Recent policy proposals aim to improve the safety of general-purpose AI, but there is little understanding of the efficacy of different regulatory approaches to AI safety. We present a strategic model that explores the interactions between the regulator, the general-purpose AI technology creators, and domain specialists--those who adapt the AI for specific applications. Our analysis examines how different regulatory measures, targeting different parts of the development chain, affect the outcome of the development process. In particular, we assume AI technology is described by two key attributes: safety and performance. The regulator first sets a minimum safety standard that applies to one or both players, with strict penalties for non-compliance. The general-purpose creator then develops the technology, establishing its initial safety and performance levels. Next, domain specialists refine the AI for their specific use cases, and the resulting revenue is distributed between the specialist and generalist through an ex-ante bargaining process. Our analysis of this game reveals two key insights: First, weak safety regulation imposed only on the domain specialists can backfire. While it might seem logical to regulate use cases (as opposed to the general-purpose technology), our analysis shows that weak regulations targeting domain specialists alone can unintentionally reduce safety. This effect persists across a wide range of settings. Second, in sharp contrast to the previous finding, we observe that stronger, well-placed regulation can in fact benefit all players subjected to it. When regulators impose appropriate safety standards on both AI creators and domain specialists, the regulation functions as a commitment mechanism, leading to safety and performance gains, surpassing what is achieved under no regulation or regulating one player only.