Auction-Based Regulation for Artificial Intelligence

Authors: Marco Bornstein, Zora Che, Suhas Julapalli, Abdirisak Mohamed, Amrit Singh Bedi, Furong Huang
Primary area: alignment, fairness, safety, privacy, and societal considerations
Keywords: Regulation, Mechanisms, Auctions, Artificial Intelligence

Abstract:
In an era of "moving fast and breaking things", regulators have moved slowly to pick up the safety, bias, and legal pieces left in the wake of broken Artificial Intelligence (AI) deployment. Since AI models, such as large language models, are able to push misinformation and stoke division within our society, it is imperative for regulators to employ a framework that mitigates these dangers and ensures user safety. While there is much-warranted discussion about how to address the safety, bias, and legal woes of state-of-the-art AI models, the number of rigorous and realistic mathematical frameworks to regulate AI safety is lacking. We take on this challenge, proposing an auction-based regulatory mechanism that provably incentivizes model-building agents (i) to deploy safer models and (ii) to participate in the regulation process. We provably guarantee, via derived Nash Equilibria, that each participating agent's best strategy is to submit a model safer than a prescribed minimum-safety threshold. Empirical results show that our regulatory auction boosts safety and participation rates by 20% and 15% respectively, outperforming simple regulatory frameworks that merely enforce minimum safety standards.

Decision: reject
Reviewer scores: 6, 5, 5, 5

Reviews and discussion:
<thread>
creation date:
1729630206684

thread_type:
official_review

<thread_object>
creator: reviewer_f4wy

<content>
summary:
The authors provides a formulation of the AI regulatory process as an all-pay auction, and design an auction-based regulatory mechanism that produces Nash Equilibria that induces safety considerations.

strengths:
- A novel and important question, and strong motivation
- Sound theoretical analysis
- Genrally well-written

weaknesses:
The authors' formulation of the regulatory process and safety components appears to be somewhat simplified and may diverge from current AI developments in a few key ways:
- (Minor) The authors assume a fixed safety threshold, denoted as $\epsilon$, for model development. While this may hold in domains such as drug approvals or medical equipment (as illustrated by the authors' N95 mask example), applying a similar framework to AI models is more challenging and complex.
- (Minor) The model assumes that the test set used by regulators is drawn from the same distribution as the agent’s evaluation data. However, in the specific context of language models, techniques such as fine-tuning and reinforcement learning from human feedback (RLHF) can easily improve performance metrics if the evaluation distribution remains consistent. This weakens the argument that a single scalar value would sufficiently capture the intricacies of regulatory inspection.
- The authors propose a strictly increasing relationship between safety and cost, arguing that "safer models cost more to develop." However, they do not explicitly account for the trade-off between safety and the model's quality or usefulness in their framework. This omission raises questions, particularly since existing alignment approaches (e.g., RLHF) are often designed to balance helpfulness and harmlessness. In practice, a model could be made extremely safe (e.g., by providing only generic responses), but this could significantly reduce its usefulness without necessarily increasing development costs. In fact, under the authors' framework, one could submit a trivial model (e.g., one that always responds with "Thank you for your input"), bid the highest possible value, and meet the safety threshold $\epsilon$ to claim the regulator's compensation. This suggests that achieving safety in some cases may not necessarily be costly unless the model’s quality or usefulness is held constant.
- This issue could be exacerbated by the presence of open-source models like LLaMA, which may further incentivize the "gaming" of the regulatory system. Agents could enter the competition with low-cost variants of open-source models that prioritize safety at the expense of quality, primarily to secure the regulator’s compensation. Put it in a different way, low-quality models (which are safe but not useful) could flood the regulatory system, making it easier to claim compensation without delivering valuable AI products. This could distort incentives, where participants optimize for regulatory approval rather than producing high-quality, well-rounded models.

For the mechanism itself, a minor concern include the use of randomization, which introduces envy into the mechanism. With development costs potentially huge, this might lead to issues and discontent and distrust with the mechanism after the outcome is realized.

questions:
Beyond the questions listed in the Weakness section, here are some additional questions I have:
- The framework assumes that the cost $M$ is the same across agents. This assumption seems unrealistic in practice, given that different agents may have varying models, training procedures, and resources, which makes the cost of aligning the safety levels different. If $M$ differs across agents, is there a way to adapt the framework to accommodate heterogeneous costs while maintaining its theoretical properties? 
- The paper didn't mention incentive compatibility, a key issue in auction literature. Is truthful report of $b_i$ guaranteed?
</content>
</thread_object>

</thread>
<thread>
creation date:
1730118665279

thread_type:
official_review

<thread_object>
creator: reviewer_lvmp

<content>
summary:
The paper addresses the challenges regulators face, particularly with the deployment of large language models that can amplify misinformation and societal division. It highlights the urgent need for effective regulatory frameworks to mitigate these risks and enhance user safety. Observing a gap in the availability of rigorous and realistic mathematical frameworks for AI regulation, the authors propose an innovative auction-based regulatory mechanism. This mechanism is designed to incentivize the development and deployment of safer AI models and encourage active participation in the regulatory process. It demonstrates through derived Nash Equilibria that the proposed auction mechanism effectively ensures that each participating agent’s optimal strategy aligns with submitting a model that exceeds a set minimum-safety threshold.

strengths:
1. The topic considered in this paper is interesting and important. Regulations are needed to ensure AI safety.

2. Theoretical results are provided whose proofs can be found in the appendix. I didn't check all the mathematical proofs.

3. The paper is overall well-written and well motivated.

weaknesses:
1. The way used by the paper to model the safety may not be realistic. It is assumed to be some safety level $s_i$ of a model $w_i$, which is expected to be less than $\epsilon$. How is the safety measured for AI models using the metric mapping $S$ in practice? For common foundation models and LLMs, it might be hard to evaluate $S$ for $w_i$, especially given the size of $w_i$. What if a model provider take advantage of the inaccuracy of the safety evaluation to benefit itself?

2. The proposed auction algorithm, together with the theoretical results and analysis seem quite standard. How does it differ from the classic all-pay auction results (for instance, Amann et al. 1996) in the setting for AI models? It is worth highlighting the technical novelty and emphasize why the proposed method is needed for AI models, given that it is claimed in Line 398-399 that "To the best of our knowledge there are no other comparable mechanisms for safety regulation in AI."

questions:
1. What is the technical challenge in the considered auction problem for AI models, compared to classic auction problems?

2. Practical AI models are often very large. How can the safety of these model be evaluated? Given that the auction is done in a one shot setting, probably it is fine even if the model is large.

3. I am more concerned about the compensation $v_i^p$, which needs to be provided by a regulator to implement the proposed auction algorithm. Why is this practical for existing AI models? How large does the compensation need to be? According to bidding equilibrium in Theorem 2,  $v_i^p$ needs to be large for safer models. How could this be made up to compensate what the commercial AI models could achieve?
</content>
</thread_object>

</thread>
<thread>
creation date:
1730386913056

thread_type:
official_review

<thread_object>
creator: reviewer_djpw

<content>
summary:
This paper presents a new AI regulatory framework known as the Safety-Incentivized Regulatory Auction (SIRA), designed as an all-pay auction. SIRA aims to motivate model-building agents to prioritize safety beyond a minimum threshold by formulating the AI regulatory process as an asymmetric all-pay auction with incomplete information. In this framework, agents submit their models to a regulator, and those that meet or exceed a specified safety level become eligible for deployment and may also receive additional rewards based on the randomized pair comparison result. The authors theoretically prove that under some assumptions and when all agents adopt a certain strategy, the system reaches a Nash Equilibrium. Empirical results indicate that when safety threshold prices are in the middle (0.2~0.8), SIRA enhances safety compliance and agent participation by 20% and 15%, respectively compared with the basic regulatory method.

strengths:
**Originality.** The approach presents a unique use of all-pay auction mechanisms in AI regulation, where each agent's utility is linked to model safety levels (training cost), model value (market returns), and premium (policy compensation), creating an incentive for improved safety compliance.

**Quality.** The paper theoretically derives Nash Equilibria to back the proposed incentive structure, demonstrating that agents' rational behavior leads them to exceed the minimum safety threshold. The experimental results align with the theoretical model.

**Clarity.** This paper is well-written and easy to follow. The authors provide clear descriptions of the auction-based model and detailed steps in the algorithmic design of SIRA, supported by both theoretical and empirical validation.

**Significance.** This paper tries to tackle an essential issue in AI regulation by encouraging safer model deployment.

weaknesses:
**Rationality of the auction framework.** Considering the regulation process as an all-pay auction is not reasonable, at least in my opinion. Intuitively, safety-driven regulation establishes a minimum cost for the model-building agent. Every model-building agent must incur this cost, regardless of whether it can successfully meet the regulatory requirements. This represents an unavoidable exploration process within the model space. Even if we assume that all competitive agents know how to train their models to meet the safety threshold, accurately estimating the value of deployment remains a challenge. Thus, the framework may be overly simplistic in its approach to "safety" regulation.

**Feasibility of Assumptions 1 and 2.** Assumption 1 fails when a model-building agent maliciously injects backdoor triggers into the model by altering the training dataset. Assumption 2 is also not straightforward. More cost (e.g., computational resources) does not necessarily equate to better safety. Safety also depends on other factors, such as the learning paradigm, model architecture, loss function design, and hyperparameter selection.

**Performance at high thresholds.** As highlighted in the experiments, SIRA demonstrates limited advantages when safety thresholds approach the upper range (e.g., above 0.8), where its performance is similar to that of simpler reserve threshold models.

1. Evan Hubinger, et al., Sleeper Agents: Training Deceptive LLMs that Persist Through Safety Training, arXiv:2401.05566.

questions:
**Q1.** Is there a reasonable mechanism for estimating the market value ($v_i^d$) of a model before it is submitted to the regulator or even before the training phase begins?

**Q2.** Considering that SIRA’s performance deteriorates at high safety thresholds, would a simple increase in the threshold serve as a better incentive in such cases, as it may more directly encourage safer model development?

**Q3.** The authors mention that safety evaluations rely on IID assumptions for both agent and regulator data. How would the proposed mechanism adapt to non-IID settings, where the agent's training data might be maliciously poisoned, or where the regulator's evaluation data is collected through other means?

**Q4.** Is the random comparison fair for all competitive agents? For example, if we have utility values such that $u_A > u_B > u_C > u_D$, and A and B are grouped together while C and D are grouped together, then B and D cannot receive the policy bonus. However, since $u_B > u_C$, this situation could be considered unfair to B.
</content>
</thread_object>

</thread>
<thread>
creation date:
1730418121280

thread_type:
official_review

<thread_object>
creator: reviewer_ft8n

<content>
summary:
This paper proposes a novel framework of auction-based regulatory mechanism as an asymmetric and incomplete all-pay auction. The mechanism is described mathematically and also shows good empirical results of enhancing safety and participation rates. The framework consists of a regulator and multiple participating agents. Overall, this is an interesting framework with good potentials to explore and create safer and more robust AI regulatory.

strengths:
The paper is well-written and well-supported by both theoretical proofs and empirical results. It addresses the important area of AI regulatory via a multi-agent economic, game-theory type framework. There are a few assumptions to simplify the mechanism but they appear to be acceptable/realistic such as i) the regulator and the participating agents use data from the same distribution to evaluate and submit the safety level, and ii) safer models cost more to develop. These assumptions perhaps need more clarification/grounding or adjustment to become more applicable and feasible in practice. A safer model can tend to cost more to develop but perhaps cost and safety might not always be strictly increasing. The paper has help enhance the current AI regulatory work with a well-formulated framework and has a potential to have some significance in this domain.

weaknesses:
While the paper is well-supported in the mathematical formulation and proofs, it perhaps could have provided more evidence on the experiments and empirical data. More description of how this framework can be applied in AI regulatory or in practice might help ground it further and make it relevant to a wider group of audiences.

questions:
* What is the rationale of choosing the Beta and Uniform distribution (beyond what is described in line 323-324). Are there any related works that you could cite to support this choice of distributions?

* What is the scaling of complexity and cost (such as evaluation and communication) as the number of the agents increase? Are there any risks of agents colluding to achieve a suboptimal safety level?
</content>
</thread_object>

</thread>
<thread>
creation date:
1731642751617

thread_type:
official_comment

<thread_object>
creator: authors

<content>
title:
Global Response

comment:
Thank you to all the reviewers for their reviewing service and paper feedback. We are happy to see that the reviewers agree that we are working on an important research problem, that our paper is well-written, and that our theory-based approach is novel and promising.

Below, we provide additional empirical results that affirm our stated relationship between safety and cost on real-world data.

## Ablation Study

---

- We conduct an ablation study to demonstrate that in realistic settings, safety is mapped to cost in a monotonically increasing way (as detailed in Assumption 2). 
 
While there are many factors to consider when gauging safe AI deployment, we analyze model fairness, via equalized odds, for image classification in this study. Equalized odds measures if different groups have similar true positive rates and false positive rates (lower is better).

- We train VGG-16 models on the Fairface dataset [Kärkkäinen 2019] for 50 epochs (repeated ten times with different random seeds), and consider a gender classification task with race as the sensitive attribute. 

Models with the largest validation classification accuracy during training are selected for testing. 

- Many types of costs exist for training safer models, such as extensive architecture and hyper-parameter search. In this study, we consider the cost of an agent acquiring more minority class data. 

This leads to a larger and more balanced dataset. We simulate various mixtures of training data, starting from a 95:5 skew and scaling up to fully balanced training data with respect to the sensitive attribute. In our study, we gauge equalized odds performance on well-balanced test data for the models trained on various mixtures of data. Below we tabulate our results. 

| Minority Class % | Mean Equalized Odds Score | 
| -------- | -------- | 
| 5%     | 22.55     | 
| 10%     | 22.31     | 
| 15%     | 18.97     | 
| 20%     | 17.46     | 
| 25%     | 15.78    | 
| 30%     | 15.44     | 
| 35%     | 13.09     | 
| 40%     | 11.01     | 
| 45%     | 9.83     | 
| 50%     | 9.38     | 

- The equalized odds score decreases (the model becomes safer) when collecting more minority class data (increased cost). 
 
To adjust equalized odds to fit into the setting where $\epsilon \in (0,1)$, one can invert and normalize the equalized odds score. We will upload a new version of our paper that includes this ablation study (with a scatter plot of the relationship between safety and cost shown in the table above). 

1. Kärkkäinen et. al, Fairface: Face attribute dataset for balanced race, gender, and age, 2019.

## Contribution

---

We want to emphasize the importance of furthering research into AI regulatory frameworks. The deployment and usage of AI models is often unchecked. Lax regulation of AI deployment has led to, and may further accelerate in the future, the proliferation of misinformation and harmful effects on society. We believe that our paper takes a big step towards a valuable societal goal of establishing an effective and mathematically-backed regulatory framework that governing bodies can implement. In summary, our paper contributes a novel mechanism to the area of AI regulation that:

1. Formulates the regulatory process realistically as an auction, where there is one regulating body and many model-building agents.
2. Leverages auction theory to derive equilibria such that rational agents are incentivized to both participate in the regulatory process and submit safer models.
3. Empirically improves model safety by over 20% and participation rates by 15% compared to baseline regulatory mechanisms.
</content>
</thread_object>

</thread>
<thread>
creation date:
1732207321514

thread_type:
official_comment

<thread_object>
creator: authors

<content>
title:
Request for Continued Discussion

comment:
Dear Reviewers,

We want to thank you again for your reviewing service. We believe that our rebuttals have answered the questions raised within your reviews. If so, confirmation that we have indeed answered your concerns would be appreciated. If not, we are happy to continue the discussion before the discussion phase ends in a few days.

Best,
Authors
</content>
</thread_object>

</thread>
<thread>
creation date:
1732898092730

thread_type:
official_comment

<thread_object>
creator: authors

<content>
title:
Update and Followup

comment:
Dear Reviewers,

Thank you for your engagement and discussion.

As an update, we have added our ablation study, including the promised figure, within our revised paper (in Appendix C.1). After the revision deadline, we also added a section exploring and explaining Assumption 2. Namely, we detail the motivation and generality of the assumption, pointing towards our new Ablation Study as evidence. Likewise, we describe that, in a space with no assumptions let alone theoretical analysis, we use Assumption 2 to establish the first theoretical results for safety-incentivized AI regulatory frameworks. We note that our future research aims to further relax the assumptions made within our paper.

With the discussion period ending this Monday, we also wanted to make sure that we have clarified all questions and concerns. If not, we are happy to clarify any questions before the deadline. If all of your concerns have been addressed, we would request a reconsideration of your scores.

Best,

Authors
</content>
</thread_object>

</thread>


Metareview:
metareview:
This paper looks at the problem of regulating AI models, specifically for safety. This is approached through theoretical framework, through an all-pay auction with companies and a regulator. The authors find Nash equilibria and have theoretical results. 

Reviewers agree that this is a very important problem, and that the approach taken is novel and interesting. Reviewers also agree that the paper is well-written, which I agree with. I agree that these are all key strengths of the paper. 

Unfortunately, all reviewers agree on a key limitation: the restrictiveness of the assumptions, specifically Assumption 2. There is of course a fine line between have realistic assumptions and those that allow for the kind of theory this paper does. The authors have defended their assumptions in rebuttal and with additional text in the paper (and an ablation study). Upon further discussion with reviewers, however, we all find that this is still a key limiting factor of this paper. I encourage the authors to take these concerns into account for a future version of the paper, actively acknowledging and tackling these issues even earlier in the paper (eg by giving specific examples of where Assumption 2 is both realistic *and not realistic*).