Fine-Tuning Games: Bargaining and Adaptation for General-Purpose Models

Recent advances in Machine Learning (ML) and Artificial Intelligence (AI) follow a familiar structure: A firm releases a large, pretrained model. It is designed to be adapted and tweaked by other entities to perform particular, domain-specific functions. The model is described as `general-purpose,' meaning it can be transferred to a wide range of downstream tasks, in a process known as adaptation or fine-tuning. Understanding this process - the strategies, incentives, and interactions involved in the development of AI tools - is crucial for making conclusions about societal implications and regulatory responses, and may provide insights beyond AI about general-purpose technologies. We propose a model of this adaptation process. A Generalist brings the technology to a certain level of performance, and one or more Domain specialist(s) adapt it for use in particular domain(s). Players incur costs when they invest in the technology, so they need to reach a bargaining agreement on how to share the resulting revenue before making their investment decisions. We find that for a broad class of cost and revenue functions, there exists a set of Pareto-optimal profit-sharing arrangements where the players jointly contribute to the technology. Our analysis, which utilizes methods based on bargaining solutions and sub-game perfect equilibria, provides insights into the strategic behaviors of firms in these types of interactions. For example, profit-sharing can arise even when one firm faces significantly higher costs than another. After demonstrating findings in the case of one domain-specialist, we provide closed-form and numerical bargaining solutions in the generalized setting with $n$ domain specialists. We find that any potential domain specialization will either contribute, free-ride, or abstain in their uptake of the technology, and provide conditions yielding these different responses.