEB constraint is used to define a CO 2 price. Table 2 gives the CO 2 price and the worldwide welfare lost.
Without CDR, more abatement is required (see Figure 2), and imply a more restrictive timeline where CO 2 emissions converge to zero at the end of the 21 st century. Moreover, this results in a significant welfare loss, 3.8% of the discounted GDP over the 2018-2100 period. When DAC and BECSS are used, however, the worldwide welfare loss is reduced to 2.8%. Without CDR technologies, the CO 2 price given by the dual variable of the budget constraint is equal to 4140$ in 2100 which corresponds to 775$ in 2030 14 . This shows the extreme stringency of the climate target when the CDR technologies are not available. With CDR technologies, the CO 2 price is 1292$ in 2100 corresponding to 480$ in 2030 15 . These figures are consistent with those in the IPCC special report on Global Warming of 1.5°C [37]. Indeed, under the Higher-2°C pathway, the range estimates in the IPCC report are equal to 15-200$ in 2030, and 175-2340$ in 2100. This shows that CDR technologies allow for reaching the net-zero emission target, and that DAC activity additionally becomes highly profitable at the end of the century. Figure 2 represents the same two mitigation scenarios showing the contribution of DAC and BECSS.   Figure 3 shows variation in global welfare loss under the scenarios with the target SCEB and CDR options. The 2°C threshold corresponds to the 1170 SCEB discussed above. The diagram shows that the 1.5°C objective appears to be very challenging [38,32], with a cost multiplied by 5. This is also suggestive that the 1.5°C scenario is highly unlikely due to its cost.  To complement this analysis, we have also simulated a scenario of full cooperation among all nations. The model assumes implementation of policy which minimizes the total cost for the whole world, without any constraints on the timing of abatements is implemented. While the "utopia" scenario decreases global percentage loss of GDP, over the second-best solution, from 2.8% to 2.1%, the two values are not entirely dissimilar.

Fair allocation of SCEB across GCC countries
Prior to designing possible fair sharing agreements, we first explore the economic impacts that would occur under the implementation of two quota allocations, extensively discussed and analyzed in the literature:"Grandfathering" and "Per Capita". Table 3 shows the budget shares and welfare losses under these two rules. In neither cases is fairness achieved, and the GCC countries are moreover disadvantaged at 11% and 13.8% of discounted GDP losses, respectively. Indeed, the relatively few permits allocated to the GCC countries -2.9% under Grandfathering, and 0.9%, under Population -appear to be largely insufficient to compensate for their revenue losses in world energy markets. Table 3 shows the effects from these rules. Grandfathering allocates quotas proportional to emissions in the BaU scenario over the whole period (2018-2100). This idea is meant to take existing situations into account as a starting point in environmental negotiations, on the basis of the principle of sovereignty. Under this allocation, energy exporting countries (Russia, the GCC countries and OEE) and the Rest of the World 16 incur a very high burden, while India, Latin America and China largely benefit. The second rule, per capita, sets the budget share proportional to the population over the 2018-2100 period. This equalitarian rule creates a large number of extreme welfare impacts. The most populated countries earn significant revenues by selling emissions. Therefore, India, the Rest of the World, and Latin America experience improvements in welfare by implementing climate mitigation policy, while energy exporting countries -as well as China and the USA -bear significant welfare loss. The difference between China and India, which have comparable populations, is because the former has a much higher per capita CO 2 emission rate stemming from higher economic development and greater dependence on coal. To address the issue of fair distribution of the SCEB, we follow the approach proposed in [16]. We propose a burden-sharing rule that equalizes welfare losses among the 10 groups of countries. This so-called "Rawlsian" allocation seeks to maximize welfare for the worst affected countries. Table 4 displays the resulting fair allocation of quotas; a breakdown of costs among abatement and DAC and BECCS activities; and GTT and permit exchanges on the international emission market. Here, the GCC countries and Russia are enabled to sell emission rights to offset losses in fossil energyexporting revenues and DAC activity cost. On the other hand, industrialized countries (e.g., USA, Europe and Japan) are the main buyers of permits, and transfer financial compensations to the GCC countries. In short, once there is agreement on the principle of an international carbon market and of distributing a global safety cumulative emissions budget, the market will generate compensations. We compare these results via a sensitivity analysis to evaluate the impact of DAC costs and potentials on the burden sharing agreement. We define a set of scenarios that: place DAC sequestration potentials from 12.5% to 50%; and costs, from 200 to 1000 US$ per ton of CO 2 sequestered. Figures  4 and 5 show global welfare loss in % of discounted GDP and the fair GCC budget shares, respectively We observe in Figure 4 that welfare loss of the total discounted GDP varies reasonably, 2.7% under the low price-high potential scenario, and 3.1% under the high price-low potential scenario. As expected, the most favorable conditions, i.e., lowest price and highest potential scenarios, lead to better cost performances.
The results shown in Figure 5 indicate that, at a fixed DAC price, permit allocations to the GCC countries under fair burden sharing agreements increase with available sequestration potential. Notably, this increase in allocation also occurs at reduced prices. That GCC countries generate even more permits from DAC under "low-price and high-potential" scenarios may seem counterintuitive; however, the explanation lies in the evolution of CO 2 permit prices, which are greatly reduced under the low-price and high-potential scenarios. Given lower permit prices, the GCC countries seek greater permit allocation to compensate for their losses. Our numerical experiments estimate the GCC budget share between 7.8% and 12.1%.

Discussion and conclusion
This paper complements previous works [41,29,36] in several ways: (i) it provides an assessment of GDP and welfare losses based on a General Equilibrium Model; (ii) it estimates the impact of CDR technologies on an International Environmental Agreement, represented by shares of a safety cumulative emissions budget; (iii) and it proposes a burden sharing scheme that limits welfare loss to 2.8% of cumulative discounted GDP for each of the 10 coalitions. Some new insights are gleaned from the simulations presented above: (i) a net-zero emissions regime by the end of the century is greatly facilitated by the implementation of CDR technologies, and DAC in particular; (ii) in a net-zero emissions regime under an international emissions trading market, captured CO 2 represents a new resource, with low extraction cost and tradable on the international carbon market 17 ; (iii) developments in DAC technology, along with a fair allocation of allowances under an international emissions trading system, mitigate risks involved with unburned carbon among GCC countries; (iv) finally, in a world where fossil fuel reserves could become stranded assets, developments in DAC technology will help to diversify GCC economies 18 . As such, the following conclusions, summarized below, derive from the main results of the simulations: • A market-based approach, with equalized marginal abatement costs and Rawlsian allocation of permits, yields a uniform discounted GDP welfare loss of 3.8% when no CDR option is available (see Table 2). For the GCC countries, this corresponds to a welfare loss of $5 trillion in discounted GDP 19 .
• Including CDR options decreases this loss by 26% (from $5.0, to $3.7, trillion), corresponding to an equalized welfare loss of 2.8% of discounted GDP. In this process, DAC penetration first yields a significant reduction of abatement costs in all countries, and particularly for the GCC countries, falling from $7.6 trillion to $4.3 trillion. Second, DAC investments and operations -estimated at $7.1 trillion for the GCC countries -enable them to obtain additional emission permits for sale on the international market. Compensation transfers remain virtually unchanged compared with the no-CDR case, since the sale of more permits offsets lower permit prices. In brief, introducing DAC reduces unburned oil and reduces the loss of oil and gas revenues for energy exporting countries. DAC technology is therefore central to the design of a fair climate agreement: it allows GCC countries to exploit a comparative advantage associated with large natural gas endowments and high CO 2 storage capacities 20 .
In a net-zero emission regime with an international emission trading market, captured CO 2 becomes a new resource, priced on an international market for emission rights. Here DAC technology enables mitigation of carbon emissions from hydrocarbons wherever they are used globally. The investment needed for such a massive DAC capability would be around $223 billion. While these numbers are daunting, given a carbon price above $480/t after 2030, such investments represent an interesting industrial diversification, ensuring a longer life to soon-to-be-unburnable assets, at no logistical cost to valorize natural gas.
Finally, GCC member states have historically been proactive in oil and gas geopolitics. This study shows a further avenue for proactivity in climate geopolitics, should they foster R&D in CDR technologies and contribute to the establishment of efficient and fair compensation mechanisms. Indeed, this study shows that, in an international emissions trading system, a coalition of the GCC countries could claim, in a fair agreement, up to 8.8% of the emissions rights from an SCEB of 1170 Gt CO 2 . It is a brighter future for the GCC countries where DAC technologies penetrate at sufficient scale. While efficient capture of CO 2 with low concentration in open air remains an open research domain, we may expect large advances in terms of cost and 20 The global carbon rent equals $290 trillion significantly higher than the one given in [6] for a 450 ppm CO2-eq and equal to $2005 32 trillion. But these discounted figures are based on a different discount factor (3% in our case and 5% in [6]) and our cumulative emission are 12% higher than their 40 ppm scenario (Using in our model a 5% discount factor and the same cumulative budget gives a global carbon rent equal to $2005 112 trillion).
availability. Similarly, the design of a fair burden sharing mechanism, based on allocation of a global safety cumulative emissions budget and trading on an international carbon market, falls to political science research. As suggested by the results of this study, these two research domains could become key priorities for GCC economies and other fossil fuel producing countries and companies.

A Model formulation
We report in this section the mathematical formulation of the meta-game model used in this paper to design and assess burden sharing agreements. β j : discount factor for coalition j equals 3%;

A.1 Model's equations
Emissions from abatement. This equation relates the abatement and emission levels relative to BaU Emission budget constraints. Let b j (τ ) denote the remaining emission budget, for region j at the end of period τ , τ = 0, . . . , T −1. We approximate the integral of net emissions up to period τ , using the trapezoidal method. The part of the emissions budget remaining at period τ is thus defined as − v j (t + 1))), j = 1, . . . , m, τ = 0, . . . , T − 1. (2) By imposing non negative remaining budgets, we eliminate the possibility for each "player" to perform short-selling of the future DAC activities. This expression can also be rewritten Note that the modeling approach in [31,29], is a Ramsey optimal growth model with a constraint on SAT increase, expressed in terms of cumulative emissions. In these cases, the optimal solution normally proposes some overshooting, with not insignificant negative emissions occurring at the end of the planning horizon; and indeed, the higher the discount rate, the greater the negative emissions at the end of the planning horizon. In contrast, our approach uses an oligopoly game model, where each coalition strives to optimize the use of a given fixed emissions budget, over a planning horizon, where a net-zero emissions regime should be reached at the end of the planning period. This will provide a natural end-of-period condition: net-zero emissions for the whole world. However, at each intermediate period, a negative remaining budget for one coalition would allow it to supply emission rights on the current market as CO 2 they promise to capture in the future: in other words, short selling, associated with high risk and temptation for each player to cheat. Under these conditions, and to ensure that each permit supplied corresponds to existing abatements or CO 2 capture, then, it would be necessary to forbid short selling.
Net-zero emissions in the final period. At the end of the planning horizon one must reach a net-zero emission regime. So there should be a coupled constraint of the form.
However, this constraint will probably be redundant with the emission budget constraints and we will not consider it.
Emissions trading. An international carbon market determines a price and emissions levels.
The price and emission levels are thus functions of the total permit supply Ω(t), thus denotedẽ(Ω(t), t) andp(Ω(t), t), respectively. As shown in Helm [17], the derivatives w.r.t. Ω of price and emission levels are given byp respectively. Since Ω(t) = m j=1 ω j (t) the derivatives w.r.t. ω j (t) are the same as the derivatives w.r.t. Ω(t).
Payoffs. The periodic net cost to coalition j includes the abatement cost plus the cost of buying permits on the market (negative if selling) and is given by The payoff coalition j is defined by the integral of the discounted periodic costs We assume that the supply of permits and the DAC activities of each coalitions are strategically defined as the open-loop Nash equilibrium for the game defined by payoffs (11) and constraints (1)- (8).

A.3 Model calibration -CO 2 emissions and payoff functions
We use the GEMINI-E3 model [7,8] to calibrate the dynamic game model. GEMINI-E3 is a worldwide multi-country, multi-sector, computable general equilibrium (CGE) model that has been specifically designed to assess energy and climate change policies. GEMINI-E3 is used to compute the CO 2 emissions and economic variables within the business as usual (BaU) scenario and calibrate the payoff functions (π j ). The methodology used to calibrate our game theory model using an applied CGE is detailed in our previous papers, e.g. see Appendix 2 in [4]. In short, various climate policies are simulated by GEMINI-E3, then we perform econometric estimations of the abatement cost ( j (q j (t), t)) and gains from term of trade (γ j ( m k=1 q k (t), t)) functions. However, the time horizon of GEMINI-E3 is limited to the first part of our century (i.e. up to 2050), therefore we have to implement a procedure extending the variables for the years 2070 and 2100. We use a versatile representation based on a steady state growth approach for the end of our century.
First, we select a demographic scenario among the projections done by the United Nations [43] and determine the working population 21 (pop j (t)). Then, we follow a production function approach linking GDP per capita (gdp j (t)/pop j (t)) to a total productivity factor (TFP) ν 1 j (t). We assume that for each region the TFP converges to a common value (ν 1 ) at the end of our century. Finally, we assume that for each region CO 2 emissions per GDP (e j (t)/gdp j (t)) decrease with an annual rate that converges to a single value ν 2 . Thus we can simulate various BaU scenarios by setting a value for the three parameters defined above, demographic scenario, ν 1 and ν 2 .
The abatement functions ( j (q j (t), t)) are extrapolated for the years 2070 and 2100 by assuming a proportionally rule with respect to the level of abatement for the year 2050. The GTT functions (γ j ( m k=1 q k (t), t)) in 2070 and 2100 are supposed unchanged with respect to 2050 figures. 21 Male and female population aged from 20 to 64.