Auction-Based Regulation for Artificial Intelligence

TL;DR

The paper addresses the regulatory gap in AI safety and ethics by designing Circa, an auction-based mechanism that enforces a compliance threshold \(\epsilon\) via a price \(p_\epsilon = M(\epsilon)\) and uses premium rewards to incentivize higher-than-threshold compliance. It frames AI regulation as an asymmetric all-pay auction with incomplete information, deriving a Nash-equilibrium bidding strategy \(\hat{b}_i^* = p_\epsilon + v_i^p F_v(v_i^p) - \int_0^{v_i^p} F_v(z)\,dz\) that ensures \(b_i^* > p_\epsilon\) and \(s_i^* > \epsilon\) under general value distributions, with closed forms for Uniform and Beta valuations. Empirical results show Circa increases compliance by about 20% and participation by about 15% compared to a simple reserve-threshold baseline, validating its incentive-compatibility and practical impact. The work provides a scalable, mathematically grounded approach to AI regulation that aligns model deployment with safety and ethical standards while motivating ongoing improvement.

Abstract

In an era of "moving fast and breaking things", regulators have moved slowly to pick up the safety, bias, and legal debris left in the wake of broken Artificial Intelligence (AI) deployment. While there is much-warranted discussion about how to address the safety, bias, and legal woes of state-of-the-art AI models, rigorous and realistic mathematical frameworks to regulate AI are lacking. Our paper addresses this challenge, proposing an auction-based regulatory mechanism that provably incentivizes devices (i) to deploy compliant models and (ii) to participate in the regulation process. We formulate AI regulation as an all-pay auction where enterprises submit models for approval. The regulator enforces compliance thresholds and further rewards models exhibiting higher compliance than their peers. We derive Nash Equilibria demonstrating that rational agents will submit models exceeding the prescribed compliance threshold. Empirical results show that our regulatory auction boosts compliance rates by 20% and participation rates by 15% compared to baseline regulatory mechanisms, outperforming simpler frameworks that merely impose minimum compliance standards.

Figures (8)

• Figure 1: Step-by-Step Circa Schematic. (Step 0) The regulator sets a compliance threshold, $\epsilon$, having corresponding price, $p_\epsilon$, required to achieve $\epsilon$. (Step 1) Agents evaluate their total value, $V_i$, from model deployment value ($v_i^d$) and potential regulator compensation ($v_i^p$). Agents only participate if their total value exceeds $p_\epsilon$. (Step 2) Participating agents submit their models to the regulator, accompanied by their bid $b_i$, which reflects the amount spent to improve their model's compliance level. Models with bids below $p_\epsilon$ are automatically rejected. (Step 3) The submitted models are randomly paired, and the more compliant model (i.e., the higher bid) in each pair wins. In this example, agent 3 wins since $b_3 > b_1$. (Step 4) Winning models receive both a premium and deployment value (i.e., agent 3 wins premium $v_3^p$ and deployment $v^d_3$ values), while losing models receive only the deployment value (i.e., agent 1 only wins deployment value $v^d_1$).
• Figure 2: Validation of Uniform Nash Bidding Equilibrium. Agent utility is maximized when agents follow the theoretically optimal bidding function shown in Equation \ref{['eq:uniform-optimal-bid']}. Across varying compliance prices, $p_\epsilon = 0.25$ (left), $0.5$ (middle), $0.75$ (right), agents attain less utility when they deviate from the optimal bid (red line) derived in Corollary \ref{['cor:uniform-valuations']}.
• Figure 3: Validation of Beta Nash Bidding Equilibrium. Akin to the Uniform results, agent utility is maximized when agents follow the theoretically optimal bidding function shown in Equation \ref{['eq:beta-optimal-bid']}. Across varying compliance prices, $p_\epsilon = 0.25$ (left), $0.5$ (middle), $0.75$ (right), agents attain less utility when they deviate from the optimal bid (red line) derived in Corollary \ref{['cor:beta-valuations']}.
• Figure 4: Improved Compliance with Uniform & Beta Values. When total value stems from a (top) Uniform $V_i \sim U(0,1)$ or (bottom) Beta distribution $V_i \sim \text{Beta}(\alpha=\beta=2)$, agents bid more compliant models in Circa than Reserve Thresholding.
• Figure 5: Improved Participation with Uniform & Beta Values. When total value stems from a (top) Uniform $V_i \sim U(0,1)$ or (bottom) Beta distribution $V_i \sim \text{Beta}(\alpha=\beta=2)$, agents participate at a higher rate in Circa than Reserve Thresholding.

Theorems & Definitions (11)

• theorem 1: Reserve Thresholding Nash Equilibrium
• remark 1: Lack of Incentive
• theorem 2
• Corollary 1: Uniform Nash Bidding Equilibrium
• Corollary 2: Beta Nash Bidding Equilibrium
• remark 2: Improved Model Compliance
• remark 3: Improved Utility & Participation
• proof
• proof
• proof