Modeling the Economic Impacts of AI Openness Regulation

TL;DR

This paper addresses how openness regulation should be designed for foundation models by modeling the strategic interaction between a generalist that releases a base model with openness level $\omega$ and a downstream specialist who fine-tunes it to a domain, under a regulatory threshold $\theta$ and penalties $p$. It develops a continuous-openness, game-theoretic framework with utilities $U_G$ and $U_D$ and costs that decompose into production, operation, and compliance terms, deriving closed-form best responses and characterizing subgame-perfect equilibria. The results reveal how the generalist's openness decision and the downstream fine-tuning investment depend on baseline performance $\alpha_0$, reputational parameter $\varepsilon$, and regulation parameters, including when to comply or abstain, and how Pareto-improving regulations can emerge near the indifference curve. The work provides a theoretical foundation to evaluate and refine open-source policies, guiding penalties and thresholds to align incentives for innovation and responsible openness.

Abstract

Regulatory frameworks, such as the EU AI Act, encourage openness of general-purpose AI models by offering legal exemptions for "open-source" models. Despite this legislative attention on openness, the definition of open-source foundation models remains ambiguous. This paper models the strategic interactions among the creator of a general-purpose model (the generalist) and the entity that fine-tunes the general-purpose model to a specialized domain or task (the specialist), in response to regulatory requirements on model openness. We present a stylized model of the regulator's choice of an open-source definition to evaluate which AI openness standards will establish appropriate economic incentives for developers. Our results characterize market equilibria -- specifically, upstream model release decisions and downstream fine-tuning efforts -- under various openness regulations and present a range of effective regulatory penalties and open-source thresholds. Overall, we find the model's baseline performance determines when increasing the regulatory penalty vs. the open-source threshold will significantly alter the generalist's release strategy. Our model provides a theoretical foundation for AI governance decisions around openness and enables evaluation and refinement of practical open-source policies.

Figures (18)

• Figure 1: Example of an openness continuum defining $\omega \in [0, 1]$ based on model access solaiman.
• Figure 2: $G$'s equilibrium strategies for $\omega^*$ (top row) and $\delta^*$ (bottom row) at $c_\omega = 0.1$ with no regulation $(p = 0)$. Low initial performance ($\alpha_0$) and high reputational benefits ($\epsilon$) lead to partial openness. Since $G$ unilaterally controls the model's release strategy, $G$ can use the openness decision to remove or weaken the bargain, explaining why a fully open model coincides with bargains that allocate no closed revenue to $G$.
• Figure 3: Overview of empirical model release strategies. (Left) Higher performance of a model corresponds to a higher percentage of closed components, determined by Eiras et al.'s assessment of model components eiras2024). (Right) For each generation, closed-weight models have higher performance than open-weight ones, despite open-weight models showing comparable performance to closed-weight models from previous time periods. The performance gap between open- vs. closed-weight models (blue region) persists even as absolute performance improves across generations. Appendix \ref{['sec:data_for_figures']} reports the figure data.
• Figure 4: Indifference curves for the generalist over $(p, \theta)$ choices for game parameters $c_\omega=0.01, \epsilon=0.15$ and $\alpha_0 \in \{0.5, 1, 5\}$. In the region of non-compliance above the indifference curve, $G$ keeps the model at an openness level $\omega^* \rightarrow 0$. In the area of compliance below the indifference curve, $G$ chooses $\omega^* = \theta$.
• Figure 5: Player utilities under various $(p, \theta)$ regulations when $\alpha_0 = 0.1, c_\omega = 0.05$, and $\epsilon=0.1$ with Nash bargaining. $(U_G, U_D)$-improving regulations are enclosed in the gray region, with the lower left corner of the gray region corresponding to the no-regulation equilibrium where $p=0$ and $\theta$ has no effect. For overly stringent $\theta$ thresholds, both players' utilities decrease.

Theorems & Definitions (15)

• Proposition 1: Characterization $D$'s Equilibrium Strategy
• Proposition 2: Characterization of $G$'s Equilibrium Strategy
• Proposition 3
• Definition 1: Pareto-Optimal Policies
• proof : Proof of Proposition \ref{['prop:D_best_response']}.
• proof : Proof of Proposition \ref{['prop:G_best_response']}.
• Proposition 4
• proof
• Proposition 5
• proof