AI for Global Climate Cooperation: Modeling Global Climate Negotiations, Agreements, and Long-Term Cooperation in RICE-N
Authors: Tianyu Zhang
Andrew Robert Williams
Phillip Wozny
Kai-Hendrik Cohrs
Koen Ponse
Marco Jiralerspong
Soham Rajesh Phade
Sunil Srinivasa
Lu Li
Yang Zhang
Prateek Gupta
Erman Acar
Irina Rish
Yoshua Bengio
Stephan Zheng
Venue: ICML 2025 poster (2025)
Keywords: reinforcement learning
climate change
mechanism design
Primary area: applications->social_sciences
TL;DR: A climate-economic simulator using multi-agent RL to evaluate global climate negotiation strategies, showing how they can improve climate outcomes and equity.

Abstract: Global cooperation on climate change mitigation is essential to limit temperature increases while supporting long-term, equitable economic growth and sustainable development. Achieving such cooperation among diverse regions, each with different incentives, in a dynamic environment shaped by complex geopolitical and economic factors, without a central authority, is a profoundly challenging game-theoretic problem. This article introduces RICE-N, a multi-region integrated assessment model that simulates the global climate, economy, and climate negotiations and agreements. RICE-N uses multi-agent reinforcement learning (MARL) to encourage agents to develop strategic behaviors based on the environmental dynamics and the actions of the others. We present two negotiation protocols: (1) Bilateral Negotiation, an exemplary protocol and (2) Basic Club, inspired from Climate Clubs and the carbon border adjustment mechanism (Nordhaus, 2015; Comissions, 2022). We compare their impact against a no-negotiation baseline with various mitigation strategies, showing that both protocols significantly reduce temperature growth at the cost of a minor drop in production while ensuring a more equitable distribution of the emission reduction costs.

AI for Global Climate Cooperation: Modeling Global Climate Negotiations, Agreements, and Long-Term Cooperation in RICE-N
Tianyu Zhang 12 Andrew Williams" 12 Phillip Wozny" Kai-Hendrik Cohrs 4
Koen Ponse
Marco Jiralerspong 12 Soham Rajesh Phade Sunil Srinivasa' Lu Li Prateek Gupta 10 Erman Acar !! Irina Rish 12
Yang Zhang"
Yoshua Bengio 1212 Stephan Zheng
Abstract
action, warning that it is "now or never" to avert a climate disaster (Pörtner ct al., 2022). Ecosystems are drastically changing: the Amazon rainforest is receding (Lovejoy & No- bre. 2018) and polar ice sheets are melting (Boers & Rypdal, 2021; DeConto et al., 2021). Extreme weather events, in- cluding the recent increase in coastal flooding and forest fires are unequivocal warning signs (Kundzewicz, 2016; Schmidt et al., 2022). These developments are increasingly being at- tributed to climate change and driving towards a system-wide tipping point (van Oldenborgh et al., 2021; Stott et al., 2016).
Global cooperation on climate change mitigation is essential limit temperature increases while supporting long-term, equitable economic growth and sustainable development. Achieving such cooperation among diverse regions, each with different incentives, in a dynamic environment shaped by complex political and economic factors, without a central authority, is profoundly challenging game-theoretie problem. This article introduces RICE-N, multi-region integrated as- sessment model that simulates the global climate, economy, and climate negotiations and agree- ments. RICE-N uses multi-agent reinforcement learning (MARL) to incentivize agents to develop strategic behaviors based on the environmental dy- namics and the actions of others. We present two negotiation protocols: (1) Bilateral Negotiation, example protocol and (2) Basic Club, inspired by Climate Clubs and the carbon border adjust- ment mechanism (Nordhaus, 2015; Commission, 2022). When we compare their impact against a no-negotiation baseline with various mitigation strategies, we find that both protocols significantly reduce temperature growth at the cost of minor drop in production while ensuring a more equitable distribution of the emissions reduction costs.
Climate change is global issue impacting all. In response. public and private financing have driven technological innovation (e.g. in renewable energy) and community initiatives for systemic change. However, mitigation investments vary across countries due to social and economic factors. For example, developing nations may prioritize basic needs, while developed nations likely have more resources to address climate impacts.' This creates "tragedy of the commons," where self-interest can lead to harmful outcomes for all (Gardiner, 2001).
As such, achieving and maintaining global cooperation is crucial to achieve the Paris Agreement's long-term goal of limiting the global temperature rise above pre-industrial levels to well below C (DeConto et al., 2021). At the same maintain economic development,
time, it is important including growth and inequality reduction. For instance, international trade treaties, foreign investment, and tech- nology transfer can help developing countries meet net-zero targets while supporting global economic growth. Such cooperation could be fostered through climate clubs, which tackle barriers to climate action (Nordhaus, 2015).
Introduction
The latest Intergovernmental Panel on Climate Change (IPCC) report emphasizes the urgent need for immediate
From a modeling perspective, achieving and maintaining global cooperation poses complex game-theoretic problem involving cooperation, communication, and competition. It can be modeled with n strategic agents, each representing a region or nation seeking to maximize their own utility through policies aimed at their own socio-economic and
"Equal contribution 'Mila - Quebee AI Institute 'DIRO, Université de Montréal 'Vrije Universiteit Amsterdam "Universitat de València 'Leiden University 'Wayve" 'NVIDIA Unniversity of Pennsylvania "Bank of Canada University of Oxford " University of Amsterdam 1CIIAAR 13 Asari AI. Correspondence to: Tianyu Zhang <tianyu.zhang @ quile..
Proceedings of the 4dnd International Conference Machine Learning. Vancouver, Canada, PMLR 267, 2025. Copyright 2025 by the author(s).
Developing countries typically pay more to reduce emissions than higher-income countries (Frickson et al., 2015).

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AI for Global Climate Cooperation
climate goals, which may conflict with those of the other agents. These agents interact through trade, diplomacy, or foreign aid and investments, with cooperation manifesting through mutual negotiation and agreements.
various climate-economic model configurations.
Negotiation Protocols As RICE-N is built for modeling negotiations, we develop two novel protocols: (1) Bilateral Negotiation, a baseline protocol that provides simple inter-agent communication; (2) Basic Club, a protocol inspired by actual climate economic policy (Nordhaus, 2015; Commission, 2022) to foster burden sharing among agents.
A key issue is the lack of central authority to enforce cooperation or compliance with the agreements in the real world. Therefore, is essential to design negotiations and agreements that promote sustained cooperation in mitigating climate change while allowing all parties to achieve their individual policy goals.
Analyzing Results To evaluate the Basic Club and Bilateral Negotiation protocols, we compare the climate- economic performance of agents trained with and without these negotation protocols. Metries include incquality in emission reduction costs as %GDP and emissions. Compared to agents trained without negotiation protocols, agents trained under the negotiation protocols reduce temperature growth at the cost of a minor drop in production while ensuring more equitable distribution of the emissions. Our code samples are available here: https: //gi thub. com/m m la- i iiqi/ climate-comme copperattoon-commeiiiio competition
Such name-theoretic problems present unresolved technical challenges. For instance, a key analysis in the 2022 IPCC report predicts climate change under five different so-called Shared Docio-Economic Pathways (SSPs), each based on set of predefined climate-economic policies for each global region (Pörtner et al., 2022). However, key limitation is that it is unclear whether these policies would be implemented by
actors, making it uncertain how likely these scenarios are to occur or how robust they are to changes in agent behavior over time.
2 Related Work
Climate-cconomic policy tradeoff's are typically modeled using integrated assessment models (IAMs), which quantify the effeects of economic activity and CO2 emissions global temperatures and long-term economic development. A pioneering example is the Dynamic Integrated model of Climate and Economy (DICE) from (Nordhaus, 2007), which models the links among climate and economic factors, such as population growth, technological change, CO2 emissions, global temperatures, and economic damages. DICE uses a single global economy. The Regional Integrated Model of Climate and Economy (RICE) extends DICE to multiple regions (Nordhaus & Yang, 1996b) and can include tariffs and trade (Nordhaus, 2015; Lessmann et al., 2009). While widely used, RICE has its limitations, such as unrealistic assumptions, lack of distributional analysis, simplistic definition of regional interaction, and no consideration of uncertainty (Pindyck, 2013; Farmer et al., 2015; Gazzotti, 2022). Thus, RICE needs significant modification in order to capture the strategic behavior in climate negotiations. To address these issues, we draw inspiration from agent- modeling (Bonabeau, 2002) as bottom-up modeling framework and advances in MARI. to identify effective policies (Zheng al., 2022a) and train strategic agents (Silver et al., 2016; Vinyals et al., 2019).
Previous work has studied climate change through various lenses: political economy and negotiations (Chan al., 2022; Bakaki, 2022), public perception and institutional dynamics (Moore et al., 2022), and coalition formation (Zenker, 2019). Although TAMs have been used to study the impacts of political negotiation (Rochedo et al., 2018), the game-theoretic aspects of climate cooperation using machine learning and calibrated IAMs remain unexplored.
Climate negotiations have been analyzed using game theory, from simple prisoner's dilemma models (DeCanio & Frem- stad, 2013) to more complex bargaining games with learning (Smead et al., 2014; Greeven et al., 2016). However, these simplified models often lack crucial real-world features like multilateral settings, strategic behavior with multiple goals, evolving dynamics, and agent heterogeneity (Madani, 2013).
Recent advances in multi-agent reinforcement learning (MARL) offer new approaches to studying strategic behavior in complex environments (Shoham & Leyton- Broown, 2008), While MARL has been applied to climate-related problems like HVAC optimization (Mai et al., 2024) and theoretical cooperation studies (Jaques et al., 2019), has not yet been extended to rich, calibrated dlimate-cconomi simulations. Our work addresses this gap by combining MARL with detailed climate-economic modeling. For an extensive review of related work, please refer to Appendix A.
Our main contributions are as follows:
RICE-N Integrated Assessment Model We introduce RICE-N, an integrated climate-cconomic model based on RICE (Nordhaus & Yang, 1996a). Designed as a simulation negotianio tool for climate negotiations, RICE-N incorporates MARL to model realistic interactions between agents. Furthermore, RICE-N is modular, allowing flexibility to accommodate
3 The RICE- Integrated Assessment Model
We introduce RICE-N, an IAM that further augments RICE with framework for negotiation protocols, and also includes international trade and tariffs, following (Lessmann et al.,
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Observations
No Negotiation Baseline
Temperature
Carbon
Population
Capital
Production
Consumption
Leaminn
Trades
Actions
Your Negotiation Protocol
Mitigation rate
Savings rate
Tariffs
Import bids
Export limits
Leaming
Negotiation
Figure J. Schematic overview how negotiation can lead to better outcomes in RICE-N, Each region (agent) uses a policy model make climate, economic, and trade decisions. For clarity, show the flow of information and actions for single agent negotiate, but negotiation protocol must be implemented, such as example negotiation protocols Section timestep, each policy chooses climate and economic actions based the observations they receive. (TOP) If there negotiation protocol. agents immediately decide their actions, which leads to high climate damage as can be seen in Figure (BOTTOM) If negotiation protocol has been implemented, agents must first negotiate before performing actions. The outcome of all negotiations is agreements (or lack thereof), which may be between two or more agents. In particular, an agreement may influence the remaining actions that an agent can take in the climate and economic domains. For the same timestep, each agent then makes decisions with respect to the climate, cconomy, and trade.
only. Agents high-level, each
2009)). As such, RICE-N shares climate, economic and social characteristics with the real world.
concentration of CO2 levels the Earth's atmosphere, and the average global temperature, well region-specific variables such as population, capital, technology level, carbon intensity of economic activity, and balance of trade. For more details, see Table 2 in Appendix B for variables and Appendix H for calibration details.
In RICE-N, there n regions, each modeled as independent decision-making agent. Regions interact with each other and the environment through their actions: setting savings rate, mitigation rate, trades and tariffs, and negotiation actions, for each time step.
RICE-N has climate and economic dynamics. The climate dynamics model how CO2 levels the atmosphere impacts global temperatures. The economic dynamics model how technology levels, capital, population, and gross domestic production evolve. Notably, the climate dynamics impact the economic dynamics through damage function, which describes how higher temperatures lead to losses in capital.
RICE-N has two main components: negotiation and climate-ecooomic activity, see Figure 1. The activity component simulates the physical actions of the agents and the resulting evolution of the environment. The negotiation component simulates communication between regions, allowing them to influence each other's behaviors and form agreements, Agreements may, in turn, adjust the available actions for each region during the activity stage.
These dynamics depend on savings and mitigation rates set by each agent, e.g., agents may choose to invest more in climate change mitigation, but this may lower economic productivity in the short-term.? As global CO2 levels and temperatures affect all agents, these dynamics mean
Each simulation episode consists of H steps, each repre- senting A years (e.g, A- 5). Thus, the simulation lasts for H A simulation years. At every step, the simulation goes through the negotiation stages, and agreements are formed between regions. The simulation then enters the activity stage where each region takes actions that are affected by the agreements formed during the negotiation stages.
II economic terms, variables such as capital, balance of trade, carbon mass, and global temperature depend the agents" actions and are called endogemous variables. On the other hand, variables such as population. technology level, and carbon intensity of cconomic activity called exogenous, i.c., their values do not depend the agent's actions. Note that the values of exogenous variables can vary across steps in predetermined manner.
Climate-economic dynamics overview. The state of the world is characterized by global variables such as the
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the decisions of each agent affect the climate-economic outcomes for other agents, too.
ing studies with various setups. In particular, the climate, eco- nomic and trade components are loosely coupled to enable isolated extensions and modifications. The order in which the dynamics act on the world state is determined in the global c i ma me..ooocmmmoyy-ooooommm accommodate extensions or modifications with minimal changes. For example, similar to (Hänsel et al., 2020), we pro- vide an updated and higher damage function based on recent meta analysis (Howard & Stemer, 2017). We also implement the climate dynamics of the famous Finite Amplitude Impulse Response (FalR) model, an emissions- climate model that is also featured in the IPCC reports (Millar et al., 2017).
The activity component encapsulates these dynamics. For each step: 1. The gross output production for each region is computed based on the state of the region, in particular, its capital investment, labor (or population), and technology factor. 2. The net economic output is the gross output production reduced by climate damages from rising global temperature, and the cost of efforts towards mitigation by this region.3 3. The region consumes domestic goods equal to the quantity of the net economic output that is left after capital investment and export. It also consumes foreign goods from imports. 4. The consumption utility for each region from consuming domestic and foreign goods computed using the Armington elasticity assumption that has become stan- dard in international computable general equilibrium models (Armington, 1969). This gives the reward corresponding to each region in every step. For more details, please refer to Appendix C.I and Table 3 in Appendix B.
() function, which can
In Figure 2, we analyze different damage and climate functions. We compare three baselines: agents that always perform the minimum mitigation, the maximumm mitigation and agents trained with no negotiation. We see that the effect of the damage function is marginal on the strategy of the agents, and even higher damage does not steer them away from maximizing their own utility. The choice of climate dynamics clearly has an effect on the resulting possible trajectories. The lowest emissions scenario for the DICE dynamics limited warming to between 2.6 C and 2.7% C by the end of the century. In contrast, the updated FaiR dynamics show that 2 is still possible, which corresponds roughly to the low GHG emission scenario (SSP1-2.6) of the IPCC (Pörtner et al., 2022). As DICE2016 remains the most ubiquitous model in use, we continue with the DICE2016 climate and damage functions for the remainder of the work.
International trade and tariffs. RICE-N features international trade to exchange and transfer goods between agents, following (Lessmann et al., 2009). Here, agents are modeled to seek diversity in their consumption according to the Armington assumption (Armington, 1969), so they want to consume goods produced by other agents and are willing to export some of their own goods in exchange. Each agent specifies the amount of goods it wishes to import and sees its orders filled partially or fully, depending on the other agents' willingmess to export. In addition, agents can choose to impose import tariffs to restrict trading. Import tariffs restrict the consumption of goods to which they are applied, implicitly increasing their prices. These price increases make imported goods without import tariff's more attractive. Therefore, trade and tariffs force agents to engage with other regions and be strategic, incentivizing negotiations and agreements. See Appendix C.2 for more details.
4 Negotiation Protocols
A negotiation protocol is a communication channel through which agents can make promises and demands that ultimately constrain their behavior. We design RICE-N to be modular such that its base dynamics can be used to test a variety of di fifferent negotiation protocols.
In principle, a negotiation protocol can have many desirable properties, including but not limited to the following (Nisan et al., 2007: Luo et al., 2024):
Extensions The climate dynamics of DICE and RICE are based on (Nordhaus, 2018; Kellett et al., 2019). Economic analysis based on these dynamics suggests that optimal policy paths limit global warming to 3.5ºC and lead to net zero economies in the next century (Nordhaus, 2019). Several works have criticized the trustworthiness of these results due to shortcomings in the model, such as missing representations of climate risk and uncertainty (Daniel et al.,
iicentive-compatibiee Agents have an incentive to act according to their true preferences. (Pavan et al., 2014),
Self-enforcing: No external body or agent is required to enforce other agents to participate in negotiations and adhere to agreements (Telser, 1980),
2019), unrealistic damage functions (Drupp & Hänsel, 2021)
and oversimplified climate dynamics (Mattauch et al., 2020).
Recent work has shown that updating the model with a more realistic climate emulator and recent damage estimates results in optimal trajectories that are more aligned with the climate targets of the Paris agreement (Hänsel al., 2020).
Fairness: Agents get comparable utilities (Luo et al., 2024).
Negotiation steps occur prior to the climate and economic step so that agents' climate-economic behavior is influ- enced by the outcome of negotiations through binding commitments.
RICE-N's 's modularity enables to easily update the equa- tions governing the dynamics, enabling comparison to exist-
RICE-N is flexible enough to serve as a basis for different
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negotiation protocols. We implement two negotiation proto- cols: Bilateral Negotiaton and Basic Club. The former serves as an example to illustrate the key phases of negotiation, and the latter is modeled on actual climate economic policy.
emission reduction target and impose a uniform tariff on all goods coming from non-club members (Nordhaus, 2015; 2021b). The latter (i.e., CBAM) is a feature of the EU Green Deal, aiming to address carbon leakage and facilitate net zero emissions by 2050 (Commission, 2020; 2022). Basic Club borrows the ideas of a uniform tariff on all goods and a variable tariff value that depends on the emission reduction target of the exporting country from Nordhaus and CBAM, respectively (Nordhaus, 2015; Commission, 2020; 2022). The legality of Basic Club with respect to World Trade Organization compliance is described in Appendix J.
Bilateral Negotiation In addition to the base dynamics of RICE-N, Bilateral Negotiation agents perform the following steps:
Proposal stage: At this stage, each agent i makes proposal, Ag), to every other agent j where ji: indicates the mitigation level that agent i promises and júj what agent i requests from agent j.
Formally, the Basic Club functions as follows:
Evaluation stage: At this stage, each agent observes the proposals made to it in the preceding stage and takes an action of accepting or rejecting each of the proposals.
Proposal: Each agent E {l,..., n) proposes ju; E [o. 11, indicative of the mitigation rate of the club they would like to join.
Commitment stage: At this stage, each agent commits to the maximum mitigation rate of all accepted proposals.
Evaluation: Each agent i E {1,..., n evaluates proposals ū from other agents j A i, by either accepting or rejecting them. Let A, be the set of mitigation rates of accepted proposals for region
Basic Club Basic Club is a multi-agent negotiation protocol based on climate clubs and the Carbon Border Adjustment Mechanism (CBAM) (Nordhaus, 2015; Commis- sion, 2022). The former was initially proposed by William Nordhaus and codified by Article 6 of the Paris Agreement; climate club is a coalition of regions that agree to common
Club Formation: We define the minimum mitigation rate of agent as μز; = max A, if A; is not empty. otherwise, it O. A club e is a subset of agents with a common minimum mitigation rate pec
Sanctions:
For each club c, non- members with lesser mini- mum mitigation rates the club mitigation rate i.e., [1 < He receive a tariff as the differences in rates i.e., Tj,e- = Pe Uí
DICE2016 Damage- + DICE2016 Climate H&S Damage DICE2016 Climate
Min,
miltgation
Temp. Aromelles
seg.
Std emor
Members and non-member with μıj 2 Me have Tj.c = O.
Exact descriptions of the action spaces for both protocols can be found in Appendix C.3.
DICE2016 Damage+ + FalR Climate
H&S Damage + FalR Climate
Temp. Anomelies (C))
Commitments made binding through action masks, which control the accessible action space during the following step. For example, negotiation could yield a binding commitment to a minimum of 20% mitigation rate. Then, the action mask only allows setting mitigation rates above that level for this region. We discuss extensions beyond this paradigm in Section 7.
Binding Commitments
2015
2035
2055
2075
2085
2015
2035
2055
2075
2005
mar
Mar
Figure 2. Extensions to the base setup of the framework. RICE-N is highly adaptable in that different components, such as the climate model or damage function, can easily be exchanged. We compare the basic oo-negotiation baseline (see Section 6) over different damage functions and climate dynamics. The DICE2016 damage function and DICE2016 climate model are taken from (Nordhaus, 2018). The H&S damage function is based on the recent estimates of (Hänsel et al., 2020), and the FalR climate model is a famous emission-basse climate emulator (Millar et al., 2017). The H&S damage function punishes temperature increases more strongly than the DICE2016 damage function, but the effect is still too mild during the roll-out period to lead to significant behavior changes in the agents under the no- negotiation scenario. The FaIR climate model implements more realistic climate dynamies and shows that a path to 2 C is still possible.
In Section 6, we will compare the of Basic Club, Bilateral Negotiation and No Negotiation.
impacts
5 Modeling Strategic Agents using MARL
f
The negotiation protocols and the climate-economic dynamics of RICE-N define game-theoretic setup between the different regions. We model the behavior of an agent i using its policy n. (arlor) that maps the agent's 's observations og to a probability distribution over its actions o, at time t.
Reason to use MARL Existing IAMs often use a pre- determined policy for each agent that is fixed exogenously. Such approaches would require handcrafted agent policies
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Global To mamurarture Anomaly from 2015
Global Carbon Emissions from 2015
region receives proportionally to how other regions tariff that region's exports (Nordhaus, 2021a) (see Appendix G for more details); The parameter 2 0 is the consumption elasticity which can represent the degree of risk aversion or the (un-jwillingness of society to sacrifice consumption today for consumption in the future. The discount models the long-term value of rewards for the agents, and as such it could differ across different agents. The discount factor for each region is often updated with the changing administration; in the absence of any consensus, we fix y to be homogeneous across agents as assumed in (Nordhaus, 2015). The aggregate consumption C2,t in the above equation is obtained by combining the domestic and foreign goods consumption using the Armington model (Armington, 1969);
Vartmam mmgzezsn
0 2000
1750
4 1550
Aetamaly
Mistrral regoratton con
1250
1000
750
500
250
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2015
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2053
2075
2005
2115
2015
20:35
2253
2075
2015
2115
Year
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1b)
Consumption
240
0.3
200
7.3
160
7.0
6.0
120
100
5.5
2013
2035
2003
2315
2015
2115
2013
2035
2035
2013
2095
2115
(c)
10)
*
Figure 3. Comparison of different baselines (mininum mitigation, maximum mitigation, and no negotiation) against negotiation protocols (Bilateral negotiation and Basic Club) with mean 1.96 stderr (see Section for more details). In respective order, we show the comparison of (a) global temperature anomaly (lower is better), (b) global carbon emissions (lower is better). (c) global output production (higher is better) and (d) global consumption (higher is better). While no negotiation performs best in the early stages of the simulation, it exhibits downward trend after 2090, suggesting that the adverse effects of rising temperatures start outweigh the economic benefits. In contrast, Basic Club surpasses no negotiation economically towards the end of the simulation while successfully maintaining a lower increase in temperature anomaly and carbon emissions.
outcomes among
C₁.t = (ydom (Cor,))
Σ eftor (Cisae
(
(3)
Oiga = -xij,(i -1155((1-Tess -
(4)
where Cr,g. is the foreign goods consumed after imposing tariffs Ti.j.t on the imported goods Tz.j.t by region from region at step I. ridom and yslor are shared parameters, and A is the Armington elasticity parameter that represents the degree to which consumers are willing to switch between domestic and imported goods when prices change.
Multi-agent reinforcement learning (MARL) Simu- lating a uullity-aximiziing agent requires computing the optimal policy for each agent". Finding the optimal utility- maximizing policy for each agent in response to complex en- vironment dynamics and other agent policies naturally leads to MARL; (Busoniu et al., 2008) provides a comprehensive overview of the topic. In short, MARL extends single-agent RL to find an optimal policy for each agent interacting in dy- namic environment solve Equation 1. The RL framework models how an agent's actions affect the state of the environ- ment and its rewards (utilities). Thus, an RL agent has to learn to anticipate the long-term effects of its actions. This is espe- cially true and challenging in multi-agent environments such as RICE-N, where agent actions affect key climatc-cconomil metrics including global temperatures, capital investments, carbon emissions, etc. In addition, MARL algorithms have to deal with the additional game-theoretic challenge of each agent's 's response to the policies of other agents. This makes the task of finding the optimal policy moving target (until a form of equilibrium is reached in the agent policies).
for each different negotiation protocol. Furthermore, the reliability of the outcomes from the simulation would depend on the modeled policies.
In contrast, we assume that each region strategically interacts with the environment and other strategic agents in it. Therefore, instead of manually setting the behavioral policy n, we use machine learning techniques to find policies that seek to maximize the objectives of the agents, and hence derive the agent policies endogenously.
Specifically, the agents are assumed to be millit-maxiimiiing such that each agent i optimizes its policy ny (axlos) to maximize its long-term aggregate dddiscounted utility:
H
max E
(1)
where ri is the utility of the region i at step / determined by its aggregate consumption Ct,t as follows:
Equilibrium Concept In contrast to the original RICE IAM (Nordhaus & Yang, 1996b), which discusses pure strategy Nash equilibria, RICE-N employs reinforcement
( Ci.e
Fie- = Uie
T- Li.e
w.
-
-1)-
(2)
Li,e)
where Li, is the population of the region at step f; w is the welfare loss multiplier that decreases the utility that a given
Although we assume the agents to he maiiity- other behavioral models could also be implemented in RICE-N.
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learning agents operating in a dynamic, partially observed environment with expanded action spaces and evolving negotiation protocols. As such, there is no single, fixed equilibrium concept that applies across all scenarios modeled in RICE-N. Instead, the emergent behavior of agents can approximate different forms of equilibria depending on the structure of the negotiation protocol:
negotiation protocols (see Section 4). We compare the climate-economic outcomes of these protocols with three baselines, namely a minimal mitigation policy, maximal mitigation policy, and a mitigation with no negotiation policy, We also examine the (group) fairness of these protocols across regional contributions by calculating the Gini Index of various climate-economic variables measured by RICE-N.
1. Equilibrium type: The negotiation protocol can give rise to the introduction of previously irrelevant equilibrium concepts, such as correlated equilibria from stochastic protocol.
Experimental Setup To compare outcomes with and without negotiation, we train five models consisting of (i) Basic Club, (ii) Bilateral Negotiation, (iii) negotiation baseline, (iv) Maximum mitigation, and (v) Minimum mitigation. The latter two models can only mitigate either the maximum or minimum possible amount, respectively; all other actions in (iv) and (v) are trained as normal. Each model is trained for 30, 000 episodes. For evaluation, we gather 50 rollouts of each model using unique seed per run to ensure a varied distribution of outputs. For more details about the concrete time series, please refer to Appendix M.
2. Punishment and enforcement: Action spaces that include tariffs or sanctions can affect the equilibrium and introduce the possibility of self-enforcement through collective punishment for defection.
3. Non-binding agreements: If commitment masks are relaxed to allow cheap talk, other solution concepts such coalition- proof Nash equilibria become relevant (Bem- heim et al., 1987).
Negotiation Protocols Can Improve Climate-Econonet Outcomes. In Figure 3, we illustrate the global temper- ature anomaly, carbon emissions, output production and consumption across time steps. To establish upper and lower bounds in performance, maximal and minimal mitigation strategies. The former consists of the maximum possible emissions reductions per time step and the latter features no emissions reduction.
4. Information structure: The negotiation protocol can affect what information is public vs private.
Thus, equilibrium behavior in RICE-N is not defined a priori, but emerges from the interaction of learning dynamics, available actions and the design of the negotiation process.
also compare our findings to
Implementing RL Agents Our code includes both CPU and GPU implementations of the full RL. pipeline using A2C (Mnih et al., 2016). RICE-N can also be used with other RL implementations. Our base implementation models each RL agent using a neural network policy that shares weights across agents, but uses agent-specific inputs. The architec- ture of the network can be adjusted, e.g., the number of layers and the dimension of each layer. Agent policies use separate heads for each action. To distinguish between agents, the policy model's 'ss input contains agent-specific features, e.g., their population, capital, technology factor, damage function, and a one-hot representation of the region's 's index, as well as the public state of the world (e.g., climate conditions). In addition, each agent receives information about negotiations, e.g., the latest proposals made to and by this agent, the min- imum mitigation rate agreed upon by this agent. Depending on the negotiation protocol, not all observations and actions are relevant to each agent. How negotiations evolve depends on the specifics of the protocol and the different actions exe- cuted by the agent, e.g.. proposals for other agents, decisions on proposals made by other agents, and setting mitigation and savings rates that may or may not be in line with what was agreed upon.
We see that Basic Club and Bilateral Negotiation perform vastly better than the minimal mitigation and no negotiation baselines, with temperature increase and carbon emission outcomes nearly matching the maximal mitigation baseline.
Economically, however, Bilateral Negotiation falls relatively short while Basic Club is not significantly worse than the minimum mitigation, maximum mitigation and no negotiation baselines at the last time step. In fact, Basic Club ends with steady output growth, as opposed the slowing economic growth of the minimum mitigation and negotia- tion baselines. The distribution of mitigation strategies under di different negotiation protocols is visible in Appendix I..
For global consumption, we see that no negotiation performs best, but this trend is unlikely to continue considering the decrease in economic production observed in later time steps because the damage from the increasing temperature would significantly limit the sustained economic growth in the long term. Minimum mitigation performs second best, but Basic Club results in nearly as much consumption at the last time step, which, paired with its promising steady growth in economic output, looks to result in more sustainable outcomes in the long run.
6 Evaluating Negotiation Protocols
Overall, the large room of improvement in the global temperature levels at the expense of relatively much smaller difference in production output shows the value of these
In this section, we use RICE-N to analyze the climate and economic outcomes of the basic club and bilateral
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protocols. To assess the robustness of our results, we conduct sensitivity analysis on selected parameters based on economic theory, which are the discount factor, welfare loss weight, consumption substitution rate, and relative preference for domestic goods. The results, discussed in Appendix K, confirm that our findings over differnt scenarios are stable under changes in critical model parameters.
While Bilateral Negotiation has limited real-world applica- bility, the On communication complexity for n agents is inefficient for large-scale international negotiations. Moreover, bilateral negotiations can lead to contradictory agreements with no feasible solution. This challenge underscores why most international climate negotiations opt for multilateral forums where all parties collectively discuss and agree upon terms, as exemplified by the United Nations Framework Convention on Climate Change (UNFCCC) process (Mantlana & Jegede, 2022).
Negotiation Protocols Impact Fairness To measure the (group) fairess of outcomes across climate economic variables of interest, we use the Gini index (Gini, 1912), statistical measure used to quantify the inequality of variables x within a population. The Gini Index ranges from 0 (perfect equality) to 1 (absolute inequality) on the variable of interest
From climate justice standpoint, both the Basic Club and Bilateral Negotiation protocols evaluated in this study do not adequately consider regional differences. The high mitigation rates achieved by these protocols may not be equitable or desirable for regions whose historical emissions are typically lower than those of others.
G(r) Dizl
j= I. 23]
12
(5)
2n225.
where n the number of agents, and represents the mean. Table 1 (left) illustrates the degree of inequality of different negotiation protocols across regions with respect to abate- ment cost, mitigation rate, carbon emission and consumption. We first note that both Basic Club and Bilateral negotiation result in lower inequality than No Negotiation when it comes to abatement cost, mitigation rate and carbon emissions. That is, the economic burden of emission reduction is more equitably shared when agents have the opportunity to negotiate with one another about their emissions reduction targets. The inequality of carbon emissions itself is less impacted, as the carbon intensity is largely region specific parameter. However, for the mitigation rate, the Bilateral Negotiation seems to have a significantly lower Gini Index than the Basic Club. Although this may appear desirable, it may not be optimal for all regions to contribute equally to mitigation efforts. In fact, in Table (right), if we contrast the Global Output Production and the Global Carbon Emissions of Basic Club and Bilateral Negotiation, it seems that Basic Club achieves significantly better economic outcomes at the cost of a slight increase in temperature while maintaining a similar Gini Index for consumption.
Potential Policy Implications Our findings suggest that the Basic Club protocol holds promise as a basis for real- world climate policy. However, the impacts of climate clubs and of border adjustment mechanisms depend significantly how they are implemented. Without complementary measures such as redistribution and technology transfer, these mechanisms risk functioning as de facto carbon taxes on developing countries that are heavily reliant on carbon- intensive development pathways (Goldthau & Tagliapietra, 2022; Perdana & Vielle, 2022). One way to mitigate this risk through instruments like the Loss and Damage Fund, which can support climate justice and compensate vulner- able countries for harms that are difficult to avoid adapt to (Boyd et al., 2021). That said, we caution that the outcomes observed in our framework should not be interpreted as direct predictions for real-world negotiations. Rather, RICE-N offers a simulation platform to explore, test, and compare the dynamics and consequences of alternative climate policy designs under controlled and transparent assumptions.
7 Limitations
Discussion and Analysis From climate oriented per- spective, Bilateral Negotiation outperforms Basic Club. This stems from the commitment mechanism used. Bilateral Ne- gotiation agents take the maximum of all accepted proposals and requests. Early on in training, those proposals exhibit a high degree of randomness. Hence, the maximum of random proposals is often near the maximum possible mitigation rate. We emphasize that Bilateral Negotiation intended as an ex- ample for RICE-N users which can illustrate the basic steps of negotiation and is not a realistic negotiation protocol. While Basic Club performs comparable, it involves a much smaller proposal action space, and is designed to reflect more realistic climate policy with real-world climate negotiations (Com- mission, 2022; Nordhaus, 2015; Commission, 2020).
RICE-N can be improved in a number of aspects. Firstly, we do not make use of regional damages and temperatures, which are captured by other RICE models. Representing regional disparities is critical for analyzing model outcomes from a climate justice perspective (Gazzotti al., 2021). Secondly, there are longer time horizon versions of RICE currently available (Biswas et al., 2024) that extend the simulation up to 300 years. Furthermore, RICE-N does not represent damage disparities within regions (Dennig et al., 2015) which may obscure the mediating role of socioeconomic class on climate damages. Finally, the reasoning and decision-making logic behind the negotiation process remains black box and lacks interpretability. as
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Table Climate-cconomic outcomes and Gini index the last time step (year 2115). In bold are the best results. If two results significantly different, we bold both.
GINI INDEX
CLINNIE- OUTCOMES
NEGOTIATION
ABATEMENT MITIGATION
CARBON CONSUMPTION
TEMP.
OUTPUT
CARBON (GIC)
CONSUMPTION (USD trillion)
PROTOCOL
COST (&GDP)
RATE (%)
(GIC)
(USD trillion)
((C)
(USD trillion)
None
0.695=0.018
0,405=0.018 0.011=0.007
0.654+0.008
0.529
5.121=0.032
233.6#3.9
1697.2425.6
8,96=0.04
Bilateral
0.333+0.005
0.565=0.020
0.54020.004
3.3420.03
209.4:5.5
487.0=15.2
8.33=0.05
Basic Club
0.339=0.006
0.030+0.006 0.579#0.017
0.541=0.003
3.422+0.018
235.1+5.0
534.7=9:50
8.55=0.05
directly stems from the actions of agents trained through multi-agent reinforcement learning (MARL) algorithms.
range of research and policy communities. Machine learning researchers can leverage the modular RL component to benchmark different reinforcement learning algorithms in dynamic, real-world-calinn entists can use the framework to compare alternative climate modules and damage functions under consistent economic and strategic assumptions. Governments may apply it to test the robustness of proposed strategic behavior and to anticipate potential impacts on inter- national trade. International organizations, such as the OECD or WTO, could use the tool to analyze the distributional and economic trade-offs associated with alternative climate policy designs and negotiation strategies. It contributes to the development of more robust and equitable climate policies, supporting efforts to mitigate climate change while maintaining sustainable economic development.
In addition to addressing the aforementioned shortcomings, we aim to extend RICE-N in the following directions. We plan to integrate multi-level reinforcement learning (Zheng et al., 2022b) to model the negotiation protocol of the Conference the Parties. Moreover, we aim to explore the inclusion of welfare redistribution mechanism (Orlov et al., 2024) as a component of negotiation. Additionally, we are ex- ploring the use of JAX (Bradbury al., 201 2018) to significantly enhance the performance of RICE-N. This would enable wide-scale sensitivity analysis across simulation parameters. Furthermore, we will leverage large language models to enhance the interpretability of the negotiation process. In our current setup, agents cannot deviate from agreed-upon actions for the specified time step years). While this assumption simplifies analysis and isolates the impact of the negotiation mechanism, it does not reflect the uncertainty and strategic mistrust present in weal-world climate negotiations (e.g., countries withdrawing from agreements). Future work should explore the incorporation of non-binding commitments, which would allow agents to deviate from agreements and engage in strategic communication or cheap talk (Crawford& & Sobel, 1982; Caparros, 2016).
environment. Climate sci-
policies to
8 Conclusion
In this paper, we introduced RICE-N, a novel integrated as- sessment model that combines climate-cconomic dynamics with aulti-agent reinforcement learning to simulate global climate negotiations and agreements. RICE-N offers flex- ible framework for testing various negotiation protocols and their impact on long-term climate and economic outcomes. We demonstrated the utility of RICE-NIr by implementing and comparing two negotiation protocols: Bilateral Negotiation and Basic Club. Our results show that both protocols can lead to improved climate outcomes compared to scenarios without negotiation while maintaining comparable economic performance. Notably, the Basic Club protocol, inspired by real-world climate policy proposals, achieved balance between emissions reduction and economic growth that surpassed the no-negotiation baseline in the long term. Beyond this specific application, RICE-N offers value to a

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Impact Statement
under scientific uncertainty. Proceedings of the National Academy of Sciences, 109(49):13722-17376 2012.
The goal of this work is to produce a climate-economic model that helps foster robust, durable negotiation protocols. Tools for collective cooperation such as RICE-N can help us move toward more sustainable, fair, and long-lasting climate-economic outcomes. However, such tools can lead to unintended consequences, including the carbon footprint of using RICE-N, economic inequality due to its limitations on the applicability to the real world.
Bernheim, B., Peleg, B., and Whinston, M. Coalition-
proof nash equilibria i. concepts. Journal of Eco-
nomic Theory, 42(1):1-12, 1987. ISSN 0022-0531. doi: http://db.oog///oo00666222221111 URL cockenne/arrticee//////222222221
Biswas, P., Zatarain Salazar, J., and Kwakkel, J. Adaptive strategies reconcile diverse equity preferences in climate policies. In EGU General Assembly Conference Abstracts, pp. 4387, 2024.
Carbon footprint It is important to acknowledge that using RICE-N inevitably results in carbon emissions. Therefore, we encourage users consider their energy usage when running experiments and offset their carbon emissions.
Boers, N. and Rypdal, M. Critical slowing down suggests that the western greenland ice sheet is close to a tipping point. Proceedings of National Academy of Sciences, 118(21), 2021.
Economic Inequality As previously discussed, economic inequality is inevitably intertwined with climate change. The consideration of approaches that address climate change should always include the economic inequalities that they could impact.
Bonabeau, E. Agent-based modeling: Methods and techniques for simulating human systems. Proceedings of the national academy of sciences, 9) 2002.
Real World Potential and Limits It is important note that predictions in RICE-N will eventually differ from actual outcomes due to inherent real-world complexity and the limitations of simulation dynamics. Therefore, decision makers should consider these limitations, and the possible gaps between simulated and real outcomes before making any policy decisions.
Boyd, H., Chaffin, B. C., Dorkenoo, K., Jackson, G., Harrington, L., N'Guetta, A., Johansson, E. L., Nord- lander, L., Paolo De Rosa, S., Raju, E., Scown, M., Soo, J., and Stuart-Smith, R. Loss and damage from climate change: new climate justice agenda. One Earth, 1(10):136--1370, 2021. ISSN 2590-3322. doi: http:///bbi.rg/////llooooooonana
Acknowledgments
URL htsps://ww..cceeceed..ccee com/ ccctene//arttieeep////5332222220
T Zhang acknowledges the support from Microsoft and Samsung. P Wozny acknowledges the support of the Fiscal Institute Tilburg. Cohrs acknowledges the support from the European Research Council (ERC) under the ERC Synergy Grant USMILE (grant agreement 855187). We ac- knowledge the support from the Canada CIFAR AI Chair Pro- gram and the Canada Excellence Research Chairs Program. We also acknowledge everyone who contributed to or joined AI4GCC (AI for Global Climate Cooperation) competition.
Bradbury, J., Frostig, R., Hawkins, P., James, M. Leary, C., Maclaurin, D., Necula, G., Paszke, A., VanderPlas, J., Wanderman-Milne, S., and Zhang, Q. JAX: Composable transformations of Python+NumPy programs, 2018.
Buitinck, L., Louppe, G., Blondel, M., Pedregosa, F., Mueller, A., Grisel, O., Niculac, V., Prettenhofer, P., Gramfort, A., Grobler, J., Layton, R., VanderPlas, J., Joly, A., Holt, B., and Varoquaux, G. API design for machine learning experiences from the scikit-learn project, 2013.
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A Extend Related Work
Multi-agent aspects of climate change. Previous work has studied the connection between political economy, negotiations, and climate change. Empirical work has found that previous climate summits have had inconsistent or too little impact (Chan et al., 2022; Bakaki, 2022). The impact of social dynamies has been studied in a stylized climate-social model, finding that public perception and institutional responsiveness are important to explain variations in emissions (Moore et al., 2022). The formation of coalitions and agreements under climate negotiations has also been studied from a game-theory perspective (Zenker, 2019). IAMs have also been used to study the impact of political bargaining on the economic burden required to meet climate targets (Rochedo et al., 2018). However, to the best of our knowledge, no work has analyzed the game-theoretic aspects of climate cooperation using machine learning and calibrated LAMs.
Social dilemmas. Our work also is also one of the social dilemmas, situations where selfish agents act to lead to collective outcomes. These dilemmas are also a subset of general-sum games. Prominent examples of social dilemmas include the Iterated Prisoner's s Dilemmaa (Rapoport & Chammah, 1965), where two agents repeatedly decide whether to cooperate or defect, and the Coin Game (Lerer & Peysakhovich, 201 8), in which two agents navigate a 3 grid to collect coins that appear in red or blue. Agents receive rewards for collecting any coin but incur penalties when their opponent collects a coin of their own color, creating tension between selfish coin-collecting and the Pareto-optimal "color-aligned" strategy. Another example is the Negotiation Game (Cao et al., 2018), where two agents simultancously propose how to divide valuable items, cach striving to secure items they highly value while risking worse outcomes if both demand large shares of the same limited resources. Furthermore. Diplomacy (Paquette), an adaptation of the classic Diplomacy board game tailored for multi-agent research, requires players to negotiate alliances, coordinate actions, and balance cooperative and adversarial incentives to expand territorial control without overextending themselves.
Strategic behavior and climate change. Game theory has long studied the collective behavior of self-interested agents, e.g., the tragedy of the commons (Hardin, 1968), negotiation and agreements of agents with conflicting and common goals (Schelling, 1980). Certain works have analyzed international negotiations on climate collaboration and agreements regarding economic activity and climate efforts, e.g., imposing tariffs on countries that do not mitigate sufficiently. Experimental research highlights the collective action dynamics of climate cooperation. Uncertainty about the likelihood of catastrophic scenarios (Barrett & Dannenberg, 2012; Milinski et al., 2008) and interagent inequality (Dannenberg et al., 2015) has been found to hinder cooperation; however, interagent communication (Loschel et al., 2011) and early mitigation commitments facilitates it (Dannenberg et al., 2015). Climate negotiations have been studied using mathematical games, e.g., coordination games or prisoner's 's dilemmas (DeCanio & Fremstad, 2013). However, the reliability of such simplified models for real-world policy has been called into question. In particular, these games lack (i) a multilateral, rather than bilateral, setting, (ii) strategic behavior from agents with multiple, possibly conflicting, goals, (iii) evolving climate dynamies and changing agent behavior that lead to non-equilibrium outcomes, and (iv) heterogeneity among agents (Madani, 2013).
Subsequent work has gone beyond equilibrium analysis by modeling climate negotiations bargaining game in which agents learn, albeit in highly simplified manner (Smead et al., 2014). Climate scenarios could be studied through the emergence of climate mitigation from these games with learning, in which regions can cooperate or compete (Greeven et al., 2016). Furthermore, other work has studied the difficulty of long- term climate collaboration (Carney, 2015), as well as potential mechanisms for overcoming associated issues (Nordhaus, 2015).
Multi-agent reinforcement learning (MARL) MARL has emerged in recent years as an attractive framework that studies how to train utility- miliittimaiiizziggggg agents that may communicate, cooperate, compete. This is rich area of research that intersects machine learning with game theory, economics, and other domains (Shoham & Leyton- Brooon, 2008). Games can be classified as cooperative, competitive, or mixture of both. In fully cooperative games, agents learn to work together, e.g., to lower the carbon power consumption of heating, ventilation and air conditioning (HVAC) systems (Mai et al., 2024; Hanumaiah& & Gene, 2021; Yu et al., 2020). or in the game of Hanabi (Yu et al., 2021). On the other hand, in a competitive game, agents may need to find strategies to defeat opponents, e.g., in Diplomacy (Paquette et al., 2019) and Go (Schrittwisser et al., 2020). However, many games are neither purely competitive nor purely cooperative (Duque et al., 2024). These are called mixed-motive games since incentives of agents are partly misaligned. A common and extensively studied example is public goods games (PGG) which describes the social dilemma between collaboration (contributing to common pot) which is the Pareto optimal outcome, and the free riding (keeping the resource for oneself) (Anderson et al., 1998; Santos et al., 2008: Orzan et al., 2024). In the context of climate change, it has also been studied studied (Tavoni et al., 2011).
Beyond abstract games, MARL has been increasingly applied to real-world scenarios where cooperation and competition are in- tertwined. For instance, Wang et al. (Wang et al., 2021) applied MARL to large-scale traffic signal control, balancing individual
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intersection throughput with global traffic flow. In energy systems, May et al.(May & Huang, 2023) used MARL model and optimize peer-to-pect prosumer markets, where agents must trade off self-interest and collective grid stability. Similarly, Hou al. (Hou et al., 2025) introduce InvestESG, MARL benchmark where agents need to navigate the trade-off between short-term profit goals and long-term climate resilience by strategically investing in mitigation, greenwashing, and adaptation measures.
Recent work has explored the link between MARL and negotiation (Cao et al., 2018), as well as cooperation social dilemmas and collaboration on climate change (Jaques et al., 2019; Chelarescu, 2021; Le Gléau et al., 2022). As such, MARL an attractive framework to analyze climate outcomes which takes strategic behavior into account. However, previous work has largely considered highly stylized environments and has not yet been applied to rich calibrated climate-economic simulations; our work fills this gap.
B Parameters and variables
Tables 2, 3, 4,5 and 7 list all (calibrated) parameters and variables.
Table 2. World-state variables. Global type variables correspond to the entire world, whereas regional type variables correspond to each region. Endogenous variables those which are affected by the agent actions, whereas exogenous variables are those that predetermined and not affected by agent actions. Note that the values of endogenous variables can vary across steps in a predetermined manner. Notation: indices are separated from subscripts referring name by semicolons (ę). For instance, the parameter 01 varies in time ! and by region i, which is denoted as O1a.c. Symbol
Variable
Type
Description
Carbon Mass
Global, endogenous
Mc. [M M. MP
A three-dimensionas vector that indicates the average carbon accumulation in the atmosphere, upper oceans, and lower oceans.
Temperature
Glohal, endogenous
T. (TAT, T
A two-dimensional vector that indicates the average temperature of the atmosphere and the lower ocean.
Population Technology
Regional, exogenous Lig Act
Population the labor in region.
Regional, exogenous
Technology factor in the production function of a region.
Capital
Regional, endogenous Regional, exogenous
Kut
Total capital accumulated by region.
Carbon intensity of economic activity Balance of trade
scalar coefficient that gives the emissions resulting from economic production. Surplus or deficit from international trade activities.
Regional, endogenous
Di,
Cost of mitigation efforts
Global, endogenous
An estimate of the cost of mitigation efforts.
Emission due to land
Regional, exogenous
Elland
Carbon emission for land use in a specific region.
Table 3. Agent-action variables. Description
Variable
Symbol
Savings rate
$6,1
The fraction of output production be invested in capital.
Mitigation rate
Pe.
The fraction mitigation efforts by a region.
Import tariffs
Te.j.t pl. bi.je
The fraction imports that are converted to tariff' revenue.
Export limits
The fraction of domestic production that regions are willing to export.
Import bids
The amount of production each region is willing to import from other regions.
C The Activity Component: Climate, Economics, Trade, and Tariffs
C.1 Climate and Economic Dynamics
We now describe the RICE-N dynamics developed from DICE and RICE models by (Nordhaus, 2018; Kellett et al., 2019) that govern the evolution of the world state from time t to t 1 for the different regions. Note that variables without an agent index are global quantities.
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Table 4. Agent-specific constants.
Variable
Symbol
Description
Initial population
Los
The imitial population for specific region.
Population convergence target
Lan
The estimated convergence population for specific region.
Population convergence
How fast the current population converges.
Initial capital
Ko
The initial capital for a specific region.
Initial carbon intensity
Ongi
The initial carbon intensity for a specific region.
Carbon intensity parameters
Gozi and &
The decay speed of the carbon intensity.
Initial technology factor
Auai
The initial carbon technology factor for a specific region.
Technology factor parameter
Gi.4
6,,A
The update pattern of the technology factor.
Initial land use emission
BLDA
The initial land use emission for specific region.
Land use emission parameter
θELS
The depreciation rate for the land use emission in a specific region.
Table 5.
Global constants.
Variable
Symbol
Description
Capital clasticity of production
X
The contribution from capital and population to the cconomy. How substitutable consumption goods from different regions are.
Armington substitution parameter Long welfare discount rate capital depreciation rate Backstop technology
p
How much short-term welfare weighted versus long-term welfare.
4x
The capital depreciation rate.
ps
Price a backstop technology that can remove carbon dioxide from the atmosphere.
Backstop technology parameter Mitigation efficiency parameter Domestic share parameter Foreign share parameter
8pb
The decay speed of the cost of backstop technology.
The efficiency loss component mitigation
26 dd
The relative preference for domestic goods
The relative preference for foreign goods
Carbon mass.
The total carbon mass in the climate system is given by:
M411 T M4
BM
E Eicto
(6)
F,,
F. ELand
+ Fi,((1
(7)
M, =
MAA
MUP
M.
]
R
(8)
C11
S12
PM
C21
C22
C23
(9)
C32
Ç33
E2
Ba* =
0
(10)
0
This describes three-reservoir model of the global carbon cycle, in which MT describes the average mass of carbon in the atmosphere, Mup is the average mass of carbon in the upper ocean, and MLo the average mass of carbon the deep or lower ocean, see Figure 5. P is the Markov transition matrix describing how carbon transfer between different reservoirs. BM describes how the weight carbon emission affects the carbon accumulation in the reservoirs.
Global temperature. Ultimately, increasing carbon mass leads to rising temperatures:
T Ti + Ft,
(11)
T. = TAT
T.o 1 1
(12)
MAT
F, F2x logg
(13)
175.
Φ1
Φ12
4
(14)
221
422
{3
Br
(15)
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Similar to the carbon mass dynamic, there are two layers in the energy balance model, see Figure 4. TAT is the combined average temperature in atmosphere, land surface, and upper ocean (simply referred to the "atmospheric layer" hereafter). Tro is the temperature in the lower ocean. Φ is the Markov transition matrix describing how heat transfers between different layers. By describes how carbon mass contributes to the temperature increases.
Output production.
The production in a region is given by the total factor productivity (TFP) (Comin, 2010) formula:
YL = K7, 1
(41)
Production depends on three factors: total factor productivity ("technology") Ar, capital Kr, and labor L.- This production function is common in the economic literature and used in the DICE/RICE models. The capital clasticity 7 E [0. 1] explains the different levels of contribution of capital and labor.
Population. The number of people in a region, denoted L, grows as:
( 1 + Last
L1,41 Li,
(39)
I I+ Lige
There are two parameters Loj and lg:i- Lost represents the convergence population of region and (g:1 shows how fast the population Li, converge to Lagi. Please refer to the Appendix H for more detailed analysis and the calibration procedure.
Level of technology. The technology factor A, describes how efficient production is, i.e., how many units of output a region achieves given fixed capital and labor:
A = (e" + gAse (
(40)
Here, represents the long-term growth of economics which is usually larger than 0, 9A represents the short-term part of economics growth, and óA represents the speed of decay of short-term growth factor. A is the time difference between steps. We use 1) = 0.33% as in (Nordhaus, 2018).
Capital. The amount of capital evolves as:
K (1 0K)
(16)
K1,t+1 = 2 Ki, + (1 a1 - a2 (IIAT) ))
(17)
x 1 (1-0 Ve,8i
(18)
The evolution of the capital comes from two parts. The first part capital inherited from the previous period with depreciation. In the second part, 8t is control variable which represents the investment/savings rate (as a fraction of production). That is, base amount, the economy invests/saves a total of St., which yields new capital. This base amount is further modified by 2 multipliers: the damage function and mitigatiion/baatement costs, which are discussed below.
Damage function. The climate damage function represents the economic damage due to climate change, e.g., increases in the atmosphere temperature TAA. That is, in Equation 37, the fraction of new capital is modified by the damage function
T.T 02 (TAT)²
(19)
following (Nordhaus, 2015). That is. higher temperatures lead to less new capital. Similarly, 1 015.e/44 of new capital after taking into account carbon emission mitigation. Mitigating carbon emissions more (higher μ4) means (dirty) production needs to be lowered, hence yields less new capital.
02 the fraction
Mitigation (abatement) cost.
Following (Kellett et al., 2019), for mitigation rate f4, the mitigation cost
(20)
where 015,e is given by Equation 38. This represents the loss in capital growth due to a fraction of production being used for mitigation.
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Ft
E
T
P1
T
21
@1
22
Figure 4. The two-reservoir temperature model.
S12
S23
E
Ena
B
MAT
M
S21
S32
C11
22
S33
Figure 5. The thrce-reservoir carbon mass model.
Carbon intensity of economic activity. A critical part of the model is the interaction between the climate and economic parts. Specifically, the RICE model describes how production leads to carbon emissions:
ELand EL (1 5EL))=1
(21)
F,,- E.Land + oi, -Me,)
(22)
01t++1 Jz,e -on (ou(1-bn1 A
(23)
Here Elud is the carbon emission due to (changes in) land use, Er.o is the carbon emission in the base year, and y is the speed of decrease of changes in land use. The rates 0 < dEL < 1.0 < 8eo < 1 are free parameters. Due to lack of data, Ellnd is set to be the same for each region.
F,, is the total carbon emission, Flland is emission from natural sources, while F,,, EEland is emission caused by economic activity. Ai, is the effective carbon intensity of economic activity: a higher technology factor lead to higher emissions, but can be modulated by lower a (which can be thought of as the degree of "clean" production), μi,r [0, 1] is a control variable called the abatement (ratio), which represents the proportion of the economics contributing reducing carbon emission. Furthermore, we have 2 parameters 9o and 6, that are fitted data. Jo is the rate of decrease in carbon emissions.
C.2 Trade
We now describe the international trade dynamics and the resulting regional consumption and utilities. Regions trade by exporting their consumption goods and importing other regions' consumption goods fixed unit price*.
Agent actions. Each region at time must first specify desired basket of consumption goods bi,t = [br, ... b...ee that they are willing to import from the other regions. These desired imports form matrix of bids B, such that the import bid by re- gion for goods from j at time / is b,, 2 0, i.e., the amount of goods region is willing to import from region at time is by.
Regions also set an upper bound pf, E [0, 1] on the proportion of their own consumption goods that they are willing to export.
Tariff's. Regions can also choose impose import tariffs on other regions. We denote an import tariff imposed by region i on a region by Ti.j. E [0, 1]. If region imposes an import tariff Ti.j.t [0, on region j. region consumes
Cuja =
R x1 Te.j.)s
(24)
and Li is added to reserve fund specific that region. Consumption. Consumption of domestic goods Ci.i, is determined according to gross output, the savings rate and exports:
Cra, (1 (1--5,,)) St,
Σ
(25)
371
Mooe generally, prices should dynamic, but the current implementation does not support this.
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The aggregated consumption Cs,e time for region is given by the Armington elasticity model (Lessmann al., 2009))
follows:
Ciee
(ydo (yddom (C
Evsto
Sstoo (Cesit)
(26)
5#1
C.3 Negotiations
Here, we outline the extra state representations and actions that are introduced when either of our two negotiation protocols active in the simulation. These variables are used in the negotiation phases, which are detailed in Section 4, on top the already available variables in Tables 2, 3, 4, and 7.
Table presents the agent actions required by the Bilateral Negotiation and Basic Club protocols. These actions are additionally incorporated into the observation space of the agents at each timestep as bilateral observations, meaning that agent will observe its own negotiation action and the action of other agents when it is part of that negotiation. In addition, each agent observes an additional indicator that signals the current phase of the environment (proposal, evaluation, or no negotiation step). Lastly, agents also privately observe the outcome of their negotiation: their minimum mitigation rate or club mitigation rate Pe-
We note that other negotiation protocols may modify these action and observations spaces as needed.
Table 6. Agent-action variables introduced when one of our negotiation protocols is enabled in RICE-N. These variables are additionally added as bilateral observations the observation space. In Basic Club protocol however, the request action is excluded, and each agent proposes a single mitigation rate to all agents. The result of these negotiation actions sets agent's minimum mitigation rate or club mitigation rate pic-
Variable
Symbol
Description
Proposed mitigation rate
Paga / Pi.t
The minimum mitigation rate proposed by agent to agent j. In basic club, single proposal is made by cach agent all other agents.
Requested mitigation rate
Pega
The minimum mitigation rate requested from agent ý by agent Only used in the Bilateral Negotiation protocol and not in Basic Club. The decision of agent on the proposal and request by agent.j.
Proposal decisions
eija
D RICE-N dynamics
At a high-level, Equations 35 and 36 capture climate dynamics (temperature and carbon mass), while Equations 37, 39, 40, and 41 capture economic dynamics. Finally, Equation 42 captures the carbon inttonnnnttettttyy of production, providing a key link between the climate and economic sectors.
E Computational Complexity
The computational complexity of our MARL approach is driven by the number of regions N (i.e., agents). Since each agent's action space scales linearly with the total action space across all agents grows quadratically (O(n)). However, the number of agents in our setting is naturally bounded by the number of countries the planet. Currently, training 27 agents for 100 thousand episodes takes approximately 3 hours on a 30 CPU cluster. Future efforts will be directed at more efficient implementations using JAX-based acceleration and model parallelism to improve runtime, which will enable large-scale sensitivity analyses and experiments.
Creating a 27-Reg Simulation
We feature 27 fictitious regions in our simulation. These are inspired by merging and splitting real-world countries, but are not exactly the same real-world regions.
We used real data from the World Bank API (WorldBank, 2022), e.g., GDP, capital stock, population, and COn-quivalent (CO2eq) emissions. Furthermore, the World Bank groups countries into regions, including Sub-Saharan Africa, South Asia, North America, the Middle East and North Africa, Latin America and the Caribbean, Europe and Central Asia, East Asia
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Algorithm 1 Activity Component (implemented by cl immat aaaaanndcoooo ewonomy.simul.....m............e www.mmaaaaiiiii.... () Note that only list imput state variables and omit model parameters.
Require: exogenous emissions, land emissions, intensily, production factor, labor, capital, previous global temperature, previous government balance
Require: actions: mitigation rates, saving rates, tariffs, export rate limit, desired imports for each region do
mitigation cost (intensity)
Equation 38
damages (previous global temperature)
b Equation 19
ahatement cost < f mmitigation rate, mitigation cost)
b. Equation 20
production (production factor, capital, labor)
Equation 41 Equation 41
gross output (damages. abatement cost. production)
government balance <- (interest rate, previous government balance) investment k- / /saaving rate, gross output)
& Using Equation 37
scaled imports f (gross output, desired imports) debt ratio - (previous government balance)
Equation 55
Equation 56
scaled imports (scaled imports, debt ratio) end for
Equation 57
for each region do
potential exports +- (gros output, investment, export rate limit)
Equation 58 b Equation 59
Scaled imports + (scaled imports, max potential exports)
end for
for each region do
tariff-ed imports, tariff revenue fsccledd imports, tariffs) domestic consumption + f( (savings, gross output, scaled imports) aggregate consumption
Equation 24
Equation 25
/ (domestic consumption, tariff-ed imports) utility <- (labor, aggregate consumption)
D. Equation 26
Equation b Equation 60
government balance <- (imports, exports) end for
temperature fprevious temperature, previous carbon mass, exogenous emissions)
carbon mass +- (previous carbon mass, intensity, mitigation rate, production, land emissions)
for each region do
capital (capittll investment)
Equation 37
labor <- flaborr)
Equation 39
production factor (capital)
b Equation 40
carbon intensity + fcarbon intensity)
b Equation 42
end for
and Pacific. In each region, the different countries (or sub-regions) are classified into 4 income groups: high income, upper middle income, lower middle income, and low income.
Merging regions. We assume the GDP, capital stock, and population for the regions are additive. We also assume the gross COAeq emissions across the regions are additive. Thus, we have
Km
Σ K
(27)
Tm
Σ Tas
(28)
Ym
Σn, Yi,
where Y. A,K,
(29)
Ym
Am
(30)
K7, 11-7
0m
Ym
(31)
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Note that the production function is scale-invariant:
Y = (A,L))
(32)
c. Y = (c- * (c. A.)( (e) L.) Ve> 0.
(33)
(34)
Hence, one cannot get the technology after merging multiple regions by simply adding the individual technology levels. Rather, the combined technology factor imputed from the combined productions, labor, and capital.
MAA MAI,1750
T.+1 PrT + BT
F2x log2
+
+FEE
FEX
(35)
M4+1 = DM Mr + BM
Σ -1. - -o, + Eq
(36)
Ki,+1 = K + A -1-ay TI- 02 (T.T)) (1 (1-0s1e1ht)) Ve.8i.
(37)
015,1 = 1000 02
Pb
(1 - 5pb)
11 Jis
(38)
1 Lai
1911
11,411 Li.1
(39)
1 Liie
A1,+1 = (E" + DAAEE A(t-)(1 Ai,t
(40)
YLA K7, 1,,77
(41)
Tit+1 Diee T -oa ((--)))
(42)
Splitting large regions.
To avoid huge economies that dominate the fictitious world, split large economies into pieces based on predetermined fractions and random sampled As:
Σ G 1,
(43)
L G.Lm
(44)
Y, = GYm:
(45)
Yi
K, A,L,
(46)
0, on.
(47)
G Welfloss
Welfloss, w stands for loss of welfare due to imposed tariffs (Nordhaus, 2015). relies on wl, the unit of welfare loss per unit of tariff which Nordhaus calibrates .4.
wl .4
(48)
Whe = wl Σ
bi.ie
Ti.i.
(49)
Yi,
H Model Calibration
The structural parameters of the RICE-N simulation were calibrated meet the following objectives:
23

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AT for Global Climate Cooperation
1. Temperatures match the real data in different versions of RICE-N with 3 regions, 7 regions, 20 regions, 27 regions, and 189 regions, under 0% and 100% mitigation.
2. The Assessment Report (Pörtner al., 2022) (2 C 5 increase in the year of 2100). Each region optimizes the target without negotiation and direct cooperation in the pessimistic case. In the optimistic case, regions negotiate with each other using the baseline bilateral negotiation protocol. Please also notice that in the extremely pessimistic case that regions ignore climate change at all and always choose 0% mitigation and 100% savings, the temperature leads to approximately 7 increase the year 2100.
temperature outcomes the projects of Shared Socioeconomic Pathways in the IPCC Sixth
The parameters that we estimated and the corresponding estimation methods are listed below:
The dynamic parameters for total factor productivity A: 9A and 6
The capital K: for the regions whose capital data is not available, we use KNN regressor (Buitinck et al., 2013) to estimate
The dynamic parameters for population L: Zg: similarly, for the regions whose convergence population data is not available, we use a KNN regressor to estimate it.
The initial carbon intensity ou: for the regions whose capital data is not available, we use a KNN regressor to estimate it.
KNN regressor: Because all regions have GDP and population data, use them as features. For each region that lacks emission data and capital data, we find the nearest 5 neighbors according to its GDP and population. We use the average of the neighbors' emission data and capital data as the estimated values.
H.1 Population dynamic calibration
Denoting Loogi == lime-+o Lig in the limit - oo we have:
1 + Liaft
Looi Loogs
(50)
1 + Looos
1 + Last
(51)
1 Tro
As long as lg:s is not zero, Loo; = Lusi- Thus, La:: is the long-tern mengttermpg population size and free parameter that is fitted to data. Assuming (1412.1..... is monotonically increasing or decreasing, the absolute value of represents how fast converges to La;i- The closer Li, is to monotonically increasing or monotonically decreasing in the real data, the easier it to fit ge and Layi-
To fit the population parameters, we take logs on both sides of Equation 39:
log Li,++1 log Li, + Ig: (log (1 + Lan) log (1 + Li,e+1));
(52)
where log Li,+1 log Li, and log (1 L2,)) are given by the data. log (1 Li,e) and lya then be estimated by linear
regression.
H.2 Technology dynamic calibration
We estimate both ga and A from the existing data {At by solving regression problem:
Dazs 8t = arg max Li.e
(53)
Sa:
C,t || - (exp 9A, exp (-6A, ex,
(54)
This can be solved by numerical optimization algorithms, e.g., as provided in SciPy (Virtanen et al., 2020).
Because the emissions data from the World Bank API do not fit the form the a dynamic as assumed by DICE2016, use the DICE2016 parameter values for do and oz.
24

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AT for Global Climate Cooperation
Table 7. Calibrated parameters for 27 regions
Region ID
Ao
Ko
Lo
La 669,594
9A
1g
1
1.872
0.239
476.878
0.139
0.122
0.034
0,456
2
8.405
3.304
68.395
93.497
0.188
0.103
0.058
0.529
3
3.558
0.109
64.122
135.074
0.161
0.127
0.026
0.816
4
1.927
1.424
284.699
465.308
0.244
0.134
0.024
1.221
5
8.111
0.268
28.141
23.574
0.163
0.106
-0.057
0.290
6
4.217
3.184
548.754
560.054
0.170
0.095
0.080
0.302
7
2.491
0.044
46.489
59.988
0.058
0.049
0.037
0,420
8
2.525
1.080
69.194
100.016
0.346
0.079
0.029
1.010
9
2,460
0.184
513.737
1867.771
1.839
0.462
0.017
0.310
10
12.158
2.642
38.101
56.990
0.131
0.063
0.020
0.350
11
0.993
0.160
522.482
1830.325
0.086
0.065
0.019
0.235
12
5.000
2.289
165.293
230.191
0.183
0.071
0.027
0.419
13
29.854
2.020
165.751
216.927
0.088
0.075
-0.002
0.254
14
23.315
3.039
109.395
143.172
0.088
0.075
-0.002
0.254
15
29.854
0.687
56.355
73.755
0.088
0.075
-0.002
0.254
16
10.922
0.606
705.465
532.497
0.096
0.168
-0.016
0.781
17
9.634
0.608
465.607
351.448
0.096
0.168
-0.016
0.781
18
8.621
0.453
239.858
181.049
0.096
0.168
-0.016
0.781
19
3.190
0.129
690.002
723.513
0.054
0.068
-0.013
0.949
20
2.034
0.381
455.401
477.518
0.054
0.068
-0.013
0.949
21
13.220
16.295
502.410
445.861
0.252
0.074
-0.033
0.170
22
3.190
0.044
234.601
245.994
0.054
0.068
-0.013
0.949
23
6.387
1.094
317.880
287.533
0.194
0.237
-0.053
0.840
24
2,481
0.090
94.484
102.997
0.203
0.201
0.037
1.665
25
10.853
17.554
222.891
168.351
0.005
0.000
-0.012
0,285
26
4.135
1.002
103.294
87.418
0.158
0.123
-0.063
0.601
27
2.716
1.034
573.818
681.210
0.097
0.101
0.043
0.638
Trade constraints
To ensure that total imports and total exports match, three constraints enforced regions' trade flows.
1. For each region i, if the region's 's total desired imports from other regions exceed its own gross output, then the imports are scaled to sum up to the region's gross output. We enforce the constraint that Σity br.j.t S Qi.t which is to say that a region may not import more goods than its current gross output capacity. This constraint helps the agents avoid insurmountable debt, thereby stabilizing trade balances over the entire time period while also easing learning. If region's desired imports exceed its production capacity, then its import bids scaled down to size:
{
Qie Eits bis.e
bi.g. - by.g.t min
(55)
Regions are allowed carry (positive or negative) trade balance D,,t- At the start of each new time step, each region's trade balance, positive negative, accumulates interest fixed rate of 10%. Based this balance, region's debt-to-initial-capiaal ratio is determined and the imports are scaled according to this ratio:
Dis
d 10
(56)
Ko
biga - j. dz.e).
(57)
3. other regions' total desired imports from region i exceed region é's upper bound on exports æ then the bids for goods from region are scaled proportionally max Otherwise, each region receives its full import bid from region In other
25

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AT for Global Climate Cooperation
words, region i cannot export more goods time / than it could consume at time I, other regions will import less from region i.
man iit
min(yi, Qiess Qia -1,,),
(58)
max
Zi.. bigir min
2,t
(59)
Eefes Dr.g.t
After all constraints have been applied, the trade balance for the next period is calculated:
Dist1 = Dia + A Easat
Σ
Faijet
(60)
J#1
J Legal Framework
Tariff enforced mechanisms, such as Basic Club, must comply with the World Trade Organization's (WTO) General Agreement on Tariff and Trade (GATT); specifically, the "most favored nation" clause which requires that tariff's be non-discriminatory, At face value, Basic Club would appear violate the clause; however, exceptions made in the following cireumstances:
The agreement promotes one of the artcee XX (g) objectives; namely, "relating the conservation of exhaustible natural resources."
The agreement should contribute the objective.
The agreement should not discriminate between countries. If it appears to, then its discrimination must be the grounds justifies the rationale.
This legal framework has precedent since the 1998 WTO Appellate Body Report "United States Import Prohibition of Certain Shrimp and Shrimp Productions" (Shaffer, 1999). Basic Club inherits this legal framework with respect to GATT compliance. Furthermore, tariffs can be WTO compliant if they correct existing trade imbalances, as is the case with carbon leaking regions which have a competitive advantage, or are used as a punitive measure against misconduct (Pihl, 2020; Mavroidis de Melo, 2015).
K Sensitivity Analysis
We carry out sensitivity analysis to test the robustness of the results under different parameter settings. Since the space of possible configurations is large, we perform a sensitivity analysis over subset of economically relevant parameters, namely the discount factor, welfare loss weight, consumption substitution rate and relative preference for domestic goods. Figure Appendix J shows the percentage change in outcome variables of interest across different scenarios when critical model parameters are perturbed by a multiplication factor ranging from 0.96 1.04. The maximum percentage change 3. 16% while the mean is -0. 0.22% and the medium -0.36%. We thus conclude that the dynamics are stable, corresponding to changes in critical model parameters.
L Mitigation Distribution
To explore the range of strategies that emerge under different negotiation protocols, we analyze the distribution of final mitigation rates of each agent. This clarifies for each negotiation protocol what proportion of agents are ambitious mitigators, free-riders, low-effort mitigators. Results are visible in Figure 9.
M Detailed Outcome and Fairness Times Series
Figure and Figure 8, provide the timeseries and equity of various variables over relevant scenarios. The bump in carbon emissions within the first time steps a result of the constraint that regions cannot abruptly change their mitigation rate, but only adapt stepwise, leading to slow ramp-up mitigation at the start the rollout. Even with the maximum mitigation rate, base emission level remains, as land emissions are assumed to non-redueible.
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AT for Global Climate Cooperation
Temperature Change (%) by Scenario and
Carbon Emissions Change (%) by Scenario and A
Change by Scenario and
1.00
4
0.12
40.4
-0.58
-0.38
-0.09
0.89
-1.51
-0.75
-0.38
0.64
0.75
3
0.00
0..77
4.21
0.64
.0.47
3
0.56
-0.47
-0.21
.0.76
-0.79
2.62
-1.83
-0.33
-0.74
-0.86
-2
0.50
2
0.41
40.57
-0.43
-0.64
40.47
0.68
-0.23
-0.54
-0.76
-0.56
3.16
-0.48
-0.62
-0.82
-0.62
0.25
-1
0.00
-0.57
0.00
-0.43
0.47
-1
0.31
-0.35
0.04
-0.42
-0.37
-1.25
-0.17
A96
00.41
00.57
0.00
0.00
0.47
-0.18
-0.29
0.16
0.23
-0.50
-0.25
0.00
.0.57
0.56
-0.77
0.04
-1.22
-0.96
-0.50
0.00
0.17
-0.43
-1.39
0.33
-0.38
1.66
-1.69
-2.15
0.27
-0.11
-0.75
-1.0
0.41
0.57
.0.21
0..11
0.00
0.74
-0.08
0.07
-0.21
40.11
3.13
-0.28
-0.62
0.39
0.04
-1.00
Basic dlub
Biattrra
Max mitigation
Min mitigation
No negotiation
Basic club
Blateral
Max mitigation
Min mitigation
No negotiation
Basic club
Bilateral
Max mitigation
Min mitigution
No negotiation
Scenario
Scenario
Scenario
Figure 6. Sensitivity analysis: heatmap showing the percentage change in variables of interest (including Temperature, Carbon Emissions, GDP) across different scenarios (x-axis) when critical model parameters (including the discount factor, welfare loss weight, consumption substitution and relative preference for domestic goods) perturbed a multiplication factor of A). The parameter A varies from -0.04 to 0.04 (y-axis). For example, looking at the bottom left corner the Temperature Change heatmap, a 1% decrease in the model param- eters leads an increase final temperature of 0.41%. Overall, the variables of interest are rather insensitive to changes the model param- eter values. For reference, the global temperature anomaly increases by over 200% from 2015 to 21 15 in the Maximum mitigation scenario.
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AT for Global Climate Cooperation
Abotement Cost WVGDP) Over Time
Canaao Duo
120
Minur Mogaton
Migeeten
300
1.2
Canton
225
(a)
(b)
Milgation Rate Over Time
Convumplinn pet Capit Dver Time
Negiloree Ho0 aecgedon sugettrae
125
15.0
Voemue sen sater
Panman Magyton
Rogobation
17.
26.0
72
12.3
17.5
(c)
(d)
Figure 7. Time series of key variables across various scenarios.
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Absterrent Cool (NGDP)) Gini coefficient
Coeff
08
Regatiaton
0.00
vediun intiadion
Nettam Hiaaatiee
273
3iaoml segorazze
179-
000
Nogdidan
Mopoton
Negetaton
(a)
(b)
Coefriient
Consumprion per Capits Givl Coeffic ert
Chreis Cup
Ritgttin
Dealerel Megoliation
337
233
Negetdtion Mamur Mosrum Mageann
Hopetaton
(c)
(d)
Figure 8. Equity of key variables across various scenarios.
Distrib ation Mitigot on Rates
Detoutt [B
Bileeral Negcttator
Bes: Dlb
(Taquecy 040
50
51
52
53
0.5
07
0.6
0.6
Midgation PllCO
Figure 9. We compare the distribution of final mitigation rates across 50 seeds. Under the default, negotiation, most regions either free ride or reduce Σ 30% of their emissions. Under the Basic Club and Bilateral Negotiation, the majority of agents reduce 80% of their emissions.
29


Reviews:
[{"review_id": "FId0bUAzbh", "reviewer": "Reviewer_qtav", "summary": "The paper introduces RICE-N, a multi-region integrated assessment model designed to simulate global climate negotiations, agreements, and long-term cooperation using multi-agent reinforcement learning (MARL). The model extends the Regional Integrated Model of Climate and Economy (RICE) by incorporating negotiation protocols and international trade dynamics. The authors propose two negotiation protocols: Bilateral Negotiation and Basic Club, inspired by real-world climate policy mechanisms like Climate Clubs and the Carbon Border Adjustment Mechanism (CBAM). The main findings are that both negotiation protocols significantly reduce temperature growth and carbon emissions compared to a no-negotiation baseline, with only a minor drop in production. The Basic Club protocol, in particular, achieves a balance between emissions reduction and economic growth, outperforming the no-negotiation baseline in the long term. The paper also highlights the importance of equitable burden-sharing in climate agreements, as measured by the Gini Index.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for their favorable assessment regarding the innovativeness and suitability of our chosen approach, as well as the constructive feedback. Below, we carefully address any outstanding concerns:\n\n### > detailed sensitivity analysis\n\nThank you for this suggestion. We select parameters based on economic theory, which are the discount factor, welfare loss weight, consumption substitution rate and relative preference for domestic goods. This analysis showcases the robustness of our findings. We will add it to the appendix and reference it in the main text. We plot heatmaps of the analysis here: https://imgur.com/a/W0194Ej . In the heatmap, we show the percentage change in variables of interest (including Temperature, Carbon Emissions, GDP) across different scenarios when critical model parameters are perturbed by a multiplication factor ranging from 0.96 to 1.04. The max percentage change is 3.16% while mean is -0.22% and medium is -0.36%. We thus conclude the dynamics are stable, corresponding to changes in critical model parameters.\n\n### > real-world applicability of the Basic Club protocol \n\nBasic Club and carbon border adjustment mechanisms (CBAM) fight carbon leakage by setting the strength of the tariff proportionally to the difference in the cost of carbon between the exporting and importing countries. Basic Club relies on a uniform tariff [1]. In contrast, CBAM targets specific goods, which can exacerbate carbon leakage by leaving large swaths of emissions unaccounted for, such as those produced for non-EU exports. Climate clubs can go further than what is modeled in RICE-N at the moment, hence the term “Basic”. Uniform tariffs, coupled with technology sharing and redistribution, are theorized to be more effective at curtailing carbon leakage [2]. Future work should implement CBAM in RICE-N, which requires disaggregating production and trade by sector to allow for targeted tariffs. This is currently a work in progress and high on our agenda.\n\n[1] Overland, I., & Huda, M. S. (2022). Climate clubs and carbon border adjustments: A review. *Environmental Research Letters*, 17(9), 093005.\n\n[2] Tarr, D. G., Kuznetsov, D. E., Overland, I., & Vakulchuk, R. (2023). Why carbon border adjustment mechanisms will not save the planet but a climate club and subsidies for transformative green technologies may. *Energy Economics*, 122, 1066\n\n### > What are the computational requirements of the MARL approach, particularly for large-scale simulations with many regions?\n\nThe computational complexity of our MARL approach is driven by the number of regions N (i.e., agents). Since each agent’s action space scales linearly with N, the total action space across all agents grows quadratically (O(N²)). However, the number of agents in our setting is naturally bounded by the number of countries on the planet. Currently, training 27 agents for 100 thousand episodes takes approximately 3 hours on a 30 CPU cluster. To improve runtime, we are exploring more efficient implementations using JAX-based acceleration and model parallelism, which would enable large-scale sensitivity analyses and experiments. \n\n### >  more detailed discussion of recent work on MARL in climate-related applications.\n\nWe extend the section on MARL in the appendix with some more references on MARL applied to real-world problems such as:\n\nHou, X., et al. (2025). InvestESG: A multi-agent reinforcement learning benchmark for studying climate investment as a social dilemma. In *Proceedings of the Thirteenth International Conference on Learning Representations (ICLR)*.\n\nMay, R., & Huang, P. (2023). A multi-agent reinforcement learning approach for investigating and optimising peer-to-peer prosumer energy markets. *Applied Energy*, 334, 120705.\n\nWang, X., et al. (2020). Large-scale traffic signal control using a novel multiagent reinforcement learning. *IEEE Transactions on Cybernetics*, 51(1), 174–187.\n\n### > discussion of the potential policy implications\n\nThe policy impacts of climate clubs (and border adjustment mechanisms for that matter) depends on their implementation. Without some degree of redistribution and technology sharing, they risk acting as a tax on carbon locked developing countries [3; 4]. A Loss and damage fund can mitigate that risk [5]. \n\n[3] Goldthau, A., & Tagliapietra, S. (2022). How an open climate club can generate carbon dividends for the poor. Bruegel-Blogs.\n\n[4] Perdana, S., & Vielle, M. (2022). Making the EU Carbon Border Adjustment Mechanism acceptable and climate friendly for least developed countries. *Energy Policy*, 170, 113245.\n\n[5] Boyd, E., et al. (2021). Loss and damage from climate change: A new climate justice agenda. *One Earth*, 4(10), 1365–1370. \n\n### > more detailed discussion of the limitations of the model.\n\nThank you for this suggestion. We will add a clarifying paragraph to the main text describing key assumptions around binding commitments, region preferences, and power imbalances.", "claims_and_evidence": "The claims made in the paper are generally supported by clear and convincing evidence. The authors provide detailed simulations and comparisons between different negotiation protocols and baselines, showing the impact on global temperature, carbon emissions, and economic output. The use of MARL to model strategic behavior in climate negotiations is well-justified, and the results are presented with appropriate statistical measures (e.g., mean ± 1.96 standard error). However, the paper could benefit from more detailed sensitivity analyses to demonstrate the robustness of the results to different parameter settings or model assumptions.", "methods_and_evaluation_criteria": "The proposed methods and evaluation criteria are appropriate for the problem at hand. The use of MARL to model strategic interactions in climate negotiations is innovative and well-suited to the complex, dynamic nature of global climate cooperation. The evaluation criteria, including global temperature anomaly, carbon emissions, and economic output, are standard metrics in climate-economic modeling. The inclusion of the Gini Index to measure inequality in emission reduction costs and consumption adds a valuable dimension to the analysis, addressing the equity concerns often raised in climate negotiations.", "theoretical_claims": "The paper does not present any formal theoretical claims or proofs, so there are no theoretical issues to evaluate. The focus is on empirical results from simulations, which are well-documented and supported by the data.", "experimental_designs_or_analyses": "The experimental design is sound, with clear comparisons between different negotiation protocols and baselines. The authors train five models (Basic Club, Bilateral Negotiation, no negotiation, maximum mitigation, and minimum mitigation) and evaluate them over 50 rollouts to ensure statistical robustness. The results are presented with appropriate confidence intervals, and the authors discuss the implications of their findings in detail. One potential limitation is the lack of sensitivity analysis to different parameter settings, which could strengthen the robustness of the results.", "relation_to_broader_scientific_literature": "The paper is well-situated within the broader scientific literature on climate-economic modeling and game-theoretic approaches to climate negotiations. The authors draw on prior work in integrated assessment models (IAMs) like DICE and RICE, as well as recent advances in MARL. The paper extends this literature by incorporating negotiation protocols and international trade dynamics, which are critical for modeling real-world climate agreements. The use of MARL to model strategic behavior in climate negotiations is a novel contribution that bridges the gap between climate economics and machine learning.", "essential_references_not_discussed": "The paper adequately covers the relevant literature, but it could benefit from a more detailed discussion of recent work on MARL in climate-related applications. For example, recent papers on MARL for energy systems optimization or climate policy design could provide additional context for the use of MARL in this domain. Additionally, the paper could discuss more recent developments in climate clubs and carbon border adjustment mechanisms, which have been the subject of ongoing policy debates.", "other_strengths_and_weaknesses": "Strengths:\n\n1. The paper addresses a critical and timely issue in climate policy, namely the challenge of achieving global cooperation on climate change mitigation.\n\n2. The use of MARL to model strategic behavior in climate negotiations is innovative and well-executed.\n\n3. The inclusion of international trade dynamics and negotiation protocols adds realism to the model and provides valuable insights into the design of effective climate agreements.\n\n4. The paper provides a comprehensive analysis of the equity implications of different negotiation protocols, which is often overlooked in climate-economic modeling.\n\nWeaknesses:\n\n1. The paper could benefit from a more detailed sensitivity analysis to demonstrate the robustness of the results to different parameter settings or model assumptions.\n\n2. The discussion of the real-world applicability of the Basic Club protocol could be expanded, particularly in light of ongoing policy debates on carbon border adjustment mechanisms.\n\n3. The paper could provide more details on the computational requirements of the MARL approach, particularly for large-scale simulations with many regions.", "other_comments_or_suggestions": "1. The paper is well-written and clearly organized, but it could benefit from a more detailed discussion of the limitations of the model, particularly in terms of its assumptions about agent behavior and the real-world applicability of the negotiation protocols.\n\n2. The authors should consider adding a discussion of the potential policy implications of their findings, particularly in light of ongoing international climate negotiations.", "questions_for_authors": "## Sensitivity Analysis\n**Question:** Have the authors conducted a sensitivity analysis to test the robustness of the results to different parameter settings or model assumptions? If so, could they provide more details on the findings?\n\n**How this affects my evaluation:** If the authors can demonstrate that the results are robust to different parameter settings, it would strengthen the validity of their conclusions.\n\n## Real-World Applicability\n**Question:** How do the authors see the Basic Club protocol being implemented in real-world climate negotiations, particularly in light of ongoing debates on carbon border adjustment mechanisms?\n\n**How this affects my evaluation:** A more detailed discussion of the real-world applicability of the Basic Club protocol would enhance the practical relevance of the paper.\n\n## Computational Requirements\n**Question:** What are the computational requirements of the MARL approach, particularly for large-scale simulations with many regions?\n\n**How this affects my evaluation:** Understanding the computational requirements would help assess the scalability of the approach and its potential for real-world applications.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "TGxrxZiO9F", "reviewer": "Reviewer_aTjF", "summary": "The paper introduces and analyses a climate policy modelling framework for assessing the effect of different international agreemtns on future climate. It introduces RICE-N, a multi-region integrated assessment model that simulates global climate negotiations and agreements using multi-agent reinforcement learning to model strategic decision-making in climate policies. It develops and evaluates two negotiation protocols, Bilateral Negotiation and Basic Club which encourage cooperation among regions to mitigate climate change while balancing economic growth. The results indicate that these protocols have the potential to reduce global temperature rise give the particular simulation environment.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for the thoughtful review and for highlighting the positive aspects, such as RICE-N’s suitability for studying strategic climate negotiations, the evidence-based claims, and the originality of our MARL application. We are pleased that you consider both the paper and the code accessible, and we hope that our response clarifies any outstanding concerns.\n\n### > Suitability for ICML.\n\nThank you for voicing your concerns. We believe that the application of MARL to a climate economic negotiation integrated assessment model provides a relevant methodological contribution to the Application-Driven Machine Learning track of ICML. Beyond its contribution to topics mentioned in the call for papers such as social sciences, and sustainability and climate for which the ML community demonstrates interest through concurrent work on climate investment [1], as well as the many potential extensions that are interesting to the ML community, such as the integration of LLMs into negotiation [2], this work also provides a useful testbed for topics of interest to MARL researchers, such as studying multi-party cooperation between AI agents in sequential social dilemmas [3].\n\n[1] Hou, X., et al. (2025). InvestESG: A multi-agent reinforcement learning benchmark for studying climate investment as a social dilemma. In ICLR 2025.\n\n[2] Vaccaro, M., et al. (2025). Advancing AI negotiations: New theory and evidence from a large-scale autonomous negotiations competition. arXiv preprint arXiv:2503.06416.\n\n[3] Leibo, J. Z., et al. (2017). Multi-agent reinforcement learning in sequential social dilemmas. In Proceedings of the 16th AAMAS. ACM.\n\n### > Additional experimental analysis on effects of variables.\n\nSince the space of possible configurations is large, we perform a sensitivity analysis over a subset of economically relevant parameters, namely the discount factor, welfare loss weight, consumption substitution rate and relative preference for domestic goods. This analysis showcases the robustness of our findings. We will add it to the appendix and reference it in the main text. We plot heatmaps of the analysis here: https://imgur.com/a/W0194Ej . We show the percentage change in outcome variables of interest across different scenarios when critical model parameters are perturbed by a multiplication factor ranging from 0.96 to 1.04. The max percentage change is 3.16% while mean is -0.22% and medium is -0.36%. We thus conclude the dynamics are stable, corresponding to changes in critical model parameters.\n\nWe will also include a discussion on the computational complexity of RICE-N (please see our response to QTAV).\n\n### > 208, column 2: clarify that the link is to Section 6\n\nThank you for spotting this.\n\n### > possible unintended consequences\n\nWe wish to highlight the importance of qualifying these claims by discussing the potential unintended consequences of climate clubs being implemented without redistributive financing and technology sharing. Uniform tariffs on developing countries with lower mitigation rates would effectively serve as a tax on less developing countries, which we do not advocate for [4,5]. Our goal is to create a simulation framework where these dynamics and alternative policies can be explored and cross compared. We will give an account of these points in the main text of the camera-ready version.\n\n[4] Goldthau, A., & Tagliapietra, S. (2022). How an open climate club can generate carbon dividends for the poor. Bruegel-Blogs.\n\n[5] Perdana, S., & Vielle, M. (2022). Making the EU Carbon Border Adjustment Mechanism acceptable and climate friendly for least developed countries. Energy Policy, 170, 113245.\n\n### > loosely coupled\n\nTo clarify: this comment refers to the structure of the code, not any functional difference. We mean that we try to reduce as much as possible the number of assumptions that each component must make about the other components, and make the necessary dependencies between dynamics both explicit and local [6]. This makes extensions to the existing codebase much easier to implement, which makes testing new ideas, such as novel negotiation protocols, much easier.\n\n[6] Leymann, F. (2016, September 5–7). Loose coupling and architectural implications. Keynote address presented at the ESOCC, Vienna, Austria.\n\n### > uncertainty estimates\n\nThe uncertainties arise from the stochasticity of the learned policy as we sample actions from the policy's distribution during evaluation. We estimate uncertainty across 50 rollouts with varying seeds (see Section 6, paragraph “Experimental Setup”). The relatively small uncertainty shows that the agents have learned robust policies. An increase could indicate that the learned policy is less reliable, potentially due to insufficient training or the model's inability to generalize effectively. Adding uncertainty to the environment (e.g., the climate component) or relevant parameters (see sensitivity analysis) would likely result in an increase of the uncertainty.", "claims_and_evidence": "The claims in the submission are generally supported by the evidence, particularly through comparisons of negotiation protocols using multi-agent simulations and integrated assessment modelling. As the claims are made within the context of the RICE-N model, they are supported. Naturally, their applicability to real-world scenarios may be questioned but the paper does not claim to provide policy advice and outlines some possible unintended consequences in the Impact Statement.", "methods_and_evaluation_criteria": "The proposed methods -- the use of MARL within the RICE-N integrated assessment model -- are suitable for studying strategic climate negotiations, as they allow agents to learn dynamic policies in a multi-region setting.", "theoretical_claims": "There are no theoretical claims in the paper apart from the set up of the model that relates back to theoretical understanding of world economy, trade and international negotiations.", "experimental_designs_or_analyses": "The experimental results provide some illustrative results for different policies though are not very extensive (e.g. in terms of comparing the effect of different variables, different assignment of regions, the computational considerations in the multi-agent RL inference). The authors mention that a more extensive sensitivity study would require a more efficient implementation of the methodology (e.g. in JAX).", "relation_to_broader_scientific_literature": "The paper includes an extensive literature review on different aspects of the paper, including climate negotiations, climate negotiations and economic actions that affect climate outcomes, as well as some relevant RL literature.", "essential_references_not_discussed": "I cannot comment on this.", "other_strengths_and_weaknesses": "The paper is well-written and includes an explanations of different aspects of climate negotiations, reinforcement learning methods, and integrated assessment modelling, making it accessible to a broad audience. Its originality lies in combining multi-agent reinforcement learning with climate-economic modelling, allowing for a more dynamic exploration of international climate agreements compared to static game-theoretic approaches. The availability of the implementation and the modularity of the it should make it easy for other users to try out their own approaches.\n\nWhile the paper presents an interesting application of multi-agent reinforcement learning, its primary focus on climate economics and policy modelling may make it less suitable for a machine learning venue. To the best of my understanding, the technical ML contributions, such as improvements to MARL methods or novel learning dynamics, are limited, and the paper leans more toward applying existing ML techniques rather than advancing them. While it may be of interest to an ML audience due to potential future directions (improving scalability with JAX or more advanced RL methodology), I would suggest that the extensions are suitable for ML audience while this paper may be better received at a climate venue.", "other_comments_or_suggestions": "208, column 2: clarify that the link is to **Section** 6.", "questions_for_authors": "Could you clarify what you mean by, the climate, economic and trade components are **loosely** coupled?\n\nMost of the results contain some uncertainty estimates but I could not find the exact explanation of its origin. Could you explain or reference the specific part of the paper that details the source the stochasticity? Could you then give some intuition of why the uncertainty seems so small for most models and what changes to the model or the inference is likely to have a significant effect on the uncertainty?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "fBv249L550", "reviewer": "Reviewer_j6L5", "summary": "The paper adds reinforcement learning to a multi-agent Nordhaus RICE model.\n\nIt allows two communication protocols between agents, whereby agents can make binding commitments to curtail their greenhouse gas emissions.\n\nSimulation allows these two protocols to be compared to the 'no negotiation' (Nordhaus RICE) baseline.  Relative to that baseline, the negotiation protocols allow higher welfare outcomes, better controlling the climate's evolution.\n\nThe paper claims that the underlying code's modularity allows climate dynamics and economic loss functions to be easily adjusted.\n\n## update after rebuttal\n\nScore maintained for existing manuscript.  A considerably revised manuscript (as discussed in the rebuttal) could receive a higher score.  \n\nI am concerned by the statement that \"no single equilibrium concept applies in all cases\", as it raises the question of whether the output corresponds to any intelligible or benchmark description of play.  I suspect that nation states are fumbling their way forward here, rather than playing anything that could be clearly rationalized as a form of Nash equilibrium, so this may be fine - but needs to be argued.\n\nAgain, the lack of realism in the modeled mechanisms weakens the paper.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for the incisive review of our submission. Below, we respond to the concerns raised.\n\n### > does the 'no negotiation' baseline match the Nordhaus-Yang results?\n\nWe can compare our results to Nordhaus’ RICE from 2010 [1]. The aforementioned has two results: baseline and optimal. The former consists of each region optimizing its own objective function and the latter of a cooperative mode with a shared objective function. We compare our results with RICE up until 2115, as that is the end year of our simulation. Looking at global temperature only for simplicity’s sake, the RICE2010 baseline and optimal temperature rises are 3.91 C and 2.92 C, respectively. Our no-negotiation baseline and basic club protocols result in increases of ~4.21 °C and ~2.97 °C, respectively. Exact matches are not expected as initial conditions differ: our rollout starts in 2015 (in line with DICE2016, which served as the basis for the implementation) and RICE2010 in 2005. Nonetheless, both no-negotiation and basic club yield temperature rises comparable to the RICE 2010 base and optimal trajectory, respectively.\n\n[1] ​​Nordhaus, W. D. (2010). Economic aspects of global warming in a post-Copenhagen environment. Proceedings of the NAS, 107(26), 11721-11726.\n\n### >  Is [the code] more modular, faster/slower?\nWhile Python is likely slower than e.g. GAMS for model optimization, the runtime is bottlenecked by the deep RL agents, not the environment dynamics. Writing RICE-N in Python makes it simpler for the simulation code to interface with the RL agent code, which can be implemented using common Deep RL frameworks in Python and reduces barriers for ML researchers to contribute to the codebase, and extend it with novel modelling components. Finally, we are working on an efficient JAX implementation, which we plan to release alongside the paper and which will improve the runtime by multiple orders of magnitude.\n\n### > My biggest concern with the paper is the specification of binding negotiations.\nIn our current setup, agents cannot deviate from agreed-upon actions for the specified time lapse (5 years). While this assumption simplifies analysis and isolates the impact of the negotiation mechanism, it does not reflect the uncertainty and strategic mistrust present in real-world climate negotiations (e.g., countries withdrawing from agreements).\n\nFuture work should explore the possibility of non-binding commitments, which would enable agents to engage in strategic communication or 'cheap talk,' thereby better capturing realistic negotiation dynamics [2]. We will add this discussion to the text. \n\n[2] Caparros, A. (2016). The Paris Agreement as a step backward to gain momentum: Lessons from and for theory. Revue d'économie politique, 126, 347.\n\n\n### > Nordhaus & Yang issues related to international transfers >\n​​The reviewer is correct to identify concerns related to international transfers at the scale required to implement RICE’s optimal pathways. For example, large-scale international transfers risk misappropriation without oversight [3]. However, in the time since Nordhaus and Yang’s 1996 comment on the practicality of international transfers, there has been a greater focus on equity and burden sharing [4], shifting the question from whether international transfers are possible to how do international transfers fit into a larger patchwork of climate finance instruments [5]. Adding an international transfers module is on the RICE-N development road map such that we can explore different means of financing mitigation. \n\n[3] Nest, M., et al. (2022). Corruption and climate finance. Brief Chr. Michelsen Institute U, 4, 14.\n\n[4] Landis, T. & Bernauer, T. (2012). Transfer payments in global climate policy. Nature Climate Change, 2(8), 628-633.\n\n[5] Pickering, J., et al. (2017). Special Issue: Managing Fragmentation and Complexity in the Emerging System of International Climate Finance. *International Environmental Agreements: Politics, Law and Economics*, 17(1), 1-16.\n\n### > too many of the paper's details were hidden in the appendix.\nThank you for this feedback. We will use the extra page of the camera-ready version to discuss more RL-related details in the main text.\n\n### > it could be useful to plot policy functions as well\nThank you for the suggestion. We will add to the final version.\n\n### > Nordhaus appears in the references as both \"W.\" and \"W.D.\" \"Stern\" and \"AI\" should be capitalised in the references.\nThank you for catching this. We have corrected this oversight.\n\n### > why are 27 fictitious countries used, rather than the full set?\nMany individual countries lack comprehensive data making modeling unreliable. By aggregating countries into regions, the errors from lacking in data from these countries would be less impactful to the whole region. We believe, for a similar reason, RICE-2010 only includes 12 regions. Besides, 27-region setting makes bilateral negotiation computational feasible due to $O(n^2)$ complexity.", "claims_and_evidence": "The headlines claims are evidenced by three figures of plots and a table in the body of the paper.\n\nOverall, I did not find the claims surprising: stronger protocols for binding commitments allow agents to better overcome the 'cost of anarchy' associated with playing Nash equilibria rather than the social planner's first best outcome.", "methods_and_evaluation_criteria": "The various runs are compared on the basis of temperature deviations, GDP impact and other standard criteria.\n\nNordhaus' RICE model is a workhorse of the theoretical literature (contributing to his Nobel prize).", "theoretical_claims": "The paper makes no theoretical claims.\n\nOn this front, I was interested to know what - for example - the equilibrium concept is.  Overall, I felt that too many of the paper's details (e.g. the equilibrium concept, details of RL) were hidden in the appendix.", "experimental_designs_or_analyses": "Have not checked anything in detail.", "relation_to_broader_scientific_literature": "Fine.", "essential_references_not_discussed": "N/A", "other_strengths_and_weaknesses": "My biggest concern with the paper is the specification of binding negotiations.\n\nIn the 'real world', significant countries withdraw from their climate change commitments, partly as they do not trust others' commitment.  This, of course, is the standard stuff of game theory - and an essential part of the problem.\n\nThe original RICE paper (Nordhaus & Yang, 1996) noted that the international transfers required to support its first best solutions would swamp international transfers, making the solutions considered infeasible.\n\nFor research to make a significant contribution to this debate, it must at least address these issues.  The current paper, to my knowledge, does not.\n\nI grade this paper as a 'weak accept': I think that this issue needs to be kept alive; I do not think that this significantly advances the debate (e.g. novel techniques, surprising results, useful policy insights), but it does help keep the issue alive.", "other_comments_or_suggestions": "1. sanity check: does the 'no negotiation' baseline match the Nordhaus-Yang results? \n1. how does the current code compare to Nordhaus code?  Is it more modular, faster/slower?  (I had seen that there were RICE implementations in Julia a decade ago, but have lost track.)\n1. it could be useful to plot policy functions as well (q.v. the comment in the Limitations section about interpretability).\n1. Nordhaus appears in the references as both \"W.\" and \"W.D.\"  \"Stern\" and \"AI\" should be capitalised in the references.", "questions_for_authors": "1. why are 27 fictitious countries used, rather than the full set?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "hc47FCX7LQ", "reviewer": "Reviewer_ntBn", "summary": "## update after rebuttal\n\nThe paper proposed a multi-agent reinforcement learning (MARL) approach to model global climate negotiations, agreements, and long-term cooperation. Two novel negotiation protocols were proposed: Bilateral Negotiation and Basic Club. The proposed approach and protocols take into account many realistic components such as climate dynamics and economic dynamics. The simulated results compared the two negotiation protocols and a baseline without negotiation. The comparison shows better results with negotiation.\n\nThe rebuttal responses helped clarification.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We thank the reviewer for their thoughtful feedback and for pointing out the positive aspects of our submission, such as the novelty of the protocols, the realism of the components, the empirical support for our claims and the overall quality of the evaluation criteria, experimental design and results analysis. We hope our response clarifies any outstanding concerns.\n\n> Could region level analysis be provided? For example, what are a region’s actions overtime and how they are different with the two negotiation protocols and without negotiation. Are there any patterns in the actions for the 27 regions studied. Could their actions be categorized into a few common groups?\n\nThank you for this suggestion. Under Basic Club, all regions tend to increase their mitigation rate as much as constraints allow until the maximum mitigation rate is reached. Without negotiation acting as a coordination mechanism, regions tend to fall into different subgroups. There are ambitious mitigators, reducing 40-60% of emissions by the end of the run, moderate mitigators reducing 20-30%, and free riders reducing 0-10%. In the camera-ready version, we will include a detailed quantitative and qualitative analysis of these phenomena.\n\n> Can you summarize possible usages of the proposed approach for different types of users: ML researchers, climate scientists, government, international organizations such as IPCC?\n\nML researchers can make use of the modularity of the RL component to evaluate how different RL algorithms perform in a real world-calibrated environment. Climate scientists can use it to compare different climate modules and damage functions. Governments can use it to evaluate the robustness of a given climate-economic policy to strategic behavior and estimate the consequences on international trade. International organizations, such as the OECD or WTO could use the tool to analyze the economic trade-offs of different climate policies and negotiation strategies. We will add these potential uses to the text, while making sure to surface the limitations.\n\n> Figures 6-15 are not explained.\n\nThank you for pointing this out. These results are additional visualizations to support Section 6. In the camera-ready, we will expand the captions for each of the images such that they are sufficiently informative to understand the figures, describing the various scenarios, as well as the variables under study, and what can be concluded from the plots. We will also point to them more strongly in the main text.", "claims_and_evidence": "The claim, the two negotiation protocols are better than the baseline without negotiation, is well supported by the experimental results.", "methods_and_evaluation_criteria": "1. The proposed multi-agent reinforcement learning method and the two negotiation protocols are novel and make sense. \n2. The evaluation criteria include both climate-economic and Gini indexes, which make sense and are comprehensive.", "theoretical_claims": "The work is a game-theoretic problem.  The paper itself does not have proof.", "experimental_designs_or_analyses": "The experimental design in Section 6 and result analyses (mostly in Table 1) are reasonable.", "relation_to_broader_scientific_literature": "The work extends existing climate-economic policy tradeoff modeling work including integrated assessment models (IAMs) and Regional Integrated Model of Climate and Economy (RICE) by capturing the strategic behavior in climate negotiations.", "essential_references_not_discussed": "I think the references in the Related Works (both main paper and appendix) are comprehensive.", "other_strengths_and_weaknesses": "W1: Most results are global macro level. Analysis of actions and goals of individual countries/regions are missing. The simulation should be reasonable at both global macro level and individual micro-level.", "other_comments_or_suggestions": "Figures 6-15 are not explained.", "questions_for_authors": "Q1. Could region level analysis be provided? For example, what are a region’s actions overtime and how they are different with the two negotiation protocols and without negotiation. Are there any patterns in the actions for the 27 regions studied. Could their actions be categorized into a few common groups? \n\nQ2. Can you summarize possible usages of the proposed approach for different types of users: ML researchers, climate scientists, government, international organizations such as IPCC?", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: The paper proposed a multi-agent reinforcement learning (MARL) approach to extend the Nordhaus Regional Integrated Model of Climate and Economy (RICE) model of global climate negotiations, agreements, and long-term cooperation on cutting greenhouse gases emissions. Two novel negotiation protocols were proposed: Bilateral Negotiation and Basic Club. The proposed approach and protocols take into account many realistic components such as climate dynamics and economic dynamics.

Reviewers ntBn, qtav and aTjF praised the novelty of incorporating MARL into negotiation protocols, and evaluating outcomes using Gini indexes. Reviewer aTjF found the paper well written. Reviewers j6L5 and aTjF  found the claims to be evidenced by the paper.

Reviewer ntBn noted that results were shown mostly at global macro level and not at regional level. Reviewer j6L5 discussed the limitation of not specifying negotiations to be binding. Reviewer aTjF found a climate focused venue could be more suitable for the paper (claim defended by the authors).

Based on the reviews and average score, I recommend accepting the paper.
Decision: Accept (poster)