In recent years, humanity has been faced with a new resource - artificial intelligence. AI can be a boon to society, or can also have negative impacts, especially with inappropriate use. My research agenda studies the societal impact of AI, particularly focusing on AI as a resource and on the strategic decisions that agents make in deciding how to use it. In this dissertation, I present work on some of the key strategic questions that arise in this framework: the decisions that agents make in jointly constructing and sharing AI models, the decisions that they make in dividing tasks between their own expertise and the expertise of a model, and the implications this has for how we think about handling societal resources. In the Part I, I present my work on "model-sharing games", which models scenarios such as federated learning or data cooperatives. In this setting, we view agents with data as game-theoretic players and analyze questions of stability, optimality, and fairness. In Part II, I discuss my work in modeling human-algorithm collaboration, specifically in scenarios where both the human and algorithm have helpful roles to play, but cannot solve the problem perfectly by themselves. Finally, in Part III I present work studying broader conceptions of resources, such as allocating resources with uncertain demand, biased crowdsourcing, and fairness in insurance rates with unequal risk levels.