(cont.)

Figure 7 b) is highly confusing. It looks like with climate information, risk is maximized and market wealth is minimized.

• Thank you so much for this catch. It turns out that it was an unintentional mistake from our side that we flipped the labels around. The actual result is that with climate information, risk is minimized and market wealth is maximized. We will correct this mistake in our updated version of the manuscript.

Figure 2b could be improved by showing the average number of events each year across many episodes, as opposed to a single episode.

• Thank you for the suggestion. We aimed to give an example of environmental dynamics and the progression of the environment in a single episode, and therefore we didn’t take the average of many episodes. However, based on your suggestion and reviewer mQaB’s suggestion to include more climate outcome metrics, we will provide additional plots of the average number of climate events across many episodes in the results for different scenarios.

Presentation and Questions

Figures and plots

• Thanks for the very constructive feedback regarding the presentation of the paper. We apologize for the inconvenience. We will increase the readability of our plots and fix the typo in the updated version accordingly.

results section could benefit from additional structure”

• Thank you for your suggestion. Our intention was to tell the story in a progressive way, starting from the baseline, then adding the ESG disclosure policy, followed by raising questions about investors with various level of environmental consciousness, and studying the impacts of greenwashing and sharing additional climate information. Following your feedback, we will restructure the result section by presenting the main story of baseline and behaviors of investors with different levels of consciousness, and delineate these central findings from the additional results from greenwashing and climate information. Would this satisfy your concerns? We will incorporate your feedback in the problem setting section in regard to introducing the important concepts.

What does a sensitivity analysis of the Beta parameter do to the results? Why do you think that agents are so insensitive to the value of Beta as shown in figure 6 b)?

• We would like to use a sensitivity analysis of greenwashing coefficient β to elaborate our point that companies’ decision to abandon greenwashing isn’t due to the relative cost of greenwashing compared to real mitigation. Although companies that achieve a high ESG score through cheap greenwashing, which is controlled by β, attract more investments from investors, the increase in investment from investors by greenwashing isn’t comparable to their capital loss when exposed to severe climate events. The company agents learned greenwashing isn’t the most cost-effective way to maximize their capital no matter how much it costs.

Do observations include past climate events?

• The observation doesn’t include the past climate events by default (in the baseline case), but it is configurable in the environmental setting. In figure 7, we studied the effects of having additional climate information on mitigation, which include the number of severe climate events that occurred in the past year.

How did you calibrate the 0.5% investment of capital into mitigation?

• Since company actions are continuous, we needed to select a specific cooperation level to illustrate the social dilemma structure in the Schelling diagram. We chose 0.5% as a representative benchmark, aligning with Patagonia's aggressive cooperative approach, where approximately $100 million (around 0.3$3 billion valuation) is allocated annually to climate initiatives. The 0.5% choice is thus in a similar order of magnitude, and the shape of the diagram remains consistent across other values we tested.

Thank you again for your valuable feedback. We hope our responses address your concerns, and we welcome any further questions or comments you may have. Your insights are instrumental in helping us strengthen this work, and we look forward to your continued guidance during the rebuttal phase.

Reference:

[1] Pástor, Ľ., Stambaugh, R. F., & Taylor, L. A. (2021). Sustainable investing in equilibrium. Journal of financial economics, 142(2), 550-571.

[2] Pedersen, L. H., Fitzgibbons, S., & Pomorski, L. (2021). Responsible investing: The ESG-efficient frontier. Journal of financial economics, 142(2), 572-597.

[3] Lyon, T. P., & Maxwell, J. W. (2011). Greenwash: Corporate environmental disclosure under threat of audit. Journal of economics & management strategy, 20(1), 3-41.

[4] Shek, Katia. (2023, January 30). Patagonia: ESG's Golden Child. https://insights.grcglobalgroup.com/patagonia-esgs-golden-child/

Thank you for the very valuable and detailed feedback. We are grateful for your insights and the time you took to review our manuscript. Below, we address your comments.

Soundness

The number of agents is limited.

• We acknowledge that the number of agents in our experiment is limited compared to the real world. Post-submission we have developed a Jax version of the environment which allows us to run the simulations much faster and at a scaled level. We will run larger-scale scenarios (e.g. 25 companies and 25 investors) to test the robustness of our findings. We believe that this number would match the expectation for a reasonably large group size as mentioned in the paper you suggested, unless you have alternative suggestions on the number of agents. We will share updates as soon as the new results are available. And we will also provide the Jax code in our updated version of the paper.

grounded in the economics literature.”

• We really appreciate your suggestion on “Starting with an existing model of economic agents (with a citation), highlighting its limitations for InvestESG and then explaining how you extend to agents to accommodate for these limitations would be a much more compelling presentation.” As a quick response, we want to note the following reasoning. We would love your feedback on if this meets the need, and we can revise the paper to make the presentation stronger as you suggested.
  • Our work is grounded in the economics and finance literature that studies similar questions with theoretical models. For example, in a recent highly impactful study published in a top finance journal, Pastor et al. (2021) built an analytical model for a single-period equilibrium that examines firm-investor tradeoffs much similar to ours. In their model, firms choose the “greenness” level, which affects their cost of capital, while investors select portfolios to maximize utility derived from both financial returns and their “taste” for green assets. Other influential studies in financial economics use comparable or even simpler frameworks. For example, Pedersen et al. (2021) model a single-period equilibrium with investors differentiated by their types of ESG preference, assuming fixed ESG characteristics for firms.
  • Our simulations agree with the key findings in these papers suggesting that ESG-conscious investors prioritize green companies and promote positive social impacts by shifting investment towards green firms.
  • Our framework, albeit still simple, allows for investigating more realistic and complex settings than the existing financial economics literature. These include (1) climate evolution, where companies mitigate emissions to attract investment and reduce long-term climate risk exposure—often omitted in financial studies (2) the potential for greenwashing, linked to information asymmetry (e.g., Lyon and Maxwell, 2011), and (3) a dynamic multi-agent game where firms and investors interact over many periods, which is more realistic. The equilibrium of such a setting is challenging to solve analytically or numerically (Pakes and McGuire, 2001), and our simulations provide insights here.
  • Despite the simplicity of the framework, our simulation results match real-world data collected from countries that have implemented an ESG disclosure mandate of some sort as we discussed in section 4.

investments in capital last and they are not flexible; longer capital investment timelines

• Thank you for your insightful point regarding the investment timeline. To address this, we propose running an additional scenario in which agents can make investment decisions only every five periods, reflecting a five-year lock-in on their choices. Would this approach adequately address your concern?

Investor decisions are binary, as opposed to continuous across all companies.

• We acknowledge that binary investor decisions simplify reality. However, to clarify, in our current setup, investors do not select only one company; they choose a set of companies to invest in each timestep, and distribute their current capital evenly to each of the selected companies, which allows for diversification within the binary framework. Further, because they can re-allocate investments at each timestep, they can achieve fine-grained diversification over the course of one episode. However, we agree that using continuous decision variables that sum to 1 would more accurately reflect real-world behavior, in which an investor does not always invest evenly. Could you please advise if you consider this a critical change that we should make during the rebuttal period? We are currently planning to prioritize experiments incorporating more agents, real-world data (based on reviewer mQaB’s suggestion), and the longer capital investment timelines experiment above.

Thank you for your detailed response to my concerns.

Below, I present the responses in the same order that the authors opted have opted for.

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Limited number of agents

Thank you for your response. Given that the closest related work mentioned ([1]) runs their version with 27 agents, 25 agents seems like more than enough. In particular, it will be of interest to see if the conclusions for policymakers are robust to this increase in the number of agents, considering the implications of figure 9 d). Also, section 9.1's reference to figure 9 d) discusses resilience spending, but the figure itself plots climate risk as a function of the number of agents.

grounded in economics literature

Thank you for your response. I believe the inclusion of such a discussion in the paper would be more than sufficient.

flexible investments

A 5-year lock-in period could certainly help simulate the lack of flexibility of capital.

binary investment decisions

Thank you for your response. Should the number and diversity of agents increase (as suggested above), it might not be necessary to modify the action space, which could complicate the learning dynamics. I do not believe this is a critical change.

results section structure

Thank you, this would more than satisfy my concerns.

Beta parameter sensitivity analysis

Thank you for your response. This highlights for me a limitation of the proposed framework. The agents, by training over many episodes, essentially learn a representation of the unobservable ground truth damage climate-economic damage function that relates climate events to economic damage as a function of their decisions. However, in reality, there is significant uncertainty in the level of economic damages (e.g. see this article, section 3.4). This clashes for me with the conclusion that companies are insensitive to greenwashing efforts, as the supposed uncertainty around climate change damages might lead certain companies to greenwashing to please investors, while simultaneously disregarding (knowingly or unknowingly) future impacts.

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Thank you again for your detailed response.

An interesting direction of future work for this would be enabling investors to learn their own ESG consciousness levels over many episodes. If you consider a setup where the increases in probabilities of catastrophic events are somewhat stochastic, then investors could learn to use the history of catastrophic events to update their preference for ESG consciousness during a given episode.

This brings up another important direction of future work: allowing for companies that go bankrupt. A different perspective on emissions is to look at them as a mostly-unmeasured negative externality vs the measured economic performance of different companies. If a company goes bankrupt in 2050 after emitting heavily for 50 years and employing no mitigation, then the mitigation effort must be undertaken by others to reach the optimal collective trajectory. Including the possibility of bankruptcy would improve the realism of the simulation, while also providing a new interesting motivation for greenwashing. I'd be interested to see what impact this would have on ESG-conscious investors. This could also include the cost of climate audits to overcome greenwashing, sharing of such information among investors, etc.

Another interesting work would be to consider investors that have a preference for companies that have a history of ESG-conscious investors.

Despite the unsound approach of learning a representation of the ground truth damage function over many episodes, I am conscious of the overwhelming diversity of design choices in such a situation. I believe this work is for the most part sound and heads in an impactful, novel research direction, paving the way for very interesting future research. Normally, I would raise my score to a 7, but this option is not available this year. Therefore, I maintain my score for now. However, I am happy to continue the discussion around now-raised ground truth limitation, should you believe this is not a caveat for the conclusions you draw, or should you have alternate solutions to propose. I am also amenable to additional results based on the Jax rewrite.

I wish to reiterate the novelty and impact of this proposed submission. I look forward to seeing where future work on this project goes.

[1] Zhang, Tianyu, et al. "AI for global climate cooperation: modeling global climate negotiations, agreements, and long-term cooperation in RICE-N." arXiv preprint arXiv:2208.07004 (2022).

(cont.)

Extend the agent types (possibly consider insurance companies/market?), add more complex agent behavior

• Thank you for suggesting insurance companies as an additional agent type. As noted in Section 5 (Future Work), we plan to continue enriching the environment, and we will include insurance companies in our future developments, as they play a critical role in climate-related risk management. However, we believe our current setup effectively captures the primary trade-offs and dynamics needed to evaluate the policy. And we would like to start inviting the ML community to collaborate with us in further building and refining the simulator.

Thank you again for your valuable feedback. Please advise whether our planned additional experiments address your concerns, and we welcome any further questions or comments you may have. Your insights are instrumental in helping us strengthen this work, and we look forward to your continued guidance during the rebuttal phase.

Reference:

[1] Miller, Zach. (2023, October 17) Nearly Half of Fortune 500 Companies Engaged in Major Climate Initiatives. David Gardiner and Associates. https://www.dgardiner.com/fortune-500-climate-initiatives-2023/

[2] European Investment Bank, Kalantzis, F., & Cimini, F. (2023). What drives firms’ investment in climate action? : evidence from the 2022-2023 EIB investment survey, European Investment Bank.

[3] Fortune global 500 climate commitments. Climate Impact Partners. (2024). https://www.climateimpact.com/news-insights/fortune-global-500-climate-commitments/

[4] LSEG Data & Analytics. (2023) Environmental, social and governance scores from LSEG. https://www.lseg.com/content/dam/data-analytics/en_us/documents/methodology/lseg-esg-scores-methodology.pdf

[5] Shek, Katia. (2023, January 30). Patagonia: ESG's Golden Child. Global Research and Consulting Group Insights. https://insights.grcglobalgroup.com/patagonia-esgs-golden-child/

[6] InfluenceMap. (2022, September). Big oil’s real agenda on Climate change 2022. https://influencemap.org/report/Big-Oil-s-Agenda-on-Climate-Change-2022-19585

[7] Buchner, Barbara. (2023, November 2). Annual finance for climate action surpasses USD 1 trillion, but far from levels needed to avoid devastating future losses. Climate Policy Initiative. https://www.climatepolicyinitiative.org/press-release/annual-finance-for-climate-action-surpasses-usd-1-trillion-but-far-from-levels-needed-to-avoid-devastating-future-losses/

[8] Damodaran, Aswath. (2024, January). Capital Expenditures by Sector. https://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/capex.html

Thank you for your insightful comments on our paper. We will work on incorporating your comments in our paper to increase the significance of our contributions. We would like to address some of your comments below.

Suggested literature: We appreciate the list of literature you provided, which covers both MARL benchmarking papers from the ML community and empirical analysis of the climate social dilemma and climate ESG awareness of insurance companies from the climate community. We will cite these references in our paper update and use them to guide our future work.

Proposed new experiments to address the detailed concerns: We appreciate the point of creating a richer environment. We propose to address your concerns by running some new scenarios as listed below. Please kindly let us know if these scenarios sufficiently address your feedback, or if there are additional analyses you would recommend.

increasing the number of companies and investors

• Thank you for the suggestion on running more agents. We agree with this. Post-submission we have developed a Jax version of the environment which allows for scalable and performant simulations. We will run larger-scale scenarios with more agents (eg. 25 companies + 25 investors) to test the robustness of our findings. We will share updates as soon as the new results are available. And we will also provide the Jax code in our updated version of the paper.

learn parameters and behaviors from real data

• To our knowledge, there isn’t a comprehensive database that currently tracks company behaviors in a way that can be readily analyzed, especially since the EU's ESG disclosure mandate only launched this year and the U.S. mandate is still pending. Therefore, we propose to use public information to estimate (1) the percentage of companies that invest in climate mitigation; and (2) for those companies, the amount of capital they allocate to mitigation.

  • According to public sources (Miller, 2023; European Investment Bank, 2023; Climate Impact Partners, 2024), about 50% of large companies are investing in mitigation.

  • We propose a range of 0.1~1% of capital allocated to climate mitigation based on the following reasoning.

    • As noted earlier, there is no readily available database that tracks companies' actual climate spending. For instance, while the UK is one of the few large economies to implement a disclosure mandate, it does not require companies to report specific climate expenditures. Moreover, fewer than 5% of companies voluntarily disclose such information (LSEG, 2023).
    • Patagonia spends ~0.3% of its capital annually on climate initiatives (GRC Insights, 2023).
    • The top five oil companies allocated 12% of CAPEX to low carbon activities annually, which translates to about 1.2% of their capital (InfluenceMap, 2022).
    • About 1% of global GDP goes to climate finance, which includes public spending (Climate Policy Initiative, 2023). We can view GDP as roughly the counterpart of a company's sales. According to an NYU database, the average sales/capital ratio across sectors is 0.8~1.28 (Damodaran, 2024), i.e. on average sales is on par with capital in terms of order of magnitude. So we can also seed with 1%, although this is likely an upper bound as public spending tends to be higher than private spending in this domain.

  • We will run a simulation where for the first 5 years 50% of companies spend 0.1~1% of capital on mitigation. We randomly select which 50% but keep it consistent. Could you please advise if this suggested experiment would meet your criteria?

include more social outcome metrics (in addition to the final climate risk level and the final total market wealth, at the end of the simulation period)

• We can add more social outcome metrics as you mentioned, such as the total number of severe climate events, or financial losses due to climate events during a certain period. Please let us know if there are other specific metrics you would recommend.

include additional features, such as agent bankruptcy

• To clarify, we do allow agents to go bankrupt if their capital turns negative. When a company goes bankrupt, it is blocked from further actions, and investors holding equity in the company lose their investment. This is briefly mentioned in Section 3 Company Action Space, and we will make it clearer in the updated version.

(cont.)

• We appreciate your point that the framework may seem oversimplified to the broader audience. We will dedicate a new section in the updated paper to discuss why we think our simulations are solid to help address these concerns.

Thank you again for your valuable feedback. We hope our responses address your concerns, and we welcome any further questions or comments you may have. Your insights are instrumental in helping us strengthen this work, and we look forward to your continued guidance during the rebuttal phase.

Reference:

[1] Pástor, Ľ., Stambaugh, R. F., & Taylor, L. A. (2021). Sustainable investing in equilibrium. Journal of financial economics, 142(2), 550-571.

[2] Pedersen, L. H., Fitzgibbons, S., & Pomorski, L. (2021). Responsible investing: The ESG-efficient frontier. Journal of financial economics, 142(2), 572-597.

[3] Lyon, T. P., & Maxwell, J. W. (2011). Greenwash: Corporate environmental disclosure under threat of audit. Journal of economics & management strategy, 20(1), 3-41.

[4] Pakes, A., & McGuire, P. (2001). Stochastic algorithms, symmetric Markov perfect equilibrium, and the ‘curse’of dimensionality. Econometrica, 69(5), 1261-1281.

[5] Fiechter, P., Hitz, J. M., & Lehmann, N. (2022). Real effects of a widespread CSR reporting mandate: Evidence from the European Union's CSR Directive. Journal of Accounting Research, 60(4), 1499-1549.

[6] Delmas, M. A., & Toffel, M. W. (2008). Organizational responses to environmental demands: Opening the black box. Strategic management journal, 29(10), 1027-1055.

[7] Bowen, F. E. (2000). Environmental visibility: a trigger of green organizational response?. Business strategy and the environment, 9(2), 92-107.

Thank you for your valuable feedback in helping us improve our work. In response to your comments, we have provided additional explanations below to address your concerns. We would greatly appreciate any further feedback on whether these revisions effectively resolve your concerns, as we are committed to strengthening the paper through the rebuttal process.

System with a limited number of agents: Thank you for raising the question of whether a limited number of agents can represent a market with thousands of real agents. Post submission, we have developed a GPU-efficient Jax version of our environment, which runs at 10x the previous speed, enabling us to scale the simulation significantly. We will run larger-scale scenarios (on the order of 50 agents) to test whether we obtain similar findings when scaling to more agents. We will share updates during the discussion period as soon as the new results are available. We will also include a link to the Jax-based implementation in the final version of the paper.

Additional scenarios: We plan to add a few additional scenarios to capture more of the real-world complexity, including seeding the first few steps of company actions with real-world company behaviors, and implementing a lock-in period for investments.

Simplicity of the framework: We acknowledge, as you noted, that our work uses a simplified framework. Considering the magnitude and complexity of the global market, there might never be a model that fully captures the climate-market dynamics. But we believe that our choice of model captures the most important trade-offs. Briefly, our reasons for this approach are as follows.

• It is grounded in the economics and finance literature that studies similar questions with theoretical models. For example, in a recent highly impactful study published in a top finance journal, Pastor et al. (2021) built an analytical model for a single-period equilibrium that examines firm-investor tradeoffs much similar to ours. In their model, firms choose the “greenness” level, which affects their cost of capital, while investors select portfolios to maximize utility derived from both financial returns and their “taste” for green assets. Other influential studies in financial economics use comparable or even simpler frameworks. For example, Pedersen et al. (2021) model a single-period equilibrium with investors differentiated by their types of ESG preference, assuming fixed ESG characteristics for firms. Going beyond these works, we provide a modeling tool that can study a system which evolves over a much longer time period (100 years), rather than a single timestep.
• Our simulations agree with the key findings in these papers suggesting that ESG-conscious investors prioritize green companies and promote positive social impacts by shifting investment towards green firms.
• Our framework, albeit still simple, allows for investigating more realistic and complex settings than the existing financial economics literature. These include (1) climate evolution, where companies mitigate emissions to attract investment and reduce long-term climate risk exposure—often omitted in financial studies (2) the potential for greenwashing, linked to information asymmetry (e.g., Lyon and Maxwell, 2011), and (3) a dynamic multi-agent game where firms and investors interact over many periods, which is more realistic. The equilibrium of such a setting is challenging to solve analytically or numerically (Pakes and McGuire, 2001), and our simulations provide insights here.
• Despite the simplicity of the framework, our simulation results match real-world data collected from countries that have implemented an ESG disclosure mandate of some sort. For example, the mandate encourages more truthful mitigation than greenwashing (Fiechter et al., 2022), as shown in Figure 6. Raising public awareness motivates positive actions (Delmas and Toffel, 2008; Bowen, 2000), which we show as Figure 7, where including more information about climate risks helps both corporations and investors resolve the dilemma (we note that the legend lines for with vs. without climate information are accidentally mislabeled (flipped) on 7b and will fix it in the revised PDF). While we discuss these connections in Section 4, we will make this more clear in the revised version. We hope that by showing our benchmark matches existing empirical evidence, but enables studying novel policy algorithms, it can provide a useful tool for attracting ML researchers to develop algorithms that can help resolve the social dilemma posed by climate change investment.
• For these reasons, we deliberately aimed to make a benchmark that is simple enough for the ML community to iterate on with reasonable computational resources (even a single GPU), without compromising the fundamental incentive structures. We believe removing the computation barrier will help us encourage greater participation from the ML community.

(cont.)

Bankruptcy graphs and a stricter bankruptcy mechanism:

Requested by reviewers mQaB, fPY9

Although our original results did include the ability for companies to go bankrupt, since both reviewers mQaB, fPY9 were interested in how more companies going bankrupt might affect the results, we implemented a stricter bankruptcy mechanism, where if a company agent has a margin worse than -10% for 3 consecutive years, it is deemed as bankrupt (see Section 11.6). Figures 10(h-k) show the results. We see that even with this stricter bankruptcy mechanism, the results are almost identical to the original status quo case, where essentially no companies go bankrupt, there is little mitigation spending and high climate risk. However, interestingly when we combine the strict bankruptcy mechanism with more uncertain economic damage, we see that the number of bankrupt companies is significantly higher. In turn, companies invest significantly more in mitigation, leading to lower climate risk. We hypothesize that in the scenario where economic damage is more uncertain, companies are more likely to go bankrupt, so we hypothesize this incentivizes them to spend more on mitigation to avoid bankruptcy (which has much lower utility). This in turn leads to lower climate risks. However, the market wealth is also lower in the case where companies more frequently go bankrupt due to climate damage.