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 presents a stylized model of the regulator's choice of an open-source definition in order to evaluate which standards will establish appropriate economic incentives for developers. In particular, we model the strategic interactions among the creator of the 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 the regulator. Our results characterize market equilibria -- specifically, upstream model release decisions and downstream fine-tuning efforts -- under various openness policies and present an optimal range of open-source thresholds as a function of model performance. Overall, we identify a curve defined by initial model performance which determines whether increasing the regulatory penalty vs. increasing the open-source threshold will meaningfully alter the generalist's model release strategy. Our model provides a theoretical foundation for AI governance decisions around openness and enables evaluation and refinement of practical open-source policies.